1
|
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: 0] [Impact Index Per Article: 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.
Collapse
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
| |
Collapse
|
2
|
Schrade C, Fu L. Quantum Computing with Majorana Kramers Pairs. PHYSICAL REVIEW LETTERS 2022; 129:227002. [PMID: 36493456 DOI: 10.1103/physrevlett.129.227002] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/17/2018] [Revised: 10/20/2022] [Accepted: 10/28/2022] [Indexed: 06/17/2023]
Abstract
We propose a universal gate set acting on a qubit formed by the degenerate ground states of a Coulomb-blockaded time-reversal invariant topological superconductor island with spatially separated Majorana Kramers pairs: the "Majorana Kramers qubit." All gate operations are implemented by coupling the Majorana Kramers pairs to conventional superconducting leads. Interestingly, in such an all-superconducting device, the energy gap of the leads provides another layer of protection from quasiparticle poisoning independent of the island charging energy. Moreover, the absence of strong magnetic fields-which typically reduce the superconducting gap size of the island-suggests a unique robustness of our qubit to quasiparticle poisoning due to thermal excitations. Consequently, the Majorana Kramers qubit should benefit from prolonged coherence times and may provide an alternative route to a Majorana-based quantum computer.
Collapse
Affiliation(s)
- Constantin Schrade
- Department of Physics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, USA
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark
| | - Liang Fu
- Department of Physics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, USA
| |
Collapse
|
3
|
Gau M, Egger R, Zazunov A, Gefen Y. Driven Dissipative Majorana Dark Spaces. PHYSICAL REVIEW LETTERS 2020; 125:147701. [PMID: 33064546 DOI: 10.1103/physrevlett.125.147701] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/30/2020] [Accepted: 09/01/2020] [Indexed: 06/11/2023]
Abstract
Pure quantum states can be stabilized in open quantum systems subject to external driving forces and dissipation by environmental modes. We show that driven dissipative (DD) Majorana devices offer key advantages for stabilizing degenerate state manifolds ("dark spaces") and for manipulating states in dark spaces, both with respect to native (non-DD) Majorana devices and to DD platforms with topologically trivial building blocks. For two tunnel-coupled Majorana boxes, using otherwise only standard hardware elements (e.g., a noisy electromagnetic environment and quantum dots with driven tunnel links), we propose a dark qubit encoding. We anticipate exceptionally high fault tolerance levels due to a conspiracy of DD-based autonomous error correction and topology.
Collapse
Affiliation(s)
- Matthias Gau
- Institut für Theoretische Physik, Heinrich-Heine-Universität, D-40225 Düsseldorf, Germany
- Department of Condensed Matter Physics, Weizmann Institute, Rehovot, Israel
| | - Reinhold Egger
- Institut für Theoretische Physik, Heinrich-Heine-Universität, D-40225 Düsseldorf, Germany
| | - Alex Zazunov
- Institut für Theoretische Physik, Heinrich-Heine-Universität, D-40225 Düsseldorf, Germany
| | - Yuval Gefen
- Department of Condensed Matter Physics, Weizmann Institute, Rehovot, Israel
| |
Collapse
|
4
|
Yang FB. Kondo-assistant Aharonov-Bohm transport in a quantum dot-Majorana wire system. PHYSICS LETTERS A 2020; 384:126424. [DOI: 10.1016/j.physleta.2020.126424] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 09/01/2023]
|
5
|
Gao F, Wang JH, Watzinger H, Hu H, Rančić MJ, Zhang JY, Wang T, Yao Y, Wang GL, Kukučka J, Vukušić L, Kloeffel C, Loss D, Liu F, Katsaros G, Zhang JJ. Site-Controlled Uniform Ge/Si Hut Wires with Electrically Tunable Spin-Orbit Coupling. ADVANCED MATERIALS (DEERFIELD BEACH, FLA.) 2020; 32:e1906523. [PMID: 32105375 DOI: 10.1002/adma.201906523] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/05/2019] [Revised: 12/30/2019] [Indexed: 06/10/2023]
Abstract
Semiconductor nanowires have been playing a crucial role in the development of nanoscale devices for the realization of spin qubits, Majorana fermions, single photon emitters, nanoprocessors, etc. The monolithic growth of site-controlled nanowires is a prerequisite toward the next generation of devices that will require addressability and scalability. Here, combining top-down nanofabrication and bottom-up self-assembly, the growth of Ge wires on prepatterned Si (001) substrates with controllable position, distance, length, and structure is reported. This is achieved by a novel growth process that uses a SiGe strain-relaxation template and can be potentially generalized to other material combinations. Transport measurements show an electrically tunable spin-orbit coupling, with a spin-orbit length similar to that of III-V materials. Also, charge sensing between quantum dots in closely spaced wires is observed, which underlines their potential for the realization of advanced quantum devices. The reported results open a path toward scalable qubit devices using nanowires on silicon.
