1
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Zhang L, Jiang Z, Guo J, Zhang C, Xu X, Shi D, Shao Y, Ai Z, Wu Y, Hao X. Deep insight into regulation mechanism of band distribution in phase junction CdS for enhanced photocatalytic H 2 production. J Colloid Interface Sci 2024; 669:146-156. [PMID: 38713954 DOI: 10.1016/j.jcis.2024.04.213] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/16/2024] [Revised: 04/28/2024] [Accepted: 04/29/2024] [Indexed: 05/09/2024]
Abstract
An in-depth understanding of structure-activity relationship between the phase constitution and solar-to-hydrogen (STH) conversion efficiency is conducive to guiding the optimization route of targeted photocatalyst candidates, further establishing advanced photocatalytic systems. Herein, based on the concept of phase engineering, we encompassed the crystalline phase of CdS and achieved precise regulation of phase proportion as well as phase boundary width in the phase junction for the first time. The above cooperative effect not only modifies energy band distribution for sufficient redox potentials, but also guarantees the reverse migration orientation of photogenerated carriers in phase junction, thereby endowing photocarriers with a prolonged lifetime. Compared to pure cubic or hexagonal phase (72.6 or 101.1 μmol h-1 g-1), this CdS system with optimized phase junction demonstrates an improved photocatalytic hydrogen evolution activity of 1.04 mmol h-1 g-1 and favorable stability without cocatalyst assistance, which mainly stems from an efficient protons reduction process interacting with long-lived photogenerated electrons. This research explores the mechanism behind phase regulation and its relationship with junction capability, providing a powerful strategy to manipulate crystal phase distribution and paving a feasible avenue for other phase-dependent photocatalysts towards rational design of heterostructures based on different phases in solar energy conversion field.
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Affiliation(s)
- Lei Zhang
- School of Materials Science and Engineering, Qilu University of Technology (Shandong Academy of Sciences), Jinan 250353, PR China
| | - Zhiyuan Jiang
- School of Materials Science and Engineering, Qilu University of Technology (Shandong Academy of Sciences), Jinan 250353, PR China
| | - Jingru Guo
- School of Materials Science and Engineering, Qilu University of Technology (Shandong Academy of Sciences), Jinan 250353, PR China
| | - Chao Zhang
- School of Materials Science and Engineering, Qilu University of Technology (Shandong Academy of Sciences), Jinan 250353, PR China
| | - Xiaolong Xu
- School of Materials Science and Engineering, Qilu University of Technology (Shandong Academy of Sciences), Jinan 250353, PR China
| | - Dong Shi
- School of Materials Science and Engineering, Qilu University of Technology (Shandong Academy of Sciences), Jinan 250353, PR China
| | - Yongliang Shao
- School of Materials Science and Engineering, Qilu University of Technology (Shandong Academy of Sciences), Jinan 250353, PR China
| | - Zizheng Ai
- School of Materials Science and Engineering, Qilu University of Technology (Shandong Academy of Sciences), Jinan 250353, PR China.
| | - Yongzhong Wu
- School of Materials Science and Engineering, Qilu University of Technology (Shandong Academy of Sciences), Jinan 250353, PR China
| | - Xiaopeng Hao
- School of Materials Science and Engineering, Qilu University of Technology (Shandong Academy of Sciences), Jinan 250353, PR China.
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2
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Niu C, Wang M, Zhang Z, Qiu G, Wang Y, Zheng D, Liao PY, Wu W, Ye PD. Superconducting Field-Effect Transistors with Pd xTe-Te Intimate Contacts. ACS NANO 2024; 18:15107-15113. [PMID: 38819119 DOI: 10.1021/acsnano.4c02352] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/01/2024]
Abstract
Superconducting-based electronic devices have shown great potential for future quantum computing applications. One key building block device is a superconducting field-effect transistor based on a superconductor-semiconductor-superconductor Josephson-junction (JJ) with a gate-tunable semiconducting channel. However, the performance of such devices is highly dependent on the quality of the superconductor to semiconductor interface. In this study, we present an alternative method to obtain a high-quality interface by using intimate contact. We investigate the proximity-induced superconductivity in chiral crystal tellurium (Te) and fabricate a PdxTe-Te-PdxTe JJ with an ambipolar supercurrent that is gate-tunable and exhibits multiple Andreev reflections. The semiconducting two-dimensional Te single crystal is grown hydrothermally and partially converted to superconducting PdxTe by controlled annealing. Our work demonstrates a promising path for realizing controllable superconducting electronic devices with high-quality superconducting interfaces; thus, we can continue to advance the field of quantum computing and other interface-based technologies.
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Affiliation(s)
- Chang Niu
- Elmore Family School of Electrical and Computer Engineering, Purdue University, West Lafayette, Indiana 47907, United States
- Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907, United States
| | - Mingyi Wang
- School of Industrial Engineering, Purdue University, West Lafayette, Indiana 47907, United States
| | - Zhuocheng Zhang
- Elmore Family School of Electrical and Computer Engineering, Purdue University, West Lafayette, Indiana 47907, United States
- Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907, United States
| | - Gang Qiu
- Elmore Family School of Electrical and Computer Engineering, Purdue University, West Lafayette, Indiana 47907, United States
- Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907, United States
| | - Yixiu Wang
- School of Industrial Engineering, Purdue University, West Lafayette, Indiana 47907, United States
| | - Dongqi Zheng
- Elmore Family School of Electrical and Computer Engineering, Purdue University, West Lafayette, Indiana 47907, United States
- Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907, United States
| | - Pai-Ying Liao
- Elmore Family School of Electrical and Computer Engineering, Purdue University, West Lafayette, Indiana 47907, United States
- Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907, United States
| | - Wenzhuo Wu
- School of Industrial Engineering, Purdue University, West Lafayette, Indiana 47907, United States
| | - Peide D Ye
- Elmore Family School of Electrical and Computer Engineering, Purdue University, West Lafayette, Indiana 47907, United States
- Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907, United States
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3
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Liang X, Shamim S, Chen D, Fürst L, Taniguchi T, Watanabe K, Buhmann H, Kleinlein J, Molenkamp LW. Graphite/h-BN van der Waals heterostructure as a gate stack for HgTe quantum wells. NANOTECHNOLOGY 2024; 35:345001. [PMID: 38788703 DOI: 10.1088/1361-6528/ad501c] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/15/2024] [Accepted: 05/24/2024] [Indexed: 05/26/2024]
Abstract
Two-dimensional topological insulators have attracted much interest due to their potential applications in spintronics and quantum computing. To access the exotic physical phenomena, a gate electric field is required to tune the Fermi level into the bulk band gap. Hexagonal boron nitride (h-BN) is a promising alternative gate dielectric due to its unique advantages such as flat and charge-free surface. Here we present a h-BN/graphite van der Waals heterostructure as a top gate on HgTe heterostructure-based Hall bar devices. We compare our results to devices with h-BN/Ti/Au and HfO2/Ti/Au gates. Devices with a h-BN/graphite gate show no charge carrier density shift compared to as-grown structures, in contrast to a significant n-type carrier density increase for HfO2/Ti/Au. We attribute this observation mainly to the comparable work function of HgTe and graphite. In addition, devices with h-BN gate dielectric show slightly higher electron mobility compared to HfO2-based devices. Our results demonstrate the compatibility between layered materials transfer and wet-etched structures and provide a strategy to solve the issue of significant shifts of the carrier density in gated HgTe heterostructures.
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Affiliation(s)
- Xianhu Liang
- Physikalisches Institut (EP3), Universität Würzburg, 97074 Würzburg, Germany
- Institute for Topological Insulators, 97074 Würzburg, Germany
| | - Saquib Shamim
- Physikalisches Institut (EP3), Universität Würzburg, 97074 Würzburg, Germany
- Institute for Topological Insulators, 97074 Würzburg, Germany
| | - Dongyun Chen
- Physikalisches Institut (EP3), Universität Würzburg, 97074 Würzburg, Germany
- Institute for Topological Insulators, 97074 Würzburg, Germany
| | - Lena Fürst
- Physikalisches Institut (EP3), Universität Würzburg, 97074 Würzburg, Germany
- Institute for Topological Insulators, 97074 Würzburg, Germany
| | - Takashi Taniguchi
- International Center for Materials Nanoarchitectonics, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan
| | - Kenji Watanabe
- Research Center for Functional Materials, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan
| | - Hartmut Buhmann
- Physikalisches Institut (EP3), Universität Würzburg, 97074 Würzburg, Germany
- Institute for Topological Insulators, 97074 Würzburg, Germany
| | - Johannes Kleinlein
- Physikalisches Institut (EP3), Universität Würzburg, 97074 Würzburg, Germany
- Institute for Topological Insulators, 97074 Würzburg, Germany
| | - Laurens W Molenkamp
- Physikalisches Institut (EP3), Universität Würzburg, 97074 Würzburg, Germany
- Institute for Topological Insulators, 97074 Würzburg, Germany
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4
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Levajac V, Barakov H, Mazur GP, van Loo N, Kouwenhoven LP, Nazarov YV, Wang JY. Supercurrent in the Presence of Direct Transmission and a Resonant Localized State. PHYSICAL REVIEW LETTERS 2024; 132:176304. [PMID: 38728734 DOI: 10.1103/physrevlett.132.176304] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/08/2023] [Revised: 01/25/2024] [Accepted: 04/02/2024] [Indexed: 05/12/2024]
Abstract
We study the current-phase relation (CPR) of an InSb-Al nanowire Josephson junction in parallel magnetic fields up to 700 mT. At high magnetic fields and in narrow voltage intervals of a gate under the junction, the CPR exhibits π shifts. The supercurrent declines within these gate intervals and shows asymmetric gate voltage dependence above and below them. We detect these features sometimes also at zero magnetic field. The observed CPR properties are reproduced by a theoretical model of supercurrent transport via interference between direct transmission and a resonant localized state.
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Affiliation(s)
- Vukan Levajac
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology, 2600 GA Delft, The Netherlands
| | - Hristo Barakov
- Kavli Institute of Nanoscience, Delft University of Technology, 2628 CJ Delft, The Netherlands
| | - Grzegorz P Mazur
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology, 2600 GA Delft, The Netherlands
| | - Nick van Loo
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology, 2600 GA Delft, The Netherlands
| | - Leo P Kouwenhoven
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology, 2600 GA Delft, The Netherlands
| | - Yuli V Nazarov
- Kavli Institute of Nanoscience, Delft University of Technology, 2628 CJ Delft, The Netherlands
| | - Ji-Yin Wang
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology, 2600 GA Delft, The Netherlands
- Beijing Academy of Quantum Information Sciences, 100193 Beijing, China
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5
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Li R, Song W, Miao W, Yu Z, Wang Z, Yang S, Gao Y, Wang Y, Chen F, Geng Z, Yang L, Xu J, Feng X, Wang T, Zang Y, Li L, Shang R, Xue Q, He K, Zhang H. Selective-Area-Grown PbTe-Pb Planar Josephson Junctions for Quantum Devices. NANO LETTERS 2024; 24:4658-4664. [PMID: 38563608 DOI: 10.1021/acs.nanolett.4c00900] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/04/2024]
Abstract
Planar Josephson junctions are predicted to host Majorana zero modes. The material platforms in previous studies are two-dimensional electron gases (InAs, InSb, InAsSb, and HgTe) coupled to a superconductor such as Al or Nb. Here, we introduce a new material platform for planar JJs, the PbTe-Pb hybrid. The semiconductor, PbTe, was grown as a thin film via selective area epitaxy. The Josephson junction was defined by a shadow wall during the deposition of superconductor Pb. Scanning transmission electron microscopy reveals a sharp semiconductor-superconductor interface. Gate-tunable supercurrents and multiple Andreev reflections are observed. A perpendicular magnetic field causes interference patterns of the switching current, exhibiting Fraunhofer-like and SQUID-like behaviors. We further demonstrate a prototype device for Majorana detection wherein phase bias and tunneling spectroscopy are applicable.
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Affiliation(s)
- Ruidong Li
- State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, China
| | - Wenyu Song
- State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, China
| | - Wentao Miao
- State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, China
| | - Zehao Yu
- State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, China
| | - Zhaoyu Wang
- State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, China
| | - Shuai Yang
- State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, China
| | - Yichun Gao
- State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, China
| | - Yuhao Wang
- State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, China
| | - Fangting Chen
- State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, China
| | - Zuhan Geng
- State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, China
| | - Lining Yang
- State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, China
| | - Jiaye Xu
- State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, China
| | - Xiao Feng
- State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, China
- Beijing Academy of Quantum Information Sciences, Beijing 100193, China
- Frontier Science Center for Quantum Information, Beijing 100084, China
- Hefei National Laboratory, Hefei 230088, China
| | - Tiantian Wang
- Beijing Academy of Quantum Information Sciences, Beijing 100193, China
- Hefei National Laboratory, Hefei 230088, China
| | - Yunyi Zang
- Beijing Academy of Quantum Information Sciences, Beijing 100193, China
- Hefei National Laboratory, Hefei 230088, China
| | - Lin Li
- Beijing Academy of Quantum Information Sciences, Beijing 100193, China
| | - Runan Shang
- Beijing Academy of Quantum Information Sciences, Beijing 100193, China
- Hefei National Laboratory, Hefei 230088, China
| | - Qikun Xue
- State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, China
- Beijing Academy of Quantum Information Sciences, Beijing 100193, China
- Frontier Science Center for Quantum Information, Beijing 100084, China
- Hefei National Laboratory, Hefei 230088, China
- Southern University of Science and Technology, Shenzhen 518055, China
| | - Ke He
- State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, China
- Beijing Academy of Quantum Information Sciences, Beijing 100193, China
- Frontier Science Center for Quantum Information, Beijing 100084, China
- Hefei National Laboratory, Hefei 230088, China
| | - Hao Zhang
- State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, China
- Beijing Academy of Quantum Information Sciences, Beijing 100193, China
- Frontier Science Center for Quantum Information, Beijing 100084, China
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6
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Matsuo S, Imoto T, Yokoyama T, Sato Y, Lindemann T, Gronin S, Gardner GC, Manfra MJ, Tarucha S. Phase engineering of anomalous Josephson effect derived from Andreev molecules. SCIENCE ADVANCES 2023; 9:eadj3698. [PMID: 38091387 PMCID: PMC10848717 DOI: 10.1126/sciadv.adj3698] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 06/22/2023] [Accepted: 11/14/2023] [Indexed: 02/12/2024]
Abstract
A Josephson junction (JJ) is a key device for developing superconducting circuits, wherein a supercurrent in the JJ is controlled by the phase difference between the two superconducting electrodes. When two JJs sharing one superconducting electrode are coherently coupled and form the Andreev molecules, a supercurrent of one JJ is expected to be nonlocally controlled by the phase difference of another JJ. Here, we evaluate the supercurrent in one of the coupled two JJs as a function of local and nonlocal phase differences. Consequently, the results exhibit that the nonlocal phase control generates a finite supercurrent even when the local phase difference is zero. In addition, an offset of the local phase difference giving the JJ ground state depends on the nonlocal phase difference. These features demonstrate the anomalous Josephson effect realized by the nonlocal phase control. Our results provide a useful concept for engineering superconducting devices such as phase batteries and dissipationless rectifiers.
