1
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Badawy G, Bakkers EPAM. Electronic Transport and Quantum Phenomena in Nanowires. Chem Rev 2024; 124:2419-2440. [PMID: 38394689 PMCID: PMC10941195 DOI: 10.1021/acs.chemrev.3c00656] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/10/2023] [Revised: 01/26/2024] [Accepted: 02/08/2024] [Indexed: 02/25/2024]
Abstract
Nanowires are natural one-dimensional channels and offer new opportunities for advanced electronic quantum transport experiments. We review recent progress on the synthesis of nanowires and methods for the fabrication of hybrid semiconductor/superconductor systems. We discuss methods to characterize their electronic properties in the context of possible future applications such as topological and spin qubits. We focus on group III-V (InAs and InSb) and group IV (Ge/Si) semiconductors, since these are the most developed, and give an outlook on other potential materials.
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Affiliation(s)
- Ghada Badawy
- Department of Applied Physics, Eindhoven University of Technology, 5600 MB Eindhoven, The Netherlands
| | - Erik P. A. M. Bakkers
- Department of Applied Physics, Eindhoven University of Technology, 5600 MB Eindhoven, The Netherlands
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2
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Bordin A, Li X, van Driel D, Wolff JC, Wang Q, Ten Haaf SLD, Wang G, van Loo N, Kouwenhoven LP, Dvir T. Crossed Andreev Reflection and Elastic Cotunneling in Three Quantum Dots Coupled by Superconductors. PHYSICAL REVIEW LETTERS 2024; 132:056602. [PMID: 38364137 DOI: 10.1103/physrevlett.132.056602] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/14/2023] [Revised: 12/03/2023] [Accepted: 01/05/2024] [Indexed: 02/18/2024]
Abstract
The formation of a topological superconducting phase in a quantum-dot-based Kitaev chain requires nearest neighbor crossed Andreev reflection and elastic cotunneling. Here, we report on a hybrid InSb nanowire in a three-site Kitaev chain geometry-the smallest system with well-defined bulk and edge-where two superconductor-semiconductor hybrids separate three quantum dots. We demonstrate pairwise crossed Andreev reflection and elastic cotunneling between both pairs of neighboring dots and show sequential tunneling processes involving all three quantum dots. These results are the next step toward the realization of topological superconductivity in long Kitaev chain devices with many coupled quantum dots.
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Affiliation(s)
- Alberto Bordin
- QuTech and Kavli Institute of NanoScience, Delft University of Technology, 2600 GA Delft, The Netherlands
| | - Xiang Li
- QuTech and Kavli Institute of NanoScience, Delft University of Technology, 2600 GA Delft, The Netherlands
| | - David van Driel
- QuTech and Kavli Institute of NanoScience, Delft University of Technology, 2600 GA Delft, The Netherlands
| | - Jan Cornelis Wolff
- 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
| | - Sebastiaan L D Ten Haaf
- QuTech and Kavli Institute of NanoScience, Delft University of Technology, 2600 GA Delft, The Netherlands
| | - Guanzhong Wang
- 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
| | - Tom Dvir
- QuTech and Kavli Institute of NanoScience, Delft University of Technology, 2600 GA Delft, The Netherlands
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3
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Reichl LE, Estrella F. Particle-hole thermalization in a composite superconducting and normal-conducting nanowire. Phys Rev E 2024; 109:014226. [PMID: 38366481 DOI: 10.1103/physreve.109.014226] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/06/2023] [Accepted: 01/03/2024] [Indexed: 02/18/2024]
Abstract
The mechanisms by which isolated condensed matter systems thermalize is a topic of growing interest. Thermalization is known to be linked to the emergence of chaos in the dynamics of a system. We show that a solid state scattering system, containing superconducting elements, can thermalize scattered states without affecting the degree of entanglement of the scattered states. We consider a composite NSNSNSNSN nanowire composed of Bi_{2}Sr_{2}CaCu_{2}O_{8+x} superconducting segments (S) and normal conducting segments (N). We consider parameter regimes where all current flow is due to tunneling currents that are facilitated by quasibound state resonances inside the SNSNSNS structure. At certain energies, scattered pure states approach ergodicity, even though they remain pure.
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Affiliation(s)
- L E Reichl
- Center for Complex Quantum Systems and Department of Physics, The University of Texas at Austin, Austin, Texas 78712, USA
| | - F Estrella
- Center for Complex Quantum Systems and Department of Physics, The University of Texas at Austin, Austin, Texas 78712, USA
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4
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de Jong D, Prosko CG, Han L, Malinowski FK, Liu Y, Kouwenhoven LP, Pfaff W. Controllable Single Cooper Pair Splitting in Hybrid Quantum Dot Systems. PHYSICAL REVIEW LETTERS 2023; 131:157001. [PMID: 37897758 DOI: 10.1103/physrevlett.131.157001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/30/2022] [Accepted: 09/07/2023] [Indexed: 10/30/2023]
Abstract
Cooper pair splitters hold utility as a platform for investigating the entanglement of electrons in Cooper pairs, but probing splitters with voltage-biased Ohmic contacts prevents the retention of electrons from split pairs since they can escape to the drain reservoirs. We report the ability to controllably split and retain single Cooper pairs in a multi-quantum-dot device isolated from lead reservoirs, and separately demonstrate a technique for detecting the electrons emerging from a split pair. First, we identify a coherent Cooper pair splitting charge transition using dispersive gate sensing at GHz frequencies. Second, we utilize a double quantum dot as an electron parity sensor to detect parity changes resulting from electrons emerging from a superconducting island.
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Affiliation(s)
- Damaz de Jong
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology, 2600 GA Delft, Netherlands
| | - Christian G Prosko
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology, 2600 GA Delft, Netherlands
| | - Lin Han
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology, 2600 GA Delft, Netherlands
| | - Filip K Malinowski
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology, 2600 GA Delft, Netherlands
| | - Yu Liu
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark
| | - Leo P Kouwenhoven
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology, 2600 GA Delft, Netherlands
| | - Wolfgang Pfaff
- Department of Physics and Frederick Seitz Materials Research Laboratory, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
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5
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Wang Q, Ten Haaf SLD, Kulesh I, Xiao D, Thomas C, Manfra MJ, Goswami S. Triplet correlations in Cooper pair splitters realized in a two-dimensional electron gas. Nat Commun 2023; 14:4876. [PMID: 37573341 PMCID: PMC10423214 DOI: 10.1038/s41467-023-40551-z] [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: 01/13/2023] [Accepted: 07/27/2023] [Indexed: 08/14/2023] Open
Abstract
Cooper pairs occupy the ground state of superconductors and are typically composed of maximally entangled electrons with opposite spin. In order to study the spin and entanglement properties of these electrons, one must separate them spatially via a process known as Cooper pair splitting (CPS). Here we provide the first demonstration of CPS in a semiconductor two-dimensional electron gas (2DEG). By coupling two quantum dots to a superconductor-semiconductor hybrid region we achieve efficient Cooper pair splitting, and clearly distinguish it from other local and non-local processes. When the spin degeneracy of the dots is lifted, they can be operated as spin-filters to obtain information about the spin of the electrons forming the Cooper pair. Not only do we observe a near perfect splitting of Cooper pairs into opposite-spin electrons (i.e. conventional singlet pairing), but also into equal