Collapse
Affiliation(s)
- Fei Gao
- National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing, 100190, China
- CAS Center for Excellence in Topological Quantum Computation and School of Physics, University of Chinese Academy of Sciences, Beijing, 100049, China
| | - Jian-Huan Wang
- National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing, 100190, China
- CAS Center for Excellence in Topological Quantum Computation and School of Physics, University of Chinese Academy of Sciences, Beijing, 100049, China
| | - Hannes Watzinger
- Institute of Science and Technology Austria, Am Campus 1, Klosterneuburg, 3400, Austria
| | - Hao Hu
- Frontier Institute of Science and Technology, Xi'an Jiaotong University, Xi'an, 710054, China
| | - Marko J Rančić
- Department of Physics, University of Basel, Klingelbergstrasse 82, Basel, CH-4056, Switzerland
| | - Jie-Yin Zhang
- National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing, 100190, China
- CAS Center for Excellence in Topological Quantum Computation and School of Physics, University of Chinese Academy of Sciences, Beijing, 100049, China
| | - Ting Wang
- National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing, 100190, China
- CAS Center for Excellence in Topological Quantum Computation and School of Physics, University of Chinese Academy of Sciences, Beijing, 100049, China
- Songshan Lake Materials Laboratory, Dongguan, Guangdong, 523808, China
| | - Yuan Yao
- National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing, 100190, China
| | - Gui-Lei Wang
- Institute of Microelectronics, Chinese Academy of Sciences, Beijing, 100029, China
| | - Josip Kukučka
- Institute of Science and Technology Austria, Am Campus 1, Klosterneuburg, 3400, Austria
| | - Lada Vukušić
- Institute of Science and Technology Austria, Am Campus 1, Klosterneuburg, 3400, Austria
| | - Christoph Kloeffel
- Department of Physics, University of Basel, Klingelbergstrasse 82, Basel, CH-4056, Switzerland
| | - Daniel Loss
- Department of Physics, University of Basel, Klingelbergstrasse 82, Basel, CH-4056, Switzerland
| | - Feng Liu
- Department of Materials Science and Engineering, University of Utah, Salt Lake City, UT, 84112, USA
| | - Georgios Katsaros
- Institute of Science and Technology Austria, Am Campus 1, Klosterneuburg, 3400, Austria
| | - Jian-Jun Zhang
- National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing, 100190, China
- CAS Center for Excellence in Topological Quantum Computation and School of Physics, University of Chinese Academy of Sciences, Beijing, 100049, China
- Songshan Lake Materials Laboratory, Dongguan, Guangdong, 523808, China
| |
Collapse
|
6
|
Manousakis J, Wille C, Altland A, Egger R, Flensberg K, Hassler F. Weak Measurement Protocols for Majorana Bound State Identification. PHYSICAL REVIEW LETTERS 2020; 124:096801. [PMID: 32202888 DOI: 10.1103/physrevlett.124.096801] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/28/2019] [Accepted: 01/22/2020] [Indexed: 06/10/2023]
Abstract
We propose a continuous weak measurement protocol testing the nonlocality of Majorana bound states through current shot noise correlations. The experimental setup contains a topological superconductor island with three normal-conducting leads weakly coupled to different Majorana states. Putting one lead at finite voltage and measuring the shot noise correlations between the other two (grounded) leads, devices with true Majorana states are distinguished from those without by strong current correlations. The presence of true Majorana states manifests itself in unusually high noise levels or the near absence of noise, depending on the chosen device configuration. Monitoring the noise statistics amounts to a weak continuous measurement of the Majorana qubit and yields information similar to that of a full braiding protocol, but at much lower experimental effort. Our theory can be adapted to different platforms and should allow for the clear identification of Majorana states.