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Affiliation(s)
- Sadashige Matsuo
- Center for Emergent Matter Science, RIKEN, Wako, Saitama 351-0198, Japan
| | - Takaya Imoto
- Center for Emergent Matter Science, RIKEN, Wako, Saitama 351-0198, Japan
- Department of Applied Physics, Tokyo University of Science, Shinjuku-ku, Tokyo 162-8601, Japan
| | - Tomohiro Yokoyama
- Department of Materials Engineering Science, Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531, Japan
| | - Yosuke Sato
- Center for Emergent Matter Science, RIKEN, Wako, Saitama 351-0198, Japan
| | - Tyler Lindemann
- Birck Nanotechnology Center, Purdue University,, West Lafayette, IN 47907, USA
- Department of Physics and Astronomy, Purdue University, West Lafayette, IN 47907, USA
| | - Sergei Gronin
- Birck Nanotechnology Center, Purdue University,, West Lafayette, IN 47907, USA
| | - Geoffrey C. Gardner
- Birck Nanotechnology Center, Purdue University,, West Lafayette, IN 47907, USA
| | - Michael J. Manfra
- Birck Nanotechnology Center, Purdue University,, West Lafayette, IN 47907, USA
- Department of Physics and Astronomy, Purdue University, West Lafayette, IN 47907, USA
- School of Materials Engineering, Purdue University, West Lafayette, IN 47907, USA
- Elmore Family School of Electrical and Computer Engineering, Purdue University, West Lafayette, IN 47907, USA
| | - Seigo Tarucha
- Center for Emergent Matter Science, RIKEN, Wako, Saitama 351-0198, Japan
- RIKEN Center for Quantum Computing, RIKEN, Wako, Saitama 351-0198, Japan
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7
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Matsuo S, Imoto T, Yokoyama T, Sato Y, Lindemann T, Gronin S, Gardner GC, Nakosai S, Tanaka Y, Manfra MJ, Tarucha S. Phase-dependent Andreev molecules and superconducting gap closing in coherently-coupled Josephson junctions. Nat Commun 2023; 14:8271. [PMID: 38092786 PMCID: PMC10719386 DOI: 10.1038/s41467-023-44111-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/02/2023] [Accepted: 11/30/2023] [Indexed: 12/17/2023] Open
Abstract
The Josephson junction (JJ) is an essential element of superconducting (SC) devices for both fundamental and applied physics. The short-range coherent coupling of two adjacent JJs forms Andreev molecule states (AMSs), which provide a new ingredient to engineer exotic SC phenomena such as topological SC states and Andreev qubits. Here we provide tunneling spectroscopy measurements on a device consisting of two electrically controllable planar JJs sharing a single SC electrode. We discover that Andreev spectra in the coupled JJ are highly modulated from those in the single JJs and possess phase-dependent AMS features reproduced in our numerical calculation. Notably, the SC gap closing due to the AMS formation is experimentally observed. Our results help in understanding SC transport derived from the AMS and promoting the use of AMS physics to engineer topological SC states and quantum information devices.
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Affiliation(s)
- Sadashige Matsuo
- Center for Emergent Matter Science, RIKEN, Saitama, 351-0198, Japan.
| | - Takaya Imoto
- Center for Emergent Matter Science, RIKEN, Saitama, 351-0198, Japan
- Department of Applied Physics, Tokyo University of Science, Tokyo, 162-8601, Japan
| | - Tomohiro Yokoyama
- Department of Materials Engineering Science, Osaka University, Osaka, 560-8531, Japan.
| | - Yosuke Sato
- Center for Emergent Matter Science, RIKEN, Saitama, 351-0198, Japan
| | - Tyler Lindemann
- Department of Physics and Astronomy, Purdue University, West Lafayette, Indiana, IN, 47907, USA
- Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana, IN, 47907, USA
| | - Sergei Gronin
- Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana, IN, 47907, USA
| | - Geoffrey C Gardner
- Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana, IN, 47907, USA
| | - Sho Nakosai
- Department of Applied Physics, Nagoya University, Nagoya, 464-8603, Japan
| | - Yukio Tanaka
- Department of Applied Physics, Nagoya University, Nagoya, 464-8603, Japan
| | - Michael J Manfra
- Department of Physics and Astronomy, Purdue University, West Lafayette, Indiana, IN, 47907, USA
- Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana, IN, 47907, USA
- School of Materials Engineering, Purdue University, West Lafayette, Indiana, IN, 47907, USA
- Elmore Family School of Electrical and Computer Engineering, Purdue University, West Lafayette, Indiana, IN, 47907, USA
| | - Seigo Tarucha
- Center for Emergent Matter Science, RIKEN, Saitama, 351-0198, Japan.
- RIKEN Center for Quantum Computing, RIKEN, Saitama, 351-0198, Japan.
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8
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Kar S. Edge state behavior in a Su-Schrieffer-Heeger like model with periodically modulated hopping. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2023; 36:065301. [PMID: 37883992 DOI: 10.1088/1361-648x/ad0766] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/19/2023] [Accepted: 10/26/2023] [Indexed: 10/28/2023]
Abstract
Su-Schrieffer-Heeger (SSH) model is one of the simplest models to show topological end/edge states and the existence of Majorana fermions. Here we consider a SSH like model both in one and two dimensions where a nearest neighbor hopping features spatially periodic modulations. In the 1D chain, we witness appearance of new in-gap end states apart from a pair of Majorana zero modes (MZMs) when the hopping periodicity go beyond two lattice spacings. The pair of MZMs, that appear in the topological regime, characterize the end modes each existing in either end of the chain. These, however, crossover to both-end end modes for small hopping modulation strength in a finite chain. Contrarily in a 2D SSH model with symmetric hopping that we consider, both non-zero and zero energy topological states appear in a finite square lattice even with a simple staggered hopping, though the zero energy modes disappear in a ribbon configuration. Apart from edge modes, the 2D system also features corner modes as well as modes with satellite peaks distributed non-randomly within the lattice. In both the dimensions, an increase in the periodicity of hopping modulation causes the zero energy Majorana modes to become available for either sign of the modulation. But interestingly with different periodicity for hopping modulations in the two directions, the zero energy modes in a 2D model become rarer and does not appear for all strength and sign of the modulation.
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Affiliation(s)
- Satyaki Kar
- AKPC Mahavidyalaya, Bengai, West Bengal 712611, India
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9
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Xie YM, Lantagne-Hurtubise É, Young AF, Nadj-Perge S, Alicea J. Gate-Defined Topological Josephson Junctions in Bernal Bilayer Graphene. PHYSICAL REVIEW LETTERS 2023; 131:146601. [PMID: 37862641 DOI: 10.1103/physrevlett.131.146601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/28/2023] [Accepted: 09/07/2023] [Indexed: 10/22/2023]
Abstract
Recent experiments on Bernal bilayer graphene (BLG) deposited on monolayer WSe_{2} revealed robust, ultraclean superconductivity coexisting with sizable induced spin-orbit coupling. Here, we propose BLG/WSe_{2} as a platform to engineer gate-defined planar topological Josephson junctions, where the normal and superconducting regions descend from a common material. More precisely, we show that if superconductivity in BLG/WSe_{2} is gapped and emerges from a parent state with intervalley coherence, then Majorana zero-energy modes can form in the barrier region upon applying weak in-plane magnetic fields. Our results spotlight a potential pathway for "internally engineered" topological superconductivity that minimizes detrimental disorder and orbital-magnetic-field effects.
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Affiliation(s)
- Ying-Ming Xie
- Department of Physics, Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong, China
- Department of Physics, California Institute of Technology, Pasadena, California 91125, USA
- Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, California 91125, USA
| | - Étienne Lantagne-Hurtubise
- Department of Physics, California Institute of Technology, Pasadena, California 91125, USA
- Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, California 91125, USA
| | - Andrea F Young
- Department of Physics, University of California at Santa Barbara, Santa Barbara, California 93106, USA
| | - Stevan Nadj-Perge
- Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, California 91125, USA
- T. J. Watson Laboratory of Applied Physics, California Institute of Technology, 1200 East California Boulevard, Pasadena, California 91125, USA
| | - Jason Alicea
- Department of Physics, California Institute of Technology, Pasadena, California 91125, USA
- Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, California 91125, USA
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10
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Haxell D, Coraiola M, Sabonis D, Hinderling M, ten Kate SC, Cheah E, Krizek F, Schott R, Wegscheider W, Nichele F. Zeeman- and Orbital-Driven Phase Shifts in Planar Josephson Junctions. ACS NANO 2023; 17:18139-18147. [PMID: 37694539 PMCID: PMC10540266 DOI: 10.1021/acsnano.3c04957] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/02/2023] [Accepted: 08/25/2023] [Indexed: 09/12/2023]
Abstract
We perform supercurrent and tunneling spectroscopy measurements on gate-tunable InAs/Al Josephson junctions (JJs) in an in-plane magnetic field and report on phase shifts in the current-phase relation measured with respect to an absolute phase reference. The impact of orbital effects is investigated by studying multiple devices with different superconducting lead sizes. At low fields, we observe gate-dependent phase shifts of up to φ0 = 0.5π, which are consistent with a Zeeman field coupling to highly transmissive Andreev bound states via Rashba spin-orbit interaction. A distinct phase shift emerges at larger fields, concomitant with a switching current minimum and the closing and reopening of the superconducting gap. These signatures of an induced phase transition, which might resemble a topological transition, scale with the superconducting lead size, demonstrating the crucial role of orbital effects. Our results elucidate the interplay of Zeeman, spin-orbit, and orbital effects in InAs/Al JJs, giving improved understanding of phase transitions in hybrid JJs and their applications in quantum computing and superconducting electronics.
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Affiliation(s)
| | - Marco Coraiola
- IBM
Research Europe−Zurich, 8803 Rüschlikon, Switzerland
| | | | | | | | - Erik Cheah
- Laboratory
for Solid State Physics, ETH Zürich, 8093 Zürich, Switzerland
| | - Filip Krizek
- IBM
Research Europe−Zurich, 8803 Rüschlikon, Switzerland
- Laboratory
for Solid State Physics, ETH Zürich, 8093 Zürich, Switzerland
- Institute
of Physics, Czech Academy of Sciences, 162 00 Prague, Czech Republic
| | - Rüdiger Schott
- Laboratory
for Solid State Physics, ETH Zürich, 8093 Zürich, Switzerland
| | - Werner Wegscheider
- Laboratory
for Solid State Physics, ETH Zürich, 8093 Zürich, Switzerland
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11
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Yan S, Su H, Pan D, Li W, Lyu Z, Chen M, Wu X, Lu L, Zhao J, Wang JY, Xu H. Supercurrent, Multiple Andreev Reflections and Shapiro Steps in InAs Nanosheet Josephson Junctions. NANO LETTERS 2023. [PMID: 37450769 DOI: 10.1021/acs.nanolett.3c01450] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 07/18/2023]
Abstract
We report an experimental study of proximity induced superconductivity in planar Josephson junction devices made from free-standing InAs nanosheets. The nanosheets are grown by molecular beam epitaxy, and the Josephson junction devices are fabricated by directly contacting the nanosheets with superconductor Al electrodes. The fabricated devices are explored by low-temperature carrier transport measurements. The measurements show that the devices exhibit a gate-tunable supercurrent, multiple Andreev reflections, and a good quality superconductor-semiconductor interface. The superconducting characteristics of the Josephson junctions are investigated at different magnetic fields and temperatures and are analyzed based on the Bardeen-Cooper-Schrieffer (BCS) theory. The measurements of the ac Josephson effect are also conducted under microwave radiations with different radiation powers and frequencies, and integer Shapiro steps are observed. Our work demonstrates that InAs nanosheet based hybrid devices are desired systems for investigating the forefront of physics, such as two-dimensional topological superconductivity.