Collapse
Affiliation(s)
- J Manousakis
- Institut für theoretische Physik, Universität zu Köln, Zülpicher Straße 77, D-50937 Köln, Germany
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, DK-2100 Copenhagen, Denmark
| | - C Wille
- Dahlem Center for Complex Quantum Systems, Physics Department, Freie Universität Berlin, D-14195 Berlin, Germany
| | - A Altland
- Institut für theoretische Physik, Universität zu Köln, Zülpicher Straße 77, D-50937 Köln, Germany
| | - R Egger
- Institut für Theoretische Physik, Heinrich Heine Universität, D-40225 Düsseldorf, Germany
| | - K Flensberg
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, DK-2100 Copenhagen, Denmark
| | - F Hassler
- JARA-Institute for Quantum Information, RWTH Aachen University, D-52056 Aachen, Germany
| |
Collapse
|
7
|
Yang FB. Aharonov-Bohm Interferometer in a T-Shaped Quantum Dot Embedded in Majorana Bound States*. COMMUNICATIONS IN THEORETICAL PHYSICS 2019; 71:1024. [DOI: 10.1088/0253-6102/71/8/1024] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 09/01/2023]
Abstract
Abstract
We theoretically study the spin-dependent transport properties of an Aharonov-Bohm (AB) interferometer composed by a T-shaped quantum dot (QD) embedded in Majorana bound states (MBS). We use the equation of motion method to calculate the conductance across the interferometer. We note that the conductance exhibits sensitive dependence on the MBS-QD coupling strength as well as the polarization strength of the leads when the phase factor of AB ring changes periodically. The conductance shows a transition from resonance to anti-resonance when the MBS-QD coupling strength changes from small to large. Also, there is different p-dependence conductance when the leads alignment changes from parallel to anti-parallel. These findings suggest that such a model could be used for a sensitive detection of MBS interactions, exploiting the high sensitivity of conductance to the AB phase in the interferometer.
Collapse
|
8
|
Rahmani A, Franz M. Interacting Majorana fermions. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2019; 82:084501. [PMID: 31185464 DOI: 10.1088/1361-6633/ab28ef] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
Majorana fermions are the real (in a mathematical sense) counterparts of complex fermions like ordinary electrons. The promise of topological quantum computing has lead to substantial experimental progress in realizing these particles in various synthetic platforms. The realization of Majorana fermions motivates a fundamental question: what phases of matter can emerge if many Majorana fermions are allowed to interact? Here we review recent progress in this direction on the proposed experimental setups, analytical and numerical results on low-dimensional lattice models, and the exactly solvable Sachdev-Ye-Kitaev model. The early progress thus far suggests that strongly correlated phases of matter with Majorana building blocks can exhibit many novel phenomena, such as emergent spacetime supersymmetry, topological order and the physics of black-holes, in condensed matter systems. They may also provide alternative avenues for universal topological quantum computing through the realization of the Fibonacci phase and measurement-based only surface codes.
Collapse
Affiliation(s)
- Armin Rahmani
- Department of Physics and Astronomy & Advanced Materials Science and Engineering Center (AMSEC), Western Washington University, Bellingham, WA 98225, United States of America
| | | |
Collapse
|
9
|
Hsu CH, Stano P, Klinovaja J, Loss D. Majorana Kramers Pairs in Higher-Order Topological Insulators. PHYSICAL REVIEW LETTERS 2018; 121:196801. [PMID: 30468588 DOI: 10.1103/physrevlett.121.196801] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/30/2018] [Revised: 08/24/2018] [Indexed: 06/09/2023]
Abstract
We propose a tune-free scheme to realize Kramers pairs of Majorana bound states in recently discovered higher-order topological insulators (HOTIs). We show that, by bringing two hinges of a HOTI into the proximity of an s-wave superconductor, the competition between local and crossed Andreev pairing leads to the formation of Majorana Kramers pairs, when the latter pairing dominates over the former. We demonstrate that such a topological superconductivity is stabilized by moderate electron-electron interactions. The proposed setup avoids the application of a magnetic field or local voltage gates, and requires weaker interactions compared with nonhelical nanowires.