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Affiliation(s)
- Shili Yan
- Beijing Academy of Quantum Information Sciences, 100193 Beijing, China
| | - Haitian Su
- Beijing Key Laboratory of Quantum Devices, Key Laboratory for the Physics and Chemistry of Nanodevices, and School of Electronics, Peking University, Beijing 100871, China
- Institute of Condensed Matter and Material Physics, School of Physics, Peking University, Beijing 100871, China
| | - Dong Pan
- State Key Laboratory of Superlattices and Microstructures, Institute of Semiconductors, Chinese Academy of Sciences, P.O. Box 912, Beijing 100083, China
| | - Weijie Li
- Beijing Key Laboratory of Quantum Devices, Key Laboratory for the Physics and Chemistry of Nanodevices, and School of Electronics, Peking University, Beijing 100871, China
- Academy for Advanced Interdisciplinary Studies, Peking University, Beijing 100871, China
| | - Zhaozheng Lyu
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences; School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100190, China
| | - Mo Chen
- Beijing Academy of Quantum Information Sciences, 100193 Beijing, China
| | - Xingjun Wu
- Beijing Academy of Quantum Information Sciences, 100193 Beijing, China
| | - Li Lu
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences; School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100190, China
| | - Jianhua Zhao
- State Key Laboratory of Superlattices and Microstructures, Institute of Semiconductors, Chinese Academy of Sciences, P.O. Box 912, Beijing 100083, China
| | - Ji-Yin Wang
- Beijing Academy of Quantum Information Sciences, 100193 Beijing, China
| | - Hongqi Xu
- Beijing Academy of Quantum Information Sciences, 100193 Beijing, China
- Beijing Key Laboratory of Quantum Devices, Key Laboratory for the Physics and Chemistry of Nanodevices, and School of Electronics, Peking University, Beijing 100871, China
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12
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Wang Y, Yang SY, Sivakumar PK, Ortiz BR, Teicher SML, Wu H, Srivastava AK, Garg C, Liu D, Parkin SSP, Toberer ES, McQueen T, Wilson SD, Ali MN. Anisotropic proximity-induced superconductivity and edge supercurrent in Kagome metal, K 1-xV 3Sb 5. SCIENCE ADVANCES 2023; 9:eadg7269. [PMID: 37436976 DOI: 10.1126/sciadv.adg7269] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/17/2023] [Accepted: 06/12/2023] [Indexed: 07/14/2023]
Abstract
Materials with Kagome nets are of particular importance for their potential combination of strong correlation, exotic magnetism, and electronic topology. KV3Sb5 was discovered to be a layered topological metal with a Kagome net of vanadium. Here, we fabricated Josephson Junctions of K1-xV3Sb5 and induced superconductivity over long junction lengths. Through magnetoresistance and current versus phase measurements, we observed a magnetic field sweeping direction-dependent magnetoresistance and an anisotropic interference pattern with a Fraunhofer pattern for in-plane magnetic field but a suppression of critical current for out-of-plane magnetic field. These results indicate an anisotropic internal magnetic field in K1-xV3Sb5 that influences the superconducting coupling in the junction, possibly giving rise to spin-triplet superconductivity. In addition, the observation of long-lived fast oscillations shows evidence of spatially localized conducting channels arising from edge states. These observations pave the way for studying unconventional superconductivity and Josephson device based on Kagome metals with electron correlation and topology.
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Affiliation(s)
- Yaojia Wang
- Max Planck Institute of Microstructure Physics, 06108 Halle, Saxony-Anhalt, Germany
- Kavli Institute of Nanoscience, Delft University of Technology, Delft, The Netherlands
| | - Shuo-Ying Yang
- Max Planck Institute of Microstructure Physics, 06108 Halle, Saxony-Anhalt, Germany
| | - Pranava K Sivakumar
- Max Planck Institute of Microstructure Physics, 06108 Halle, Saxony-Anhalt, Germany
| | - Brenden R Ortiz
- Materials Department, University of California Santa Barbara, Santa Barbara, CA 93106, USA
| | - Samuel M L Teicher
- Materials Department, University of California Santa Barbara, Santa Barbara, CA 93106, USA
| | - Heng Wu
- Max Planck Institute of Microstructure Physics, 06108 Halle, Saxony-Anhalt, Germany
- Kavli Institute of Nanoscience, Delft University of Technology, Delft, The Netherlands
| | - Abhay K Srivastava
- Max Planck Institute of Microstructure Physics, 06108 Halle, Saxony-Anhalt, Germany
| | - Chirag Garg
- Max Planck Institute of Microstructure Physics, 06108 Halle, Saxony-Anhalt, Germany
- IBM Almaden Research Center, San Jose, CA 95120, USA
| | - Defa Liu
- Max Planck Institute of Microstructure Physics, 06108 Halle, Saxony-Anhalt, Germany
- Department of Physics, Beijing Normal University, Beijing 100875, China
| | - Stuart S P Parkin
- Max Planck Institute of Microstructure Physics, 06108 Halle, Saxony-Anhalt, Germany
| | | | | | - Stephen D Wilson
- Materials Department, University of California Santa Barbara, Santa Barbara, CA 93106, USA
| | - Mazhar N Ali
- Max Planck Institute of Microstructure Physics, 06108 Halle, Saxony-Anhalt, Germany
- Kavli Institute of Nanoscience, Delft University of Technology, Delft, The Netherlands
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13
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Yazdani A, von Oppen F, Halperin BI, Yacoby A. Hunting for Majoranas. Science 2023; 380:eade0850. [PMID: 37347870 DOI: 10.1126/science.ade0850] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/25/2022] [Accepted: 05/22/2023] [Indexed: 06/24/2023]
Abstract
Over the past decade, there have been considerable efforts to observe non-abelian quasiparticles in novel quantum materials and devices. These efforts are motivated by the goals of demonstrating quantum statistics of quasiparticles beyond those of fermions and bosons and of establishing the underlying science for the creation of topologically protected quantum bits. In this Review, we focus on efforts to create topological superconducting phases that host Majorana zero modes. We consider the lessons learned from existing experimental efforts, which are motivating both improvements to present platforms and the exploration of new approaches. Although the experimental detection of non-abelian quasiparticles remains challenging, the knowledge gained thus far and the opportunities ahead offer high potential for discovery and advances in this exciting area of quantum physics.
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Affiliation(s)
- Ali Yazdani
- Joseph Henry Laboratories and Department of Physics, Princeton University, Princeton, NJ 08540, USA
| | - Felix von Oppen
- Dahlem Center for Complex Quantum Systems and Fachbereich Physik, Freie Universität Berlin, 14195 Berlin, Germany
| | | | - Amir Yacoby
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
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14
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Banerjee A, Geier M, Rahman MA, Sanchez DS, Thomas C, Wang T, Manfra MJ, Flensberg K, Marcus CM. Control of Andreev Bound States Using Superconducting Phase Texture. PHYSICAL REVIEW LETTERS 2023; 130:116203. [PMID: 37001098 DOI: 10.1103/physrevlett.130.116203] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/31/2022] [Accepted: 01/20/2023] [Indexed: 06/19/2023]
Abstract
Andreev bound states with opposite phase-inversion asymmetries are observed in local tunneling spectra at the two ends of a superconductor-semiconductor-superconductor planar Josephson junction in the presence of a perpendicular magnetic field, while the nonlocal spectra remain phase symmetric. Spectral signatures agree with a theoretical model, yielding a physical picture in which phase textures in superconducting leads localize and control the position of Andreev bound states in the junction, demonstrating a simple means of controlling the position and size of Andreev states within a planar junction.
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Affiliation(s)
- Abhishek Banerjee
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
| | - Max Geier
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
| | - M Ahnaf Rahman
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
| | - Daniel S Sanchez
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
| | - Candice Thomas
- Department of Physics and Astronomy and Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907, USA
| | - Tian Wang
- Department of Physics and Astronomy and Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907, USA
| | - Michael J Manfra
- Department of Physics and Astronomy and Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907, USA
- School of Materials Engineering and Elmore Family School of Electrical and Computer Engineering, Purdue University, West Lafayette, Indiana 47907, USA
| | - Karsten Flensberg
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
| | - Charles M Marcus
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
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15
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Elfeky B, Cuozzo JJ, Lotfizadeh N, Schiela WF, Farzaneh SM, Strickland WM, Langone D, Rossi E, Shabani J. Evolution of 4π-Periodic Supercurrent in the Presence of an In-Plane Magnetic Field. ACS NANO 2023; 17:4650-4658. [PMID: 36800544 PMCID: PMC10018771 DOI: 10.1021/acsnano.2c10880] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 11/01/2022] [Accepted: 02/15/2023] [Indexed: 06/18/2023]
Abstract
In the presence of a 4π-periodic contribution to the current phase relation, for example in topological Josephson junctions, odd Shapiro steps are expected to be missing. While missing odd Shapiro steps have been observed in several material systems and interpreted in the context of topological superconductivity, they have also been observed in topologically trivial junctions. Here, we study the evolution of such trivial missing odd Shapiro steps in Al-InAs junctions in the presence of an in-plane magnetic field Bθ. We find that the odd steps reappear at a crossover Bθ value, exhibiting an in-plane field angle anisotropy that depends on spin-orbit coupling effects. We interpret this behavior by theoretically analyzing the Andreev bound state spectrum and the transitions induced by the nonadiabatic dynamics of the junction and attribute the observed anisotropy to mode-to-mode coupling. Our results highlight the complex phenomenology of missing Shapiro steps and the underlying current phase relations in planar Josephson junctions designed to realize Majorana states.
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Affiliation(s)
- Bassel
Heiba Elfeky
- Center
for Quantum Information Physics, Department of Physics, New York University, New York, New York 10003, United States
| | - Joseph J. Cuozzo
- Department
of Physics, William & Mary, Williamsburg, Virginia 23187, United States
| | - Neda Lotfizadeh
- Center
for Quantum Information Physics, Department of Physics, New York University, New York, New York 10003, United States
| | - William F. Schiela
- Center
for Quantum Information Physics, Department of Physics, New York University, New York, New York 10003, United States
| | - Seyed M. Farzaneh
- Center
for Quantum Information Physics, Department of Physics, New York University, New York, New York 10003, United States
| | - William M. Strickland
- Center
for Quantum Information Physics, Department of Physics, New York University, New York, New York 10003, United States
| | - Dylan Langone
- Center
for Quantum Information Physics, Department of Physics, New York University, New York, New York 10003, United States
| | - Enrico Rossi
- Department
of Physics, William & Mary, Williamsburg, Virginia 23187, United States
| | - Javad Shabani
- Center
for Quantum Information Physics, Department of Physics, New York University, New York, New York 10003, United States
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16
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Ziesen A, Altland A, Egger R, Hassler F. Statistical Majorana Bound State Spectroscopy. PHYSICAL REVIEW LETTERS 2023; 130:106001. [PMID: 36962051 DOI: 10.1103/physrevlett.130.106001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/28/2022] [Accepted: 02/21/2023] [Indexed: 06/18/2023]
Abstract
Tunnel spectroscopy data for the detection of Majorana bound states (MBS) is often criticized for its proneness to misinterpretation of genuine MBS with low-lying Andreev bound states. Here, we suggest a protocol removing this ambiguity by extending single shot measurements to sequences performed at varying system parameters. We demonstrate how such sampling, which we argue requires only moderate effort for current experimental platforms, resolves the statistics of Andreev side lobes, thus providing compelling evidence for the presence or absence of a Majorana center peak.
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Affiliation(s)
- Alexander Ziesen
- JARA Institute for Quantum Information, RWTH Aachen University, 52056 Aachen, Germany
| | - Alexander Altland
- Institut für Theoretische Physik, Universität zu Köln, Zülpicher Straße 77, 50937 Köln, Germany
| | - Reinhold Egger
- Institut für Theoretische Physik, Heinrich-Heine-Universität, D-40225 Düsseldorf, Germany
| | - Fabian Hassler
- JARA Institute for Quantum Information, RWTH Aachen University, 52056 Aachen, Germany
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17
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Banerjee A, Lesser O, Rahman MA, Thomas C, Wang T, Manfra MJ, Berg E, Oreg Y, Stern A, Marcus CM. Local and Nonlocal Transport Spectroscopy in Planar Josephson Junctions. PHYSICAL REVIEW LETTERS 2023; 130:096202. [PMID: 36930915 DOI: 10.1103/physrevlett.130.096202] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/19/2022] [Accepted: 01/11/2023] [Indexed: 06/18/2023]
Abstract
We report simultaneously acquired local and nonlocal transport spectroscopy in a phase-biased planar Josephson junction based on an epitaxial InAs-Al hybrid two-dimensional heterostructure. Quantum point contacts at the junction ends allow measurement of the 2×2 matrix of local and nonlocal tunneling conductances as a function of magnetic field along the junction, phase difference across the junction, and carrier density. A closing and reopening of a gap was observed in both the local and nonlocal tunneling spectra as a function of magnetic field. For particular tunings of junction density, gap reopenings were accompanied by zero-bias conductance peaks (ZBCPs) in local conductances. End-to-end correlation of gap reopening was strong, while correlation of local ZBCPs was weak. A model of the device, with disorder treated phenomenologically, shows comparable conductance matrix behavior associated with a topological phase transition. Phase dependence helps distinguish possible origins of the ZBCPs.
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Affiliation(s)
- A Banerjee
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
| | - O Lesser
- Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot, Israel 76100
| | - M A Rahman
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
| | - C Thomas
- Department of Physics and Astronomy, and Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907 USA
| | - T Wang
- Department of Physics and Astronomy, and Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907 USA
| | - M J Manfra
- Department of Physics and Astronomy, and Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907 USA
- School of Materials Engineering, and School of Electrical and Computer Engineering, Purdue University, West Lafayette, Indiana 47907 USA
| | - E Berg
- Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot, Israel 76100
| | - Y Oreg
- Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot, Israel 76100
| | - Ady Stern
- Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot, Israel 76100
| | - C M Marcus
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
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18
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Tam PM, Kane CL. Probing Fermi Sea Topology by Andreev State Transport. PHYSICAL REVIEW LETTERS 2023; 130:096301. [PMID: 36930895 DOI: 10.1103/physrevlett.130.096301] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/14/2022] [Accepted: 01/16/2023] [Indexed: 06/18/2023]
Abstract
We show that the topology of the Fermi sea of a two-dimensional electron gas (2DEG) is reflected in the ballistic Landauer transport along a long and narrow Josephson π junction that proximitizes the 2DEG. The low-energy Andreev states bound to the junction are shown to exhibit a dispersion that is sensitive to the Euler characteristic of the Fermi sea (χ_{F}). We highlight two important relations: one connects the electron or hole nature of Andreev states to the convex or concave nature of Fermi surface critical points, and one relates these critical points to χ_{F}. We then argue that the transport of Andreev states leads to a quantized conductance that probes χ_{F}. An experiment is proposed to measure this effect, from which we predict an I-V characteristic that not only captures the topology of the Fermi sea in metals, but also resembles the rectification effect in diodes. Finally, we evaluate the feasibility of measuring this quantized response in graphene, InAs and HgTe 2DEGs.
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Affiliation(s)
- Pok Man Tam
- Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Charles L Kane
- Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
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19
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Haxell DZ, Cheah E, Křížek F, Schott R, Ritter MF, Hinderling M, Belzig W, Bruder C, Wegscheider W, Riel H, Nichele F. Measurements of Phase Dynamics in Planar Josephson Junctions and SQUIDs. PHYSICAL REVIEW LETTERS 2023; 130:087002. [PMID: 36898094 DOI: 10.1103/physrevlett.130.087002] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/12/2022] [Revised: 09/15/2022] [Accepted: 01/19/2023] [Indexed: 06/18/2023]
Abstract
We experimentally investigate the stochastic phase dynamics of planar Josephson junctions (JJs) and superconducting quantum interference devices (SQUIDs) defined in epitaxial InAs/Al heterostructures, and characterized by a large ratio of Josephson energy to charging energy. We observe a crossover from a regime of macroscopic quantum tunneling to one of phase diffusion as a function of temperature, where the transition temperature T^{*} is gate-tunable. The switching probability distributions are shown to be consistent with a small shunt capacitance and moderate damping, resulting in a switching current which is a small fraction of the critical current. Phase locking between two JJs leads to a difference in switching current between that of a JJ measured in isolation and that of the same JJ measured in an asymmetric SQUID loop. In the case of the loop, T^{*} is also tuned by a magnetic flux.
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Affiliation(s)
- D Z Haxell
- IBM Research Europe-Zurich, Säumerstrasse 4, 8803 Rüschlikon, Switzerland
| | - E Cheah
- Solid State Physics Laboratory, ETH Zurich, 8093 Zurich, Switzerland
| | - F Křížek
- IBM Research Europe-Zurich, Säumerstrasse 4, 8803 Rüschlikon, Switzerland
- Solid State Physics Laboratory, ETH Zurich, 8093 Zurich, Switzerland
| | - R Schott
- Solid State Physics Laboratory, ETH Zurich, 8093 Zurich, Switzerland
| | - M F Ritter
- IBM Research Europe-Zurich, Säumerstrasse 4, 8803 Rüschlikon, Switzerland
| | - M Hinderling
- IBM Research Europe-Zurich, Säumerstrasse 4, 8803 Rüschlikon, Switzerland
| | - W Belzig
- Fachbereich Physik, Universität Konstanz, D-78457 Konstanz, Germany
| | - C Bruder
- Department of Physics, University of Basel, Klingelbergstrasse 82, CH-4056 Basel, Switzerland
| | - W Wegscheider
- Solid State Physics Laboratory, ETH Zurich, 8093 Zurich, Switzerland
| | - H Riel
- IBM Research Europe-Zurich, Säumerstrasse 4, 8803 Rüschlikon, Switzerland
| | - F Nichele
- IBM Research Europe-Zurich, Säumerstrasse 4, 8803 Rüschlikon, Switzerland
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20
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Dvir T, Wang G, van Loo N, Liu CX, Mazur GP, Bordin A, Ten Haaf SLD, Wang JY, van Driel D, Zatelli F, Li X, Malinowski FK, Gazibegovic S, Badawy G, Bakkers EPAM, Wimmer M, Kouwenhoven LP. Realization of a minimal Kitaev chain in coupled quantum dots. Nature 2023; 614:445-450. [PMID: 36792741 DOI: 10.1038/s41586-022-05585-1] [Citation(s) in RCA: 19] [Impact Index Per Article: 19.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/16/2022] [Accepted: 11/22/2022] [Indexed: 02/17/2023]
Abstract
Majorana bound states constitute one of the simplest examples of emergent non-Abelian excitations in condensed matter physics. A toy model proposed by Kitaev shows that such states can arise at the ends of a spinless p-wave superconducting chain1. Practical proposals for its realization2,3 require coupling neighbouring quantum dots (QDs) in a chain through both electron tunnelling and crossed Andreev reflection4. Although both processes have been observed in semiconducting nanowires and carbon nanotubes5-8, crossed-Andreev interaction was neither easily tunable nor strong enough to induce coherent hybridization of dot states. Here we demonstrate the simultaneous presence of all necessary ingredients for an artificial Kitaev chain: two spin-polarized QDs in an InSb nanowire strongly coupled by both elastic co-tunnelling (ECT) and crossed Andreev reflection (CAR). We fine-tune this system to a sweet spot where a pair of poor man's Majorana states is predicted to appear. At this sweet spot, the transport characteristics satisfy the theoretical predictions for such a system, including pairwise correlation, zero charge and stability against local perturbations. Although the simple system presented here can be scaled to simulate a full Kitaev chain with an emergent topological order, it can also be used imminently to explore relevant physics related to non-Abelian anyons.
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Affiliation(s)
- Tom Dvir
- QuTech, Delft University of Technology, Delft, The Netherlands.
- Kavli Institute of Nanoscience, Delft University of Technology, Delft, The Netherlands.
| | - Guanzhong Wang
- QuTech, Delft University of Technology, Delft, The Netherlands
- Kavli Institute of Nanoscience, Delft University of Technology, Delft, The Netherlands
| | - Nick van Loo
- QuTech, Delft University of Technology, Delft, The Netherlands
- Kavli Institute of Nanoscience, Delft University of Technology, Delft, The Netherlands
| | - Chun-Xiao Liu
- QuTech, Delft University of Technology, Delft, The Netherlands
- Kavli Institute of Nanoscience, Delft University of Technology, Delft, The Netherlands
| | - Grzegorz P Mazur
- QuTech, Delft University of Technology, Delft, The Netherlands
- Kavli Institute of Nanoscience, Delft University of Technology, Delft, The Netherlands
| | - Alberto Bordin
- QuTech, Delft University of Technology, Delft, The Netherlands
- Kavli Institute of Nanoscience, Delft University of Technology, Delft, The Netherlands
| | - Sebastiaan L D Ten Haaf
- QuTech, Delft University of Technology, Delft, The Netherlands
- Kavli Institute of Nanoscience, Delft University of Technology, Delft, The Netherlands
| | - Ji-Yin Wang
- QuTech, Delft University of Technology, Delft, The Netherlands
- Kavli Institute of Nanoscience, Delft University of Technology, Delft, The Netherlands
| | - David van Driel
- QuTech, Delft University of Technology, Delft, The Netherlands
- Kavli Institute of Nanoscience, Delft University of Technology, Delft, The Netherlands
| | - Francesco Zatelli
- QuTech, Delft University of Technology, Delft, The Netherlands
- Kavli Institute of Nanoscience, Delft University of Technology, Delft, The Netherlands
| | - Xiang Li
- QuTech, Delft University of Technology, Delft, The Netherlands
- Kavli Institute of Nanoscience, Delft University of Technology, Delft, The Netherlands
| | - Filip K Malinowski
- QuTech, Delft University of Technology, Delft, The Netherlands
- Kavli Institute of Nanoscience, Delft University of Technology, Delft, The Netherlands
| | - Sasa Gazibegovic
- Department of Applied Physics, Eindhoven University of Technology, Eindhoven, The Netherlands
| | - Ghada Badawy
- Department of Applied Physics, Eindhoven University of Technology, Eindhoven, The Netherlands
| | - Erik P A M Bakkers
- Department of Applied Physics, Eindhoven University of Technology, Eindhoven, The Netherlands
| | - Michael Wimmer
- QuTech, Delft University of Technology, Delft, The Netherlands
- Kavli Institute of Nanoscience, Delft University of Technology, Delft, The Netherlands
| | - Leo P Kouwenhoven
- QuTech, Delft University of Technology, Delft, The Netherlands.
- Kavli Institute of Nanoscience, Delft University of Technology, Delft, The Netherlands.
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21
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Hu LH, Wu X, Liu CX, Zhang RX. Competing Vortex Topologies in Iron-Based Superconductors. PHYSICAL REVIEW LETTERS 2022; 129:277001. [PMID: 36638298 DOI: 10.1103/physrevlett.129.277001] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/03/2021] [Accepted: 12/07/2022] [Indexed: 06/17/2023]
Abstract
In this Letter, we establish a new theoretical paradigm for vortex Majorana physics in the recently discovered topological iron-based superconductors (TFeSCs). While TFeSCs are widely accepted as an exemplar of topological insulators (TIs) with intrinsic s-wave superconductivity, our theory implies that such a common belief could be oversimplified. Our main finding is that the normal-state bulk Dirac nodes, usually ignored in TI-based vortex Majorana theories for TFeSCs, will play a key role of determining the vortex state topology. In particular, the interplay between TI and Dirac nodal bands will lead to multiple competing topological phases for a superconducting vortex line in TFeSCs, including an unprecedented hybrid topological vortex state that carries both Majorana bound states and a gapless dispersion. Remarkably, this exotic hybrid vortex phase generally exists in the vortex phase diagram for our minimal model for TFeSCs and is directly relevant to TFeSC candidates such as LiFeAs. When the fourfold rotation symmetry is broken by vortex-line tilting or curving, the hybrid vortex gets topologically trivialized and becomes Majorana free, which could explain the puzzle of ubiquitous trivial vortices observed in LiFeAs. The origin of the Majorana signal in other TFeSC candidates such as FeTe_{x}Se_{1-x} and CaKFe_{4}As_{4} is also interpreted within our theory framework. Our theory sheds new light on theoretically understanding and experimentally engineering Majorana physics in high-temperature iron-based systems.
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Affiliation(s)
- Lun-Hui Hu
- Department of Physics and Astronomy, The University of Tennessee, Knoxville, Tennessee 37996, USA
- Institute for Advanced Materials and Manufacturing, The University of Tennessee, Knoxville, Tennessee 37920, USA
- Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802, USA
| | - Xianxin Wu
- CAS Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China
- Max-Planck-Institut für Festkörperforschung, Heisenbergstrasse 1, D-70569 Stuttgart, Germany
| | - Chao-Xing Liu
- Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802, USA
| | - Rui-Xing Zhang
- Department of Physics and Astronomy, The University of Tennessee, Knoxville, Tennessee 37996, USA
- Institute for Advanced Materials and Manufacturing, The University of Tennessee, Knoxville, Tennessee 37920, USA
- Department of Materials Science and Engineering, The University of Tennessee, Knoxville, Tennessee 37996, USA
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22
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Wang Z, Feng JJ, Huang Z, Niu Q. Transport Theory for Topological Josephson Junctions with a Majorana Qubit. PHYSICAL REVIEW LETTERS 2022; 129:257001. [PMID: 36608237 DOI: 10.1103/physrevlett.129.257001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/26/2022] [Accepted: 11/15/2022] [Indexed: 06/17/2023]
Abstract
We construct a semiclassical theory for the transport of topological Josephson junctions starting from a microscopic Hamiltonian that comprehensively includes the interplay among the Majorana qubit, the Josephson phase, and the dissipation process. With the path integral approach, we derive a set of semiclassical equations of motion that can be used to calculate the time evolution of the Josephson phase and the Majorana qubit. In the equations we reveal rich dynamical phenomena such as the qubit-induced charge pumping, the effective spin-orbit torque, and the Gilbert damping. We demonstrate the influence of these dynamical phenomena on the transport signatures of the junction. We apply the theory to study the Shapiro steps of the junction, and find the suppression of the first Shapiro step due to the dynamical feedback of the Majorana qubit.
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Affiliation(s)
- Zhi Wang
- School of Physics, Sun Yat-sen University, Guangzhou 510275, China
- Guangdong Provincial Key Laboratory of Magnetoelectric Physics and Devices, Sun Yat-sen University, Guangzhou 510275, China
| | - Jia-Jin Feng
- International Center for Quantum Materials, Peking University, Beijing 100871, China
| | - Zhao Huang
- Texas Center for Superconductivity, University of Houston, Houston, Texas 77204, USA
| | - Qian Niu
- School of Physical Sciences, University of Science and Technology of China, Hefei 230026, China
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23
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Moehle C, Rout PK, Jainandunsing NA, Kuiri D, Ke CT, Xiao D, Thomas C, Manfra MJ, Nowak MP, Goswami S. Controlling Andreev Bound States with the Magnetic Vector Potential. NANO LETTERS 2022; 22:8601-8607. [PMID: 36279222 PMCID: PMC9650727 DOI: 10.1021/acs.nanolett.2c03130] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 08/07/2022] [Revised: 10/16/2022] [Indexed: 06/16/2023]
Abstract
Tunneling spectroscopy measurements are often used to probe the energy spectrum of Andreev bound states (ABSs) in semiconductor-superconductor hybrids. Recently, this spectroscopy technique has been incorporated into planar Josephson junctions (JJs) formed in two-dimensional electron gases, a potential platform to engineer phase-controlled topological superconductivity. Here, we perform ABS spectroscopy at the two ends of planar JJs and study the effects of the magnetic vector potential on the ABS spectrum. We show that the local superconducting phase difference arising from the vector potential is equal in magnitude and opposite in sign at the two ends, in agreement with a model that assumes localized ABSs near the tunnel barriers. Complemented with microscopic simulations, our experiments demonstrate that the local phase difference can be used to estimate the relative position of localized ABSs separated by a few hundred nanometers.