Collapse
Affiliation(s)
- Chen-Hsuan Hsu
- RIKEN Center for Emergent Matter Science (CEMS), Wako, Saitama 351-0198, Japan
| | - Peter Stano
- RIKEN Center for Emergent Matter Science (CEMS), Wako, Saitama 351-0198, Japan
- Department of Applied Physics, School of Engineering, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan
- Institute of Physics, Slovak Academy of Sciences, 845 11 Bratislava, Slovakia
| | - Jelena Klinovaja
- RIKEN Center for Emergent Matter Science (CEMS), Wako, Saitama 351-0198, Japan
- Department of Physics, University of Basel, Klingelbergstrasse 82, CH-4056 Basel, Switzerland
| | - Daniel Loss
- RIKEN Center for Emergent Matter Science (CEMS), Wako, Saitama 351-0198, Japan
- Department of Physics, University of Basel, Klingelbergstrasse 82, CH-4056 Basel, Switzerland
| |
Collapse
|
10
|
Schrade C, Fu L. Parity-Controlled 2π Josephson Effect Mediated by Majorana Kramers Pairs. PHYSICAL REVIEW LETTERS 2018; 120:267002. [PMID: 30004723 DOI: 10.1103/physrevlett.120.267002] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/10/2018] [Indexed: 06/08/2023]
Abstract
We study a time-reversal-invariant topological superconductor island hosting spatially separated Majorana Kramers pairs, with weak tunnel couplings to two s-wave superconducting leads. When the topological superconductor island is in the Coulomb blockade regime, we predict that a Josephson current flows between the two leads due to a nonlocal transfer of Cooper pairs mediated by the Majorana Kramers pairs. Interestingly, we find that the sign of the Josephson current is controlled by the joint parity of all four Majorana bound states on the island. Consequently, this parity-controlled Josephson effect can be used for qubit readout in Majorana-based quantum computing.
Collapse
Affiliation(s)
- Constantin Schrade
- Department of Physics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, USA
| | - Liang Fu
- Department of Physics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, USA
| |
Collapse
|
11
|
Zazunov A, Iks A, Alvarado M, Levy Yeyati A, Egger R. Josephson effect in junctions of conventional and topological superconductors. BEILSTEIN JOURNAL OF NANOTECHNOLOGY 2018; 9:1659-1676. [PMID: 29977700 PMCID: PMC6009709 DOI: 10.3762/bjnano.9.158] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 01/30/2018] [Accepted: 04/27/2018] [Indexed: 06/08/2023]
Abstract
We present a theoretical analysis of the equilibrium Josephson current-phase relation in hybrid devices made of conventional s-wave spin-singlet superconductors (S) and topological superconductor (TS) wires featuring Majorana end states. Using Green's function techniques, the topological superconductor is alternatively described by the low-energy continuum limit of a Kitaev chain or by a more microscopic spinful nanowire model. We show that for the simplest S-TS tunnel junction, only the s-wave pairing correlations in a spinful TS nanowire model can generate a Josephson effect. The critical current is much smaller in the topological regime and exhibits a kink-like dependence on the Zeeman field along the wire. When a correlated quantum dot (QD) in the magnetic regime is present in the junction region, however, the Josephson current becomes finite also in the deep topological phase as shown for the cotunneling regime and by a mean-field analysis. Remarkably, we find that the S-QD-TS setup can support φ0-junction behavior, where a finite supercurrent flows at vanishing phase difference. Finally, we also address a multi-terminal S-TS-S geometry, where the TS wire acts as tunable parity switch on the Andreev bound states in a superconducting atomic contact.
Collapse
Affiliation(s)
- Alex Zazunov
- Institut für Theoretische Physik, Heinrich-Heine-Universität, D-40225 Düsseldorf, Germany
| | - Albert Iks
- Institut für Theoretische Physik, Heinrich-Heine-Universität, D-40225 Düsseldorf, Germany
| | - Miguel Alvarado
- Departamento de Física Teórica de la Materia Condensada C-V, Condensed Matter Physics Center (IFIMAC) and Instituto Nicolás Cabrera, Universidad Autónoma de Madrid, E-28049 Madrid, Spain
| | - Alfredo Levy Yeyati
- Departamento de Física Teórica de la Materia Condensada C-V, Condensed Matter Physics Center (IFIMAC) and Instituto Nicolás Cabrera, Universidad Autónoma de Madrid, E-28049 Madrid, Spain
| | - Reinhold Egger
- Institut für Theoretische Physik, Heinrich-Heine-Universität, D-40225 Düsseldorf, Germany
| |
Collapse
|
12
|
Ramos-Andrade JP, Orellana PA, Ulloa SE. Detecting coupling of Majorana bound states with an Aharonov-Bohm interferometer. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2018; 30:045301. [PMID: 29239309 DOI: 10.1088/1361-648x/aaa1b2] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
We study the transport properties of an interferometer composed by a quantum dot (QD) coupled with two normal leads and two one-dimensional topological superconductor nanowires (TNWs) hosting Majorana bound states (MBS) at their ends. The geometry considered is such that one TNW has both ends connected with the QD, forming an Aharonov-Bohm (AB) interferometer threaded by an external magnetic flux, while the other TNW is placed near the interferometer TNW. This geometry can alternatively be seen as a long wire contacted across a local defect, with possible coupling between independent-MBS. We use the Green's function formalism to calculate the conductance across normal current leads on the QD. We find that the conductance exhibits a half-quantum value regardless of the AB phase and location of the dot energy level, whenever the interferometer configuration interacts with the neighboring TNW. These findings suggest that such a geometry could be used for a sensitive detection of MBS interactions across TNWs, exploiting the high sensitivity of conductance to the AB phase in the interferometer.