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Affiliation(s)
- Christian
M. Moehle
- QuTech
and Kavli Institute of Nanoscience, Delft
University of Technology, 2600 GADelft, The Netherlands
| | - Prasanna K. Rout
- QuTech
and Kavli Institute of Nanoscience, Delft
University of Technology, 2600 GADelft, The Netherlands
| | - Nayan A. Jainandunsing
- QuTech
and Kavli Institute of Nanoscience, Delft
University of Technology, 2600 GADelft, The Netherlands
| | - Dibyendu Kuiri
- Academic
Centre for Materials and Nanotechnology, AGH University of Science and Technology, 30-059Krakow, Poland
| | - Chung Ting Ke
- QuTech
and Kavli Institute of Nanoscience, Delft
University of Technology, 2600 GADelft, The Netherlands
| | - Di Xiao
- Department
of Physics and Astronomy, Purdue University, West Lafayette, Indiana47907, United States
| | - Candice Thomas
- Department
of Physics and Astronomy, Purdue University, West Lafayette, Indiana47907, United States
| | - Michael J. Manfra
- Department
of Physics and Astronomy, Purdue University, West Lafayette, Indiana47907, United States
- Elmore
School of Electrical and Computer Engineering, Purdue University, West Lafayette, Indiana47907, United States
- School
of Materials Engineering, Purdue University, West Lafayette, Indiana47907, United States
- Microsoft
Quantum Lab West Lafayette, West
Lafayette, Indiana47907, United States
| | - Michał P. Nowak
- Academic
Centre for Materials and Nanotechnology, AGH University of Science and Technology, 30-059Krakow, Poland
| | - Srijit Goswami
- QuTech
and Kavli Institute of Nanoscience, Delft
University of Technology, 2600 GADelft, The Netherlands
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24
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Selective control of conductance modes in multi-terminal Josephson junctions. Nat Commun 2022; 13:5933. [PMID: 36209199 PMCID: PMC9547902 DOI: 10.1038/s41467-022-33682-2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/14/2022] [Accepted: 09/29/2022] [Indexed: 11/18/2022] Open
Abstract
The Andreev bound state spectra of multi-terminal Josephson junctions form an artificial band structure, which is predicted to host tunable topological phases under certain conditions. However, the number of conductance modes between the terminals of a multi-terminal Josephson junction must be few in order for this spectrum to be experimentally accessible. In this work, we employ a quantum point contact geometry in three-terminal Josephson devices to demonstrate independent control of conductance modes between each pair of terminals and access to the single-mode regime coexistent with the presence of superconducting coupling. These results establish a full platform on which to realize tunable Andreev bound state spectra in multi-terminal Josephson junctions. Multiterminal Josephson junctions may provide a novel way to realize topologically non-trivial band structures in an n-dimensional phase space. Here, the authors experimentally demonstrate the proposed necessary conditions to measure these states.
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25
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Vacancy-engineered nodal-line semimetals. Sci Rep 2022; 12:14981. [PMID: 36056065 DOI: 10.1038/s41598-022-18519-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/16/2022] [Accepted: 08/09/2022] [Indexed: 11/08/2022] Open
Abstract
Symmetry-enforced nodal-line semimetals are immune to perturbations that preserve the underlying symmetries. This intrinsic robustness enables investigations of fundamental phenomena and applications utilizing diverse materials design techniques. The drawback of symmetry-enforced nodal-line semimetals is that the crossings of energy bands are constrained to symmetry-invariant momenta in the Brillouin zone. On the other end are accidental nodal-line semimetals whose band crossings, not being enforced by symmetry, are easily destroyed by perturbations. Some accidental nodal-line semimetals have, however, the advantage that their band crossings can occur in generic locations in the Brillouin zone, and thus can be repositioned to tailor material properties. We show that lattice engineering with periodic distributions of vacancies yields a hybrid type of nodal-line semimetals which possess symmetry-enforced nodal lines and accidental nodal lines, with the latter endowed with an enhanced robustness to perturbations. Both types of nodal lines are explained by a symmetry analysis of an effective model which captures the relevant characteristics of the proposed materials, and are verified by first-principles calculations of vacancy-engineered borophene polymorphs. Our findings offer an alternative path to relying on complicated compounds to design robust nodal-line semimetals; one can instead remove atoms from a common monoatomic material.
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26
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Lu B, Zhang Y. Tunable Majorana corner modes by orbital-dependent exchange interaction in a two-dimensional topological superconductor. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2022; 34:305302. [PMID: 35580592 DOI: 10.1088/1361-648x/ac709e] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/28/2022] [Accepted: 05/17/2022] [Indexed: 06/15/2023]
Abstract
We theoretically study the effect of orbital-dependent exchange field in the formation of second order topological superconductors. We demonstrate that changing the orbital difference can induce topological transition and the Majorana corner modes therein can be manipulated. We further propose to detect the corner modes via a normal probe terminal. The conductance quantization is found to be robust to changes of the relevant system parameters.
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Affiliation(s)
- Bo Lu
- Center for Joint Quantum Studies and Department of Physics, Tianjin University, Tianjin 300072, People's Republic of China
| | - Yiying Zhang
- Center for Joint Quantum Studies and Department of Physics, Tianjin University, Tianjin 300072, People's Republic of China
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27
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Zhou T, Dartiailh MC, Sardashti K, Han JE, Matos-Abiague A, Shabani J, Žutić I. Fusion of Majorana bound states with mini-gate control in two-dimensional systems. Nat Commun 2022; 13:1738. [PMID: 35365644 PMCID: PMC8976011 DOI: 10.1038/s41467-022-29463-6] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/21/2021] [Accepted: 03/16/2022] [Indexed: 11/09/2022] Open
Abstract
A hallmark of topological superconductivity is the non-Abelian statistics of Majorana bound states (MBS), its chargeless zero-energy emergent quasiparticles. The resulting fractionalization of a single electron, stored nonlocally as a two spatially-separated MBS, provides a powerful platform for implementing fault-tolerant topological quantum computing. However, despite intensive efforts, experimental support for MBS remains indirect and does not probe their non-Abelian statistics. Here we propose how to overcome this obstacle in mini-gate controlled planar Josephson junctions (JJs) and demonstrate non-Abelian statistics through MBS fusion, detected by charge sensing using a quantum point contact, based on dynamical simulations. The feasibility of preparing, manipulating, and fusing MBS in two-dimensional (2D) systems is supported in our experiments which demonstrate the gate control of topological transition and superconducting properties with five mini gates in InAs/Al-based JJs. While we focus on this well-established platform, where the topological superconductivity was already experimentally detected, our proposal to identify elusive non-Abelian statistics motivates also further MBS studies in other gate-controlled 2D systems.
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Affiliation(s)
- Tong Zhou
- Department of Physics, University at Buffalo, State University of New York, Buffalo, NY, 14260, USA.
| | - Matthieu C Dartiailh
- Center for Quantum Phenomena, Department of Physics, New York University, New York, NY, 10003, USA
| | - Kasra Sardashti
- Center for Quantum Phenomena, Department of Physics, New York University, New York, NY, 10003, USA
| | - Jong E Han
- Department of Physics, University at Buffalo, State University of New York, Buffalo, NY, 14260, USA
| | - Alex Matos-Abiague
- Department of Physics and Astronomy, Wayne State University, Detroit, MI, 48201, USA
| | - Javad Shabani
- Center for Quantum Phenomena, Department of Physics, New York University, New York, NY, 10003, USA
| | - Igor Žutić
- Department of Physics, University at Buffalo, State University of New York, Buffalo, NY, 14260, USA.
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28
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Phan D, Senior J, Ghazaryan A, Hatefipour M, Strickland WM, Shabani J, Serbyn M, Higginbotham AP. Detecting Induced p±ip Pairing at the Al-InAs Interface with a Quantum Microwave Circuit. PHYSICAL REVIEW LETTERS 2022; 128:107701. [PMID: 35333085 DOI: 10.1103/physrevlett.128.107701] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/14/2021] [Revised: 12/15/2021] [Accepted: 01/31/2022] [Indexed: 06/14/2023]
Abstract
Superconductor-semiconductor hybrid devices are at the heart of several proposed approaches to quantum information processing, but their basic properties remain to be understood. We embed a two-dimensional Al-InAs hybrid system in a resonant microwave circuit, probing the breakdown of superconductivity due to an applied magnetic field. We find a fingerprint from the two-component nature of the hybrid system, and quantitatively compare with a theory that includes the contribution of intraband p±ip pairing in the InAs, as well as the emergence of Bogoliubov-Fermi surfaces due to magnetic field. Separately resolving the Al and InAs contributions allows us to determine the carrier density and mobility in the InAs.
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Affiliation(s)
- D Phan
- IST Austria, Am Campus 1, 3400 Klosterneuburg, Austria
| | - J Senior
- IST Austria, Am Campus 1, 3400 Klosterneuburg, Austria
| | - A Ghazaryan
- IST Austria, Am Campus 1, 3400 Klosterneuburg, Austria
| | - M Hatefipour
- Department of Physics, New York University, New York, New York 10003, USA
| | - W M Strickland
- Department of Physics, New York University, New York, New York 10003, USA
| | - J Shabani
- Department of Physics, New York University, New York, New York 10003, USA
| | - M Serbyn
- IST Austria, Am Campus 1, 3400 Klosterneuburg, Austria
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29
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Wu X, Liu X, Thomale R, Liu CX. High- T c superconductor Fe(Se,Te) monolayer: an intrinsic, scalable and electrically tunable Majorana platform. Natl Sci Rev 2022; 9:nwab087. [PMID: 35308561 PMCID: PMC8924703 DOI: 10.1093/nsr/nwab087] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/27/2020] [Revised: 04/25/2021] [Accepted: 04/25/2021] [Indexed: 11/30/2022] Open
Abstract
Iron-based superconductors have been identified as a novel platform for realizing Majorana zero modes (MZMs) without heterostructures, due to their intrinsic topological properties and high-T c superconductivity. In the two-dimensional limit, the FeTe1-x Se x monolayer, a topological band inversion has recently been experimentally observed. Here, we propose to create MZMs by applying an in-plane magnetic field to the FeTe1-x Se x monolayer and tuning the local chemical potential via electric gating. Owing to the anisotropic magnetic couplings on edges, an in-plane magnetic field drives the system into an intrinsic high-order topological superconductor phase with Majorana corner modes. Furthermore, MZMs can occur at the domain wall of chemical potentials at either one edge or certain type of tri-junction in the two-dimensional bulk. Our study not only reveals the FeTe1-x Se x monolayer as a promising Majorana platform with scalability and electrical tunability and within reach of contemporary experimental capability, but also provides a general principle to search for realistic realization of high-order topological superconductivity.
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Affiliation(s)
- Xianxin Wu
- Institut für Theoretische Physik und Astrophysik, Julius-Maximilians-Universität Würzburg, 97074 Würzburg, Germany
| | - Xin Liu
- School of Physics, Huazhong University of Science and Technology, Wuhan 430074, China
- Wuhan National High Magnetic Field Center, Huazhong University of Science and Technology, Wuhan 430074, China
| | - Ronny Thomale
- Institut für Theoretische Physik und Astrophysik, Julius-Maximilians-Universität Würzburg, 97074 Würzburg, Germany
| | - Chao-Xing Liu
- Department of Physics, the Pennsylvania State University, University Park, PA 16802, USA
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30
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Moehle CM, Ke CT, Wang Q, Thomas C, Xiao D, Karwal S, Lodari M, van de Kerkhof V, Termaat R, Gardner GC, Scappucci G, Manfra MJ, Goswami S. InSbAs Two-Dimensional Electron Gases as a Platform for Topological Superconductivity. NANO LETTERS 2021; 21:9990-9996. [PMID: 34793173 DOI: 10.1021/acs.nanolett.1c03520] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
Topological superconductivity can be engineered in semiconductors with strong spin-orbit interaction coupled to a superconductor. Experimental advances in this field have often been triggered by the development of new hybrid material systems. Among these, two-dimensional electron gases (2DEGs) are of particular interest due to their inherent design flexibility and scalability. Here, we discuss results on a 2D platform based on a ternary 2DEG (InSbAs) coupled to in situ grown aluminum. The spin-orbit coupling in these 2DEGs can be tuned with the As concentration, reaching values up to 400 meV Å, thus exceeding typical values measured in its binary constituents. In addition to a large Landé g-factor of ∼55 (comparable to that of InSb), we show that the clean superconductor-semiconductor interface leads to a hard induced superconducting gap. Using this new platform, we demonstrate the basic operation of phase-controllable Josephson junctions, superconducting islands, and quasi-1D systems, prototypical device geometries used to study Majorana zero modes.
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Affiliation(s)
- Christian M Moehle
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology, 2600 GA Delft, The Netherlands
| | - Chung Ting Ke
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology, 2600 GA Delft, The Netherlands
| | - Qingzhen Wang
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology, 2600 GA Delft, The Netherlands
| | - Candice Thomas
- Department of Physics and Astronomy, Purdue University, West Lafayette, Indiana 47907, United States
- Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907, United States
| | - Di Xiao
- Department of Physics and Astronomy, Purdue University, West Lafayette, Indiana 47907, United States
- Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907, United States
| | - Saurabh Karwal
- QuTech and Netherlands Organization for Applied Scientific Research (TNO), 2628 CK Delft, The Netherlands
| | - Mario Lodari
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology, 2600 GA Delft, The Netherlands
| | - Vincent van de Kerkhof
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology, 2600 GA Delft, The Netherlands
| | - Ruben Termaat
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology, 2600 GA Delft, The Netherlands
| | - Geoffrey C Gardner
- Microsoft Quantum Purdue, Purdue University, West Lafayette, Indiana 47907, United States
| | - Giordano Scappucci
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology, 2600 GA Delft, The Netherlands
| | - Michael J Manfra
- Department of Physics and Astronomy, Purdue University, West Lafayette, Indiana 47907, United States
- Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907, United States
- Microsoft Quantum Purdue, Purdue University, West Lafayette, Indiana 47907, United States
- School of Electrical and Computer Engineering, Purdue University, West Lafayette, Indiana 47907, United States
- School of Materials Engineering, Purdue University, West Lafayette, Indiana 47907, United States
| | - Srijit Goswami
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology, 2600 GA Delft, The Netherlands
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31
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Elfeky BH, Lotfizadeh N, Schiela WF, Strickland WM, Dartiailh M, Sardashti K, Hatefipour M, Yu P, Pankratova N, Lee H, Manucharyan VE, Shabani J. Local Control of Supercurrent Density in Epitaxial Planar Josephson Junctions. NANO LETTERS 2021; 21:8274-8280. [PMID: 34570504 DOI: 10.1021/acs.nanolett.1c02771] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
The critical current response to an applied out-of-plane magnetic field in a Josephson junction provides insight into the uniformity of its current distribution. In Josephson junctions with semiconducting weak links, the carrier density, and therefore the overall current distribution, can be modified electrostatically via metallic gates. Here, we show local control of the current distribution in an epitaxial Al-InAs Josephson junction equipped with five minigates. We demonstrate that not only can the junction width be electrostatically defined but also the current profile can be locally adjusted to form superconducting quantum interference devices. Our studies show enhanced edge conduction in such long junctions, which can be eliminated by minigates to create a uniform current distribution.
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Affiliation(s)
- Bassel Heiba Elfeky
- Department of Physics, New York University, New York, New York 10003, United States
| | - Neda Lotfizadeh
- Department of Physics, New York University, New York, New York 10003, United States
| | - William F Schiela
- Department of Physics, New York University, New York, New York 10003, United States
| | - William M Strickland
- Department of Physics, New York University, New York, New York 10003, United States
| | - Matthieu Dartiailh
- Department of Physics, New York University, New York, New York 10003, United States
| | - Kasra Sardashti
- Department of Physics, New York University, New York, New York 10003, United States
| | - Mehdi Hatefipour
- Department of Physics, New York University, New York, New York 10003, United States
| | - Peng Yu
- Department of Physics, New York University, New York, New York 10003, United States
| | - Natalia Pankratova
- Department of Physics, Joint Quantum Institute, and Quantum Materials Center, University of Maryland, College Park, Maryland 20742, United States
| | - Hanho Lee
- Department of Physics, Joint Quantum Institute, and Quantum Materials Center, University of Maryland, College Park, Maryland 20742, United States
| | - Vladimir E Manucharyan
- Department of Physics, Joint Quantum Institute, and Quantum Materials Center, University of Maryland, College Park, Maryland 20742, United States
| | - Javad Shabani
- Department of Physics, New York University, New York, New York 10003, United States
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32
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Hassan SA, Wu BH, Xu XF, Wang CR, Cao JC. Bending effect on the Majorana bound states in planar Josephson junctions. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2021; 33:385001. [PMID: 34171850 DOI: 10.1088/1361-648x/ac0ea7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/29/2021] [Accepted: 06/25/2021] [Indexed: 06/13/2023]
Abstract
We consider the bending effect on the formation of Majorana bound states (MBSs) in planar Josephson junctions where the normal stripe is tilted in a V shape. Our results show that the MBSs remain robust for moderate bending angles. Beyond some critical angles, the degradation of MBSs can be revealed by its eigenspectrum as well as the Majorana polarization (MP). Our results show that the parameter space of bending angle for robust MBSs can be significantly enlarged by tuning the superconducting phase difference across the Josephson junction. These findings suggest that the interplay of the junction geometry and the device parameters provides richer degree of freedom in designing topological superconducting devices for future applications. The MP analysis is an indispensable tool for characterizing the Majorana states.
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Affiliation(s)
- S A Hassan
- Department of Applied Physics, Donghua University, 2999 North Renmin Road, Shanghai, 201620, People's Republic of China
| | - B H Wu
- Department of Applied Physics, Donghua University, 2999 North Renmin Road, Shanghai, 201620, People's Republic of China
| | - X F Xu
- Department of Applied Physics, Donghua University, 2999 North Renmin Road, Shanghai, 201620, People's Republic of China
| | - C R Wang
- Department of Applied Physics, Donghua University, 2999 North Renmin Road, Shanghai, 201620, People's Republic of China
| | - J C Cao
- Key Laboratory of Terahertz Solid-State Technology, Shanghai Institute of Microsystem and Information Technology, Chinese Academy of Sciences, 865 Changning Road, Shanghai 200050, People's Republic of China
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33
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Wang Z, Cheng S, Liu X, Jiang H. Topological kink states in graphene. NANOTECHNOLOGY 2021; 32:402001. [PMID: 34161935 DOI: 10.1088/1361-6528/ac0dd8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/18/2021] [Accepted: 06/23/2021] [Indexed: 06/13/2023]
Abstract
Due to the unique band structure, graphene exhibits a number of exotic electronic properties that have not been observed in other materials. Among them, it has been demonstrated that there exist the one-dimensional valley-polarized topological kink states localized in the vicinity of the domain wall of graphene systems, where a bulk energy gap opens due to the inversion symmetry breaking. Notably, the valley-momentum locking nature makes the topological kink states attractive to the property manipulation in valleytronics. This paper systematically reviews both the theoretical research and experimental progress on topological kink states in monolayer graphene, bilayer graphene and graphene-like classical wave systems. Besides, various applications of topological kink states, including the valley filter, current partition, current manipulation, Majorana zero modes and etc, are also introduced.
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Affiliation(s)
- Zibo Wang
- College of Physics and Electronic Engineering, Sichuan Normal University, Chengdu 610068, People's Republic of China
- Center for Computational Sciences, Sichuan Normal University, Chengdu 610068, People's Republic of China
| | - Shuguang Cheng
- Department of Physics, Northwest University, Xi'an 710069, People's Republic of China
| | - Xiao Liu
- School of Physical Science and Technology, Soochow University, Suzhou 215006, People's Republic of China
| | - Hua Jiang
- School of Physical Science and Technology, Soochow University, Suzhou 215006, People's Republic of China
- Institute for Advanced Study of Soochow University, Suzhou 215006, People's Republic of China
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34
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Phase-induced topological superconductivity in a planar heterostructure. Proc Natl Acad Sci U S A 2021; 118:2107377118. [PMID: 34183403 DOI: 10.1073/pnas.2107377118] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
Topological superconductivity in quasi-one-dimensional systems is a novel phase of matter with possible implications for quantum computation. Despite years of effort, a definitive signature of this phase in experiments is still debated. A major cause of this ambiguity is the side effects of applying a magnetic field: induced in-gap states, vortices, and alignment issues. Here we propose a planar semiconductor-superconductor heterostructure as a platform for realizing topological superconductivity without applying a magnetic field to the two-dimensional electron gas hosting the topological state. Time-reversal symmetry is broken only by phase biasing the proximitizing superconductors, which can be achieved using extremely small fluxes or bias currents far from the quasi-one-dimensional channel. Our platform is based on interference between this phase biasing and the phase arising from strong spin-orbit coupling in closed electron trajectories. The principle is demonstrated analytically using a simple model, and then shown numerically for realistic devices. We show a robust topological phase diagram, as well as explicit wavefunctions of Majorana zero modes. We discuss experimental issues regarding the practical implementation of our proposal, establishing it as an accessible scheme with contemporary experimental techniques.
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35
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Liu F, Qu F, Žutić I, Xie S, Liu D, Fonseca ALA, Malard M. Robust Topological Nodal-Line Semimetals from Periodic Vacancies in Two-Dimensional Materials. J Phys Chem Lett 2021; 12:5710-5715. [PMID: 34128659 DOI: 10.1021/acs.jpclett.1c01249] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
A nodal-line semimetal (NLSM) is suppressed in the presence of spin-orbit coupling unless it is protected by a nonsymmorphic symmetry. We show that two-dimensional (2D) materials can realize robust NLSMs when vacancies are introduced on the lattice. As a case study we investigate borophene, a boron honeycomb-like sheet. While the Dirac cones of pristine borophene are shown to be gapped out by spin-orbit coupling and by magnetic exchange, robust nodal lines (NLs) emerge in the spectrum when selected atoms are removed. We propose an effective 2D model and a symmetry analysis to demonstrate that these NLs are topological and protected by a nonsymmorphic glide plane. Our findings offer a paradigm shift to the design of NLSMs: instead of searching for nonsymmorphic materials, robust NLSMs may be realized simply by removing atoms from ordinary symmorphic crystals.
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Affiliation(s)
- F Liu
- Instituto de Física, Universidade de Brasília, Brasília-DF, Brazil
| | - F Qu
- Instituto de Física, Universidade de Brasília, Brasília-DF, Brazil
| | - I Žutić
- Department of Physics, University at Buffalo, the State University of New York, Buffalo, New York 14260, United States
| | - S Xie
- School of Physics, State Key Laboratory of Crystal Materials, Shandong University, Jinan, China
| | - D Liu
- School of Physics, State Key Laboratory of Crystal Materials, Shandong University, Jinan, China
| | - A L A Fonseca
- Instituto de Física, Universidade de Brasília, Brasília-DF, Brazil
| | - M Malard
- Faculdade UnB Planaltina, Universidade de Brasília, Brasília-DF, Brazil
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36
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Assessing Bound States in a One-Dimensional Topological Superconductor: Majorana versus Tamm. Symmetry (Basel) 2021. [DOI: 10.3390/sym13061100] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022] Open
Abstract
Majorana bound states in topological superconductors have attracted intense research activity in view of applications in topological quantum computation. However, they are not the only example of topological bound states that can occur in such systems. Here, we study a model in which both Majorana and Tamm bound states compete. We show both numerically and analytically that, surprisingly, the Tamm state remains partially localized even when the spectrum becomes gapless. Despite this fact, we demonstrate that the Majorana polarization shows a clear transition between the two regimes.
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37
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Rosenbach D, Schmitt TW, Schüffelgen P, Stehno MP, Li C, Schleenvoigt M, Jalil AR, Mussler G, Neumann E, Trellenkamp S, Golubov AA, Brinkman A, Grützmacher D, Schäpers T. Reappearance of first Shapiro step in narrow topological Josephson junctions. SCIENCE ADVANCES 2021; 7:7/26/eabf1854. [PMID: 34162537 PMCID: PMC8221618 DOI: 10.1126/sciadv.abf1854] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 10/09/2020] [Accepted: 05/12/2021] [Indexed: 06/13/2023]
Abstract
In Josephson junctions, a supercurrent across a nonsuperconducting weak link is carried by electron-hole bound states. Because of the helical spin texture of nondegenerate topological surface states, gapless bound states are established in junctions with topological weak link. These have a characteristic 4π-periodic current phase relation (CΦR) that leads to twice the conventional Shapiro step separation voltage in radio frequency-dependent measurements. In this context, we identify an attenuated first Shapiro step in (Bi0.06Sb0.94)2Te3 (BST) Josephson junctions with AlO x capping layer. We further investigate junctions on narrow, selectively deposited BST nanoribbons, where surface charges are confined to the perimeter of the nanoribbon. Within these junctions, previously identified signatures of gapless bound states are absent. Because of confinement, transverse momentum sub-bands are quantized and a topological gap opening is observed. Surface states within these quantized sub-bands are spin degenerate, which evokes bound states of conventional 2π-periodic CΦR within the BST nanoribbon weak link.
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Affiliation(s)
- Daniel Rosenbach
- Peter Grünberg Institute (PGI-9), Forschungszentrum Jülich, 52425 Jülich, Germany.