Collapse
Affiliation(s)
- J P Ramos-Andrade
- Departamento de Física, Universidad Técnica Federico Santa María, Casilla 110 V, Valparaíso, Chile. Department of Physics and Astronomy, and Nanoscale and Quantum Phenomena Institute, Ohio University, Athens, OH 45701-2979, United States of America
| | | | | |
Collapse
|
13
|
Roy A, Terhal BM, Hassler F. Quantum Phase Transitions of the Majorana Toric Code in the Presence of Finite Cooper-Pair Tunneling. PHYSICAL REVIEW LETTERS 2017; 119:180508. [PMID: 29219553 DOI: 10.1103/physrevlett.119.180508] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/15/2017] [Indexed: 06/07/2023]
Abstract
The toric code based on Majorana fermions on mesoscopic superconducting islands is a promising candidate for quantum information processing. In the limit of vanishing Cooper-pair tunneling, it has been argued that the phase transition separating the topologically ordered phase of the toric code from the trivial one is in the universality class of the (2+1)D XY model. On the other hand, in the limit of infinitely large Cooper-pair tunneling, the phase transition is in the universality class of the (2+1)D Ising model. In this work, we treat the case of finite Cooper-pair tunneling and address the question of how the continuous XY symmetry breaking phase transition turns into a discrete Z_{2} symmetry breaking one when the Cooper-pair tunneling rate is increased. We show that this happens through a couple of tricritical points and first order phase transitions. Using a Jordan-Wigner transformation, we map the problem to that of spins coupled to quantum rotors and subsequently, propose a Landau field theory for this model that matches the known results in the respective limits. We calculate the effective field theories and provide the relevant critical exponents for the different phase transitions. Our results are relevant for predicting the stability of the topological phase in realistic experimental implementations.
Collapse
Affiliation(s)
- Ananda Roy
- JARA Institute for Quantum Information, RWTH Aachen University, 52056 Aachen, Germany
| | - Barbara M Terhal
- JARA Institute for Quantum Information, RWTH Aachen University, 52056 Aachen, Germany
| | - Fabian Hassler
- JARA Institute for Quantum Information, RWTH Aachen University, 52056 Aachen, Germany
| |
Collapse
|
14
|
Lutchyn RM, Glazman LI. Transport through a Majorana Island in the Strong Tunneling Regime. PHYSICAL REVIEW LETTERS 2017; 119:057002. [PMID: 28949747 DOI: 10.1103/physrevlett.119.057002] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/10/2017] [Indexed: 06/07/2023]
Abstract
In the presence of Rashba spin-orbit coupling, a magnetic field can drive a proximitized nanowire into a topological superconducting phase [R. M. Lutchyn, J. D. Sau, and S. Das Sarma, Phys. Rev. Lett. 105, 077001 (2010).PRLTAO0031-900710.1103/PhysRevLett.105.077001 and Y. Oreg, G. Refael, and F. von Oppen, Phys. Rev. Lett. 105, 177002 (2010).PRLTAO0031-900710.1103/PhysRevLett.105.177002]. We study the transport properties of such nanowires in the Coulomb blockade regime. The associated with topological superconductivity Majorana modes significantly modify transport and lead to single-electron coherent transmission through the nanowire-a nonlocal signature of topological superconductivity. In this Letter, we focus on the case of strong hybridization of the Majorana modes with normal leads. The induced by hybridization broadening of the Majorana zero-energy states competes with the charging energy, leading to a considerable modification of the Coulomb blockade in a nanowire contacted by two normal leads. We evaluate the two-terminal conductance as a function of the gate voltage, junctions transmission coefficients, and the geometric capacitance of and the induced superconducting gap in the nanowire.