- Helmholtz Virtual Institute for Topological Insulators (VITI), Forschungszentrum Jülich, 52425 Jülich, Germany
- JARA-Fundamentals of Future Information Technology, Jülich-Aachen Research Alliance, Forschungszentrum Jülich and RWTH Aachen University, Aachen, Germany
| | - Tobias W Schmitt
- Peter Grünberg Institute (PGI-9), Forschungszentrum Jülich, 52425 Jülich, Germany
- JARA-FIT Institute Green IT, RWTH Aachen University, 52062 Aachen, Germany
| | - Peter Schüffelgen
- Peter Grünberg Institute (PGI-9), Forschungszentrum Jülich, 52425 Jülich, Germany
- Helmholtz Virtual Institute for Topological Insulators (VITI), Forschungszentrum Jülich, 52425 Jülich, Germany
| | - Martin P Stehno
- Physikalisches Institut EP3, University of Würzburg, Am Hubland 97070, Würzburg, Germany
| | - Chuan Li
- MESA+ Institute for Nanotechnology, University of Twente, 7500AE Enschede, The Netherlands
| | - Michael Schleenvoigt
- Peter Grünberg Institute (PGI-9), Forschungszentrum Jülich, 52425 Jülich, Germany
| | - Abdur R Jalil
- Peter Grünberg Institute (PGI-9), Forschungszentrum Jülich, 52425 Jülich, Germany
| | - Gregor Mussler
- Peter Grünberg Institute (PGI-9), Forschungszentrum Jülich, 52425 Jülich, Germany
- Helmholtz Virtual Institute for Topological Insulators (VITI), Forschungszentrum Jülich, 52425 Jülich, Germany
| | - Elmar Neumann
- Helmholtz Nano Facility (HNF), Forschungszentrum Jülich, 52425 Jülich, Germany
| | - Stefan Trellenkamp
- Helmholtz Nano Facility (HNF), Forschungszentrum Jülich, 52425 Jülich, Germany
| | - Alexander A Golubov
- MESA+ Institute for Nanotechnology, University of Twente, 7500AE Enschede, The Netherlands
| | - Alexander Brinkman
- MESA+ Institute for Nanotechnology, University of Twente, 7500AE Enschede, The Netherlands
| | - Detlev Grützmacher
- Peter Grünberg Institute (PGI-9), Forschungszentrum Jülich, 52425 Jülich, Germany
- Helmholtz Virtual Institute for Topological Insulators (VITI), Forschungszentrum Jülich, 52425 Jülich, Germany
| | - Thomas Schäpers
- Peter Grünberg Institute (PGI-9), Forschungszentrum Jülich, 52425 Jülich, Germany
- Helmholtz Virtual Institute for Topological Insulators (VITI), Forschungszentrum Jülich, 52425 Jülich, Germany
- JARA-Fundamentals of Future Information Technology, Jülich-Aachen Research Alliance, Forschungszentrum Jülich and RWTH Aachen University, Aachen, Germany
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38
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Qiu D, Gong C, Wang S, Zhang M, Yang C, Wang X, Xiong J. Recent Advances in 2D Superconductors. ADVANCED MATERIALS (DEERFIELD BEACH, FLA.) 2021; 33:e2006124. [PMID: 33768653 DOI: 10.1002/adma.202006124] [Citation(s) in RCA: 28] [Impact Index Per Article: 9.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/08/2020] [Revised: 10/22/2020] [Indexed: 06/12/2023]
Abstract
The emergence of superconductivity in 2D materials has attracted much attention and there has been rapid development in recent years because of their fruitful physical properties, such as high transition temperature (Tc ), continuous phase transition, and enhanced parallel critical magnetic field (Bc ). Tremendous efforts have been devoted to exploring different physical parameters to figure out the mechanisms behind the unexpected superconductivity phenomena, including adjusting the thickness of samples, fabricating various heterostructures, tuning the carrier density by electric field and chemical doping, and so on. Here, different types of 2D superconductivity with their unique characteristics are introduced, including the conventional Bardeen-Cooper-Schrieffer superconductivity in ultrathin films, high-Tc superconductivity in Fe-based and Cu-based 2D superconductors, unconventional superconductivity in newly discovered twist-angle bilayer graphene, superconductivity with enhanced Bc , and topological superconductivity. A perspective toward this field is then proposed based on academic knowledge from the recently reported literature. The aim is to provide researchers with a clear and comprehensive understanding about the newly developed 2D superconductivity and promote the development of this field much further.
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Affiliation(s)
- Dong Qiu
- State Key Laboratory of Electronic Thin Film and Integrated Devices, University of Electronic Science and Technology of China, Chengdu, 610054, China
| | - Chuanhui Gong
- State Key Laboratory of Electronic Thin Film and Integrated Devices, University of Electronic Science and Technology of China, Chengdu, 610054, China
| | - SiShuang Wang
- State Key Laboratory of Electronic Thin Film and Integrated Devices, University of Electronic Science and Technology of China, Chengdu, 610054, China
| | - Miao Zhang
- State Key Laboratory of Electronic Thin Film and Integrated Devices, University of Electronic Science and Technology of China, Chengdu, 610054, China
| | - Chao Yang
- State Key Laboratory of Electronic Thin Film and Integrated Devices, University of Electronic Science and Technology of China, Chengdu, 610054, China
| | - Xianfu Wang
- State Key Laboratory of Electronic Thin Film and Integrated Devices, University of Electronic Science and Technology of China, Chengdu, 610054, China
| | - Jie Xiong
- State Key Laboratory of Electronic Thin Film and Integrated Devices, University of Electronic Science and Technology of China, Chengdu, 610054, China
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39
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Fragility of surface states in topological superfluid 3He. Nat Commun 2021; 12:1574. [PMID: 33692358 PMCID: PMC7946958 DOI: 10.1038/s41467-021-21831-y] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/20/2020] [Accepted: 01/28/2021] [Indexed: 11/23/2022] Open
Abstract
Superfluid 3He, with unconventional spin-triplet p-wave pairing, provides a model system for topological superconductors, which have attracted significant interest through potential applications in topologically protected quantum computing. In topological insulators and quantum Hall systems, the surface/edge states, arising from bulk-surface correspondence and the momentum space topology of the band structure, are robust. Here we demonstrate that in topological superfluids and superconductors the surface Andreev bound states, which depend on the momentum space topology of the emergent order parameter, are fragile with respect to the details of surface scattering. We confine superfluid 3He within a cavity of height D comparable to the Cooper pair diameter ξ0. We precisely determine the superfluid transition temperature Tc and the suppression of the superfluid energy gap, for different scattering conditions tuned in situ, and compare to the predictions of quasiclassical theory. We discover that surface magnetic scattering leads to unexpectedly large suppression of Tc, corresponding to an increased density of low energy bound states. Surface states in topological quantum matter are protected by their band structure. Here, on confined superfluid 3He as a model for topological superconductors, the authors report experimental evidence on the fragility of surface Andreev bound states with respect to the details of surface scattering.
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40
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Udupa A, Banerjee A, Sengupta K, Sen D. One-dimensional spin-orbit coupled Dirac system with extended s-wave superconductivity: Majorana modes and Josephson effects. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2021; 33:145301. [PMID: 33470985 DOI: 10.1088/1361-648x/abdd63] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/12/2020] [Accepted: 01/19/2021] [Indexed: 06/12/2023]
Abstract
Motivated by the spin-momentum locking of electrons at the boundaries of certain topological insulators, we study a one-dimensional system of spin-orbit coupled massless Dirac electrons withs-wave superconducting pairing. As a result of the spin-orbit coupling, our model has only two kinds of linearly dispersing modes, and we take these to be right-moving spin-up and left-moving spin-down. Both lattice and continuum models are studied. In the lattice model, we find that a single Majorana zero energy mode appears at each end of a finite system provided that thes-wave pairing has an extended form, with the nearest-neighbor pairing being larger than the on-site pairing. We confirm this both numerically and analytically by calculating the winding number. We find that the continuum model also has zero energy end modes. Next we study a lattice version of a model with both Schrödinger and Dirac-like terms and find that the model hosts a topological transition between topologically trivial and non-trivial phases depending on the relative strength of the Schrödinger and Dirac terms. We then study a continuum system consisting of twos-wave superconductors with different phases of the pairing, with aδ-function potential barrier lying at the junction of the two superconductors. Remarkably, we find that the system has asingleAndreev bound state (ABS) which is localized at the junction. When the pairing phase difference crosses a multiple of 2π, an ABS touches the top of the superconducting gap and disappears, and a different state appears from the bottom of the gap. We also study the AC Josephson effect in such a junction with a voltage bias that has both a constantV0and a term which oscillates with a frequencyω. We find that, in contrast to standard Josephson junctions, Shapiro plateaus appear when the Josephson frequencyωJ= 2eV0/ℏis a rational fraction ofω. We discuss experiments which can realize such junctions.
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Affiliation(s)
- Adithi Udupa
- Center for High Energy Physics, Indian Institute of Science, Bengaluru 560012, India
| | - Abhishek Banerjee
- Center for High Energy Physics, Indian Institute of Science, Bengaluru 560012, India
- Center for Quantum Devices and Microsoft Quantum Lab Copenhagen, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
| | - K Sengupta
- School of Physical Sciences, Indian Association for the Cultivation of Science, Jadavpur, Kolkata 700032, India
| | - Diptiman Sen
- Center for High Energy Physics, Indian Institute of Science, Bengaluru 560012, India
- Department of Physics, Indian Institute of Science, Bengaluru 560012, India
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41
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Papaj M, Fu L. Creating Majorana modes from segmented Fermi surface. Nat Commun 2021; 12:577. [PMID: 33495471 PMCID: PMC7835351 DOI: 10.1038/s41467-020-20690-3] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/12/2020] [Accepted: 12/15/2020] [Indexed: 11/09/2022] Open
Abstract
Majorana bound states provide a fertile ground for both investigation of fundamental phenomena as well as for applications in quantum computation. However, despite enormous experimental and theoretical efforts, the currently available Majorana platforms suffer from a multitude of issues that prevent full realization of their potential. Therefore, improved Majorana systems are still highly sought after. Here we present a platform for creating Majorana bound states from 2D gapless superconducting state in spin-helical systems under the in-plane magnetic or Zeeman field. Topological 1D channels are formed by quantum confinement of quasiparticles via Andreev reflection from the surrounding fully gapped superconducting region. Our proposal can be realized using narrow strips of magnetic insulators on top of proximitized 3D topological insulators. This setup has key advantages that include: small required fields, no necessity of fine-tuning of chemical potential, removal of the low-energy detrimental states, and large attainable topological gap.
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Affiliation(s)
- Michał Papaj
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA.
| | - Liang Fu
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA.
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42
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Baumgartner C, Fuchs L, Frész L, Reinhardt S, Gronin S, Gardner GC, Manfra MJ, Paradiso N, Strunk C. Josephson Inductance as a Probe for Highly Ballistic Semiconductor-Superconductor Weak Links. PHYSICAL REVIEW LETTERS 2021; 126:037001. [PMID: 33543978 DOI: 10.1103/physrevlett.126.037001] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/21/2020] [Accepted: 12/21/2020] [Indexed: 06/12/2023]
Abstract
We present simultaneous measurements of Josephson inductance and dc transport characteristics of ballistic Josephson junctions based upon an epitaxial Al-InAs heterostructure. The Josephson inductance at finite current bias directly reveals the current-phase relation. The proximity-induced gap, the critical current and the average value of the transparency τ[over ¯] are extracted without need for phase bias, demonstrating, e.g., a near-unity value of τ[over ¯]=0.94. Our method allows us to probe the devices deeply in the nondissipative regime, where ordinary transport measurements are featureless. In perpendicular magnetic field the junctions show a nearly perfect Fraunhofer pattern of the critical current, which is insensitive to the value of τ[over ¯]. In contrast, the signature of supercurrent interference in the inductance turns out to be extremely sensitive to τ[over ¯].
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Affiliation(s)
- Christian Baumgartner
- Institut für Experimentelle und Angewandte Physik, University of Regensburg, 93040 Regensburg, Germany
| | - Lorenz Fuchs
- Institut für Experimentelle und Angewandte Physik, University of Regensburg, 93040 Regensburg, Germany
| | - Linus Frész
- Institut für Experimentelle und Angewandte Physik, University of Regensburg, 93040 Regensburg, Germany
| | - Simon Reinhardt
- Institut für Experimentelle und Angewandte Physik, University of Regensburg, 93040 Regensburg, Germany
| | - Sergei Gronin
- Microsoft Quantum Purdue, Purdue University, West Lafayette, Indiana 47907, USA
- Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907, USA
| | - Geoffrey C Gardner
- Microsoft Quantum Purdue, Purdue University, West Lafayette, Indiana 47907, USA
- Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907 USA
| | - Michael J Manfra
- Microsoft Quantum Purdue, Purdue University, West Lafayette, Indiana 47907, USA
- Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907 USA
- Department of Physics and Astronomy, Purdue University, West Lafayette, Indiana 47907, USA
- School of Materials Engineering, Purdue University, West Lafayette, Indiana 47907, USA
- School of Electrical and Computer Engineering, Purdue University, West Lafayette, Indiana 47907, USA
| | - Nicola Paradiso
- Institut für Experimentelle und Angewandte Physik, University of Regensburg, 93040 Regensburg, Germany
| | - Christoph Strunk
- Institut für Experimentelle und Angewandte Physik, University of Regensburg, 93040 Regensburg, Germany
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43
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Dartiailh MC, Mayer W, Yuan J, Wickramasinghe KS, Matos-Abiague A, Žutić I, Shabani J. Phase Signature of Topological Transition in Josephson Junctions. PHYSICAL REVIEW LETTERS 2021; 126:036802. [PMID: 33543950 DOI: 10.1103/physrevlett.126.036802] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/18/2020] [Accepted: 12/16/2020] [Indexed: 06/12/2023]
Abstract
Topological superconductivity holds promise for fault-tolerant quantum computing. While planar Josephson junctions are attractive candidates to realize this exotic state, direct phase measurements as the fingerprint of the topological transition are missing. By embedding two gate-tunable Al/InAs Josephson junctions in a loop geometry, we measure a π jump in the junction phase with an increasing in-plane magnetic field B_{∥}. This jump is accompanied by a minimum of the critical current, indicating a closing and reopening of the superconducting gap, strongly anisotropic in B_{∥}. Our theory confirms that these signatures of a topological transition are compatible with the emergence of Majorana bound states.
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Affiliation(s)
- Matthieu C Dartiailh
- Center for Quantum Phenomena, Department of Physics, New York University, New York, New York 10003, USA
| | - William Mayer
- Center for Quantum Phenomena, Department of Physics, New York University, New York, New York 10003, USA
| | - Joseph Yuan
- Center for Quantum Phenomena, Department of Physics, New York University, New York, New York 10003, USA
| | - Kaushini S Wickramasinghe
- Center for Quantum Phenomena, Department of Physics, New York University, New York, New York 10003, USA
| | - Alex Matos-Abiague
- Department of Physics and Astronomy, Wayne State University, Detroit, Michigan 48201, USA
| | - Igor Žutić
- Department of Physics, University at Buffalo, State University of New York, Buffalo, New York 14260, USA
| | - Javad Shabani
- Center for Quantum Phenomena, Department of Physics, New York University, New York, New York 10003, USA
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44
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Li CZ, Wang AQ, Li C, Zheng WZ, Brinkman A, Yu DP, Liao ZM. Topological Transition of Superconductivity in Dirac Semimetal Nanowire Josephson Junctions. PHYSICAL REVIEW LETTERS 2021; 126:027001. [PMID: 33512215 DOI: 10.1103/physrevlett.126.027001] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/20/2020] [Accepted: 12/18/2020] [Indexed: 06/12/2023]
Abstract
We report the topological transition by gate control in a Cd_{3}As_{2} Dirac semimetal nanowire Josephson junction with diameter of about 64 nm. In the electron branch, the quantum confinement effect enforces the surface band into a series of gapped subbands and thus nontopological states. In the hole branch, however, because the hole mean free path is smaller than the nanowire perimeter, the quantum confinement effect is inoperative and the topological property maintained. The superconductivity is enhanced by gate tuning from electron to hole conduction, manifested by a larger critical supercurrent and a larger critical magnetic field, which is attributed to the topological transition from gapped surface subbands to a gapless surface band. The gate-controlled topological transition of superconductivity should be valuable for manipulation of Majorana zero modes, providing a platform for future compatible and scalable design of topological qubits.
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Affiliation(s)
- Cai-Zhen Li
- Shenzhen Institute for Quantum Science and Engineering, and Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China
- State Key Laboratory for Mesoscopic Physics and Frontiers Science Center for Nano-optoelectronics, School of Physics, Peking University, Beijing 100871, China
| | - An-Qi Wang
- State Key Laboratory for Mesoscopic Physics and Frontiers Science Center for Nano-optoelectronics, School of Physics, Peking University, Beijing 100871, China
- Academy for Advanced Interdisciplinary Studies, Peking University, Beijing 100871, China
| | - Chuan Li
- MESA+ Institute for Nanotechnology, University of Twente, 7500 AE Enschede, The Netherlands
| | - Wen-Zhuang Zheng
- State Key Laboratory for Mesoscopic Physics and Frontiers Science Center for Nano-optoelectronics, School of Physics, Peking University, Beijing 100871, China
| | - Alexander Brinkman
- MESA+ Institute for Nanotechnology, University of Twente, 7500 AE Enschede, The Netherlands
| | - Da-Peng Yu
- Shenzhen Institute for Quantum Science and Engineering, and Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China
| | - Zhi-Min Liao
- State Key Laboratory for Mesoscopic Physics and Frontiers Science Center for Nano-optoelectronics, School of Physics, Peking University, Beijing 100871, China
- Beijing Key Laboratory of Quantum Devices, Peking University, Beijing 100871, China
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45
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AFM Analysis of Micron and Sub-Micron Sized Bridges Fabricated Using the Femtosecond Laser on YBCO Thin Films. MICROMACHINES 2020; 11:mi11121088. [PMID: 33302556 PMCID: PMC7764433 DOI: 10.3390/mi11121088] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 11/10/2020] [Revised: 11/18/2020] [Accepted: 11/24/2020] [Indexed: 12/01/2022]
Abstract
The research arose as a result of the need to use the femtosecond laser to fabricate sub-micron and nano-sized bridges that could be analyzed for the Josephson effect. The femtosecond laser has a low pulse duration of 130 femtoseconds. Hence in an optical setup it was assumed that it could prevent the thermal degradation of the superconductive material during fabrication. In this paper a series of micron and sub-micron sized bridges where fabricated on superconductive yttrium barium copper oxide (YBCO) thin film using the femtosecond laser, a spherical convex lens of focal length 30 mm and the G-code control programming language applied to a translation stage. The dimensions of the bridges fabricated where analyzed using the atomic force microscope (AFM). As a result, micron sized superconductive bridges of width 1.68 μm, 1.39 μm, 1.23 μm and sub-micron sized bridges of width 858 nm, 732 nm where fabricated. The length of this bridges ranged from 9.6 μm to 12.8 μm. The femtosecond laser technique and the spherical convex lens can be used to fabricate bridges in the sub-micron dimension.
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46
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Laeven T, Nijholt B, Wimmer M, Akhmerov AR. Enhanced Proximity Effect in Zigzag-Shaped Majorana Josephson Junctions. PHYSICAL REVIEW LETTERS 2020; 125:086802. [PMID: 32909794 DOI: 10.1103/physrevlett.125.086802] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/11/2019] [Revised: 03/10/2020] [Accepted: 07/06/2020] [Indexed: 06/11/2023]
Abstract
High density superconductor-semiconductor-superconductor junctions have a small induced superconducting gap due to the quasiparticle trajectories with a large momentum parallel to the junction having a very long flight time. Because a large induced gap protects Majorana modes, these long trajectories constrain Majorana devices to a low electron density. We show that a zigzag-shaped geometry eliminates these trajectories, allowing the robust creation of Majorana states with both the induced gap E_{gap} and the Majorana size ξ_{M} improved by more than an order of magnitude for realistic parameters. In addition to the improved robustness of Majoranas, this new zigzag geometry is insensitive to the geometric details and the device tuning.
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Affiliation(s)
- Tom Laeven
- Kavli Institute of Nanoscience, Delft University of Technology, P.O. Box 4056, 2600 GA Delft, Netherlands
| | - Bas Nijholt
- Kavli Institute of Nanoscience, Delft University of Technology, P.O. Box 4056, 2600 GA Delft, Netherlands
| | - Michael Wimmer
- Kavli Institute of Nanoscience, Delft University of Technology, P.O. Box 4056, 2600 GA Delft, Netherlands
- QuTech, Delft University of Technology, P.O. Box 4056, 2600 GA Delft, Netherlands
| | - Anton R Akhmerov
- Kavli Institute of Nanoscience, Delft University of Technology, P.O. Box 4056, 2600 GA Delft, Netherlands
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47
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Nichele F, Portolés E, Fornieri A, Whiticar AM, Drachmann ACC, Gronin S, Wang T, Gardner GC, Thomas C, Hatke AT, Manfra MJ, Marcus CM. Relating Andreev Bound States and Supercurrents in Hybrid Josephson Junctions. PHYSICAL REVIEW LETTERS 2020; 124:226801. [PMID: 32567899 DOI: 10.1103/physrevlett.124.226801] [Citation(s) in RCA: 14] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/18/2019] [Revised: 03/03/2020] [Accepted: 04/27/2020] [Indexed: 06/11/2023]
Abstract
We demonstrate concomitant measurement of phase-dependent critical current and Andreev bound state spectrum in a highly transmissive InAs Josephson junction embedded in a dc superconducting quantum interference device (SQUID). Tunneling spectroscopy reveals Andreev bound states with near unity transmission probability. A nonsinusoidal current-phase relation is derived from the Andreev spectrum, showing excellent agreement with the one extracted from the SQUID critical current. Both measurements are reconciled within a short junction model where multiple Andreev bound states, with various transmission probabilities, contribute to the entire supercurrent flowing in the junction.
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Affiliation(s)
- F Nichele
- Center for Quantum Devices and Microsoft Quantum Lab-Copenhagen, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
- IBM Research-Zurich, Säumerstrasse 4, 8803 Rüschlikon, Switzerland
| | - E Portolés
- Center for Quantum Devices and Microsoft Quantum Lab-Copenhagen, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
| | - A Fornieri
- Center for Quantum Devices and Microsoft Quantum Lab-Copenhagen, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
| | - A M Whiticar
- Center for Quantum Devices and Microsoft Quantum Lab-Copenhagen, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
| | - A C C Drachmann
- Center for Quantum Devices and Microsoft Quantum Lab-Copenhagen, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
| | - S Gronin
- Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907, USA
- Microsoft Quantum Purdue, Purdue University, West Lafayette, Indiana 47907, USA
| | - T Wang
- Department of Physics and Astronomy, Purdue University, West Lafayette, Indiana 47907, USA
- Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907, USA
| | - G C Gardner
- Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907, USA
- Microsoft Quantum Purdue, Purdue University, West Lafayette, Indiana 47907, USA
| | - C Thomas
- Department of Physics and Astronomy, Purdue University, West Lafayette, Indiana 47907, USA
- Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907, USA
| | - A T Hatke
- Department of Physics and Astronomy, Purdue University, West Lafayette, Indiana 47907, USA
- Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907, USA
| | - M J Manfra
- Department of Physics and Astronomy, Purdue University, West Lafayette, Indiana 47907, USA
- Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907, USA
- School of Materials Engineering, Purdue University, West Lafayette, Indiana 47907, USA
- School of Electrical and Computer Engineering, Purdue University, West Lafayette, Indiana 47907, USA
- Microsoft Quantum Purdue, Purdue University, West Lafayette, Indiana 47907, USA
| | - C M Marcus
- Center for Quantum Devices and Microsoft Quantum Lab-Copenhagen, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
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48
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Głodzik S, Domański T. In-gap states of magnetic impurity in quantum spin Hall insulator proximitized to a superconductor. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2020; 32:235501. [PMID: 32079006 DOI: 10.1088/1361-648x/ab786d] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
We study in-gap states of a single magnetic impurity embedded in a honeycomb monolayer which is deposited on superconducting substrate. The intrinsic spin-orbit coupling induces the quantum spin Hall insulating (QSHI) phase gapped around the Fermi energy. Under such circumstances we consider the emergence of Shiba-like bound states driven by the superconducting proximity effect. We investigate their topography, spin-polarization and signatures of the quantum phase transition manifested by reversal of the local currents circulating around the magnetic impurity. These phenomena might be important for more exotic in-gap quasiparticles in such complex nanostructures as magnetic nanowires or islands, where the spin-orbit interaction along with the proximity induced electron pairing give rise to topological phases hosting the protected boundary modes.
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49
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Wang AQ, Ye XG, Yu DP, Liao ZM. Topological Semimetal Nanostructures: From Properties to Topotronics. ACS NANO 2020; 14:3755-3778. [PMID: 32286783 DOI: 10.1021/acsnano.9b07990] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
Characterized by bulk Dirac or Weyl cones and surface Fermi-arc states, topological semimetals have sparked enormous research interest in recent years. The nanostructures, with large surface-to-volume ratio and easy field-effect gating, provide ideal platforms to detect and manipulate the topological quantum states. Exotic physical properties originating from these topological states endow topological semimetals attractive for future topological electronics (topotronics). For example, the linear energy dispersion relation is promising for broadband infrared photodetectors, the spin-momentum locking nature of topological surface states is valuable for spintronics, and the topological superconductivity is highly desirable for fault-tolerant qubits. For real-life applications, topological semimetals in the form of nanostructures are necessary in terms of convenient fabrication and integration. Here, we review the recent progresses in topological semimetal nanostructures and start with the quantum transport properties. Then topological semimetal-based electronic devices are introduced. Finally, we discuss several important aspects that should receive great effort in the future, including controllable synthesis, manipulation of quantum states, topological field effect transistors, spintronic applications, and topological quantum computation.
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Affiliation(s)
- An-Qi Wang
- State Key Laboratory for Mesoscopic Physics and Frontiers Science Center for Nano-optoelectronics, School of Physics, Peking University, Beijing 100871, China
- Academy for Advanced Interdisciplinary Studies, Peking University, Beijing 100871, China
| | - Xing-Guo Ye
- State Key Laboratory for Mesoscopic Physics and Frontiers Science Center for Nano-optoelectronics, School of Physics, Peking University, Beijing 100871, China
| | - Da-Peng Yu
- Shenzhen Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China
| | - Zhi-Min Liao
- State Key Laboratory for Mesoscopic Physics and Frontiers Science Center for Nano-optoelectronics, School of Physics, Peking University, Beijing 100871, China
- Collaborative Innovation Center of Quantum Matter, Peking University, Beijing 100871, China
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50
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Manna S, Wei P, Xie Y, Law KT, Lee PA, Moodera JS. Signature of a pair of Majorana zero modes in superconducting gold surface states. Proc Natl Acad Sci U S A 2020; 117:8775-8782. [PMID: 32253317 PMCID: PMC7183215 DOI: 10.1073/pnas.1919753117] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
Under certain conditions, a fermion in a superconductor can separate in space into two parts known as Majorana zero modes, which are immune to decoherence from local noise sources and are attractive building blocks for quantum computers. Promising experimental progress has been made to demonstrate Majorana zero modes in materials with strong spin-orbit coupling proximity coupled to superconductors. Here we report signatures of Majorana zero modes in a material platform utilizing the surface states of gold. Using scanning tunneling microscope to probe EuS islands grown on top of gold nanowires, we observe two well-separated zero-bias tunneling conductance peaks aligned along the direction of the applied magnetic field, as expected for a pair of Majorana zero modes. This platform has the advantage of having a robust energy scale and the possibility of realizing complex designs using lithographic methods.
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Affiliation(s)
- Sujit Manna
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139
- Department of Physics, Indian Institute of Technology Delhi, 110 016 New Delhi, India
| | - Peng Wei
- Department of Physics and Astronomy, University of California, Riverside, CA 92521;
| | - Yingming Xie
- Department of Physics, Hong Kong University of Science and Technology, Hong Kong
| | - Kam Tuen Law
- Department of Physics, Hong Kong University of Science and Technology, Hong Kong
| | - Patrick A Lee
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139;
| | - Jagadeesh S Moodera
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139;
- Francis Bitter Magnet Laboratory, Massachusetts Institute of Technology, Cambridge, MA 02139
- Plasma Science and Fusion Center, Massachusetts Institute of Technology, Cambridge, MA 02139
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