Collapse
Affiliation(s)
- Roman M Lutchyn
- Station Q, Microsoft Research, Santa Barbara, California 93106-6105, USA
| | - Leonid I Glazman
- Department of Physics, Yale University, New Haven, Connecticut 06520, USA
| |
Collapse
|
15
|
Sato M, Ando Y. Topological superconductors: a review. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2017; 80:076501. [PMID: 28367833 DOI: 10.1088/1361-6633/aa6ac7] [Citation(s) in RCA: 247] [Impact Index Per Article: 35.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/12/2023]
Abstract
This review elaborates pedagogically on the fundamental concept, basic theory, expected properties, and materials realizations of topological superconductors. The relation between topological superconductivity and Majorana fermions are explained, and the difference between dispersive Majorana fermions and a localized Majorana zero mode is emphasized. A variety of routes to topological superconductivity are explained with an emphasis on the roles of spin-orbit coupling. Present experimental situations and possible signatures of topological superconductivity are summarized with an emphasis on intrinsic topological superconductors.
Collapse
Affiliation(s)
- Masatoshi Sato
- Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502, Japan
| | | |
Collapse
|
16
|
Nigg SE, Fuhrer A, Loss D. Superconducting Grid-Bus Surface Code Architecture for Hole-Spin Qubits. PHYSICAL REVIEW LETTERS 2017; 118:147701. [PMID: 28430480 DOI: 10.1103/physrevlett.118.147701] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/10/2017] [Indexed: 05/14/2023]
Abstract
We present a scalable hybrid architecture for the 2D surface code combining superconducting resonators and hole-spin qubits in nanowires with tunable direct Rashba spin-orbit coupling. The backbone of this architecture is a square lattice of capacitively coupled coplanar waveguide resonators each of which hosts a nanowire hole-spin qubit. Both the frequency of the qubits and their coupling to the microwave field are tunable by a static electric field applied via the resonator center pin. In the dispersive regime, an entangling two-qubit gate can be realized via a third order process, whereby a virtual photon in one resonator is created by a first qubit, coherently transferred to a neighboring resonator, and absorbed by a second qubit in that resonator. Numerical simulations with state-of-the-art coherence times yield gate fidelities approaching the 99% fault tolerance threshold.
Collapse
Affiliation(s)
- Simon E Nigg
- Department of Physics, University of Basel, Klingelbergstrasse 82, 4056 Basel, Switzerland
| | - Andreas Fuhrer
- IBM Research-Zurich Säumerstrasse 4, 8803 Rüschlikon, Switzerland
| | - Daniel Loss
- Department of Physics, University of Basel, Klingelbergstrasse 82, 4056 Basel, Switzerland
| |
Collapse
|
17
|
Yan Z, Bi R, Wang Z. Majorana Zero Modes Protected by a Hopf Invariant in Topologically Trivial Superconductors. PHYSICAL REVIEW LETTERS 2017; 118:147003. [PMID: 28430502 DOI: 10.1103/physrevlett.118.147003] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/10/2017] [Indexed: 06/07/2023]
Abstract
Majorana zero modes are usually attributed to topological superconductors. We study a class of two-dimensional topologically trivial superconductors without chiral edge modes, which nevertheless host robust Majorana zero modes in topological defects. The construction of this minimal single-band model is facilitated by the Hopf map and the Hopf invariant. This work will stimulate investigations of Majorana zero modes in superconductors in the topologically trivial regime.
Collapse
Affiliation(s)
- Zhongbo Yan
- Institute for Advanced Study, Tsinghua University, Beijing 100084, China
| | - Ren Bi
- Institute for Advanced Study, Tsinghua University, Beijing 100084, China
| | - Zhong Wang
- Institute for Advanced Study, Tsinghua University, Beijing 100084, China
- Collaborative Innovation Center of Quantum Matter, Beijing 100871, China
| |
Collapse
|
18
|
Albrecht SM, Hansen EB, Higginbotham AP, Kuemmeth F, Jespersen TS, Nygård J, Krogstrup P, Danon J, Flensberg K, Marcus CM. Transport Signatures of Quasiparticle Poisoning in a Majorana Island. PHYSICAL REVIEW LETTERS 2017; 118:137701. [PMID: 28409973 DOI: 10.1103/physrevlett.118.137701] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/17/2016] [Indexed: 06/07/2023]
Abstract
We investigate effects of quasiparticle poisoning in a Majorana island with strong tunnel coupling to normal-metal leads. In addition to the main Coulomb blockade diamonds, "shadow" diamonds appear, shifted by 1e in gate voltage, consistent with transport through an excited (poisoned) state of the island. Comparison to a simple model yields an estimate of parity lifetime for the strongly coupled island (∼1 μs) and sets a bound for a weakly coupled island (>10 μs). Fluctuations in the gate-voltage spacing of Coulomb peaks at high field, reflecting Majorana hybridization, are enhanced by the reduced lever arm at strong coupling. When converted from gate voltage to energy units, fluctuations are consistent with previous measurements.
Collapse
Affiliation(s)
- S M Albrecht
- Center for Quantum Devices and Station Q Copenhagen, Niels Bohr Institute, University of Copenhagen, Copenhagen 2100, Denmark
| | - E B Hansen
- Center for Quantum Devices and Station Q Copenhagen, Niels Bohr Institute, University of Copenhagen, Copenhagen 2100, Denmark
| | - A P Higginbotham
- Center for Quantum Devices and Station Q Copenhagen, Niels Bohr Institute, University of Copenhagen, Copenhagen 2100, Denmark
- JILA, University of Colorado and NIST, Boulder, Colorado 80309, USA
| | - F Kuemmeth
- Center for Quantum Devices and Station Q Copenhagen, Niels Bohr Institute, University of Copenhagen, Copenhagen 2100, Denmark
| | - T S Jespersen
- Center for Quantum Devices and Station Q Copenhagen, Niels Bohr Institute, University of Copenhagen, Copenhagen 2100, Denmark
| | - J Nygård
- Center for Quantum Devices and Station Q Copenhagen, Niels Bohr Institute, University of Copenhagen, Copenhagen 2100, Denmark
| | - P Krogstrup
- Center for Quantum Devices and Station Q Copenhagen, Niels Bohr Institute, University of Copenhagen, Copenhagen 2100, Denmark
| | - J Danon
- Center for Quantum Devices and Station Q Copenhagen, Niels Bohr Institute, University of Copenhagen, Copenhagen 2100, Denmark
- Department of Physics, NTNU, Norwegian University of Science and Technology, 7491 Trondheim, Norway
| | - K Flensberg
- Center for Quantum Devices and Station Q Copenhagen, Niels Bohr Institute, University of Copenhagen, Copenhagen 2100, Denmark
| | - C M Marcus
- Center for Quantum Devices and Station Q Copenhagen, Niels Bohr Institute, University of Copenhagen, Copenhagen 2100, Denmark
| |
Collapse
|
19
|
Deng MT, Vaitiekėnas S, Hansen EB, Danon J, Leijnse M, Flensberg K, Nygård J, Krogstrup P, Marcus CM. Majorana bound state in a coupled quantum-dot hybrid-nanowire system. Science 2016; 354:1557-1562. [DOI: 10.1126/science.aaf3961] [Citation(s) in RCA: 687] [Impact Index Per Article: 85.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/03/2016] [Accepted: 11/16/2016] [Indexed: 11/02/2022]
|
20
|
Li Y. Noise Threshold and Resource Cost of Fault-Tolerant Quantum Computing with Majorana Fermions in Hybrid Systems. PHYSICAL REVIEW LETTERS 2016; 117:120403. [PMID: 27689257 DOI: 10.1103/physrevlett.117.120403] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/11/2016] [Indexed: 06/06/2023]
Abstract
Fault-tolerant quantum computing in systems composed of both Majorana fermions and topologically unprotected quantum systems, e.g., superconducting circuits or quantum dots, is studied in this Letter. Errors caused by topologically unprotected quantum systems need to be corrected with error-correction schemes, for instance, the surface code. We find that the error-correction performance of such a hybrid topological quantum computer is not superior to a normal quantum computer unless the topological charge of Majorana fermions is insusceptible to noise. If errors changing the topological charge are rare, the fault-tolerance threshold is much higher than the threshold of a normal quantum computer and a surface-code logical qubit could be encoded in only tens of topological qubits instead of about 1,000 normal qubits.
Collapse
Affiliation(s)
- Ying Li
- Department of Materials, University of Oxford, Parks Road, Oxford OX1 3PH, United Kingdom
| |
Collapse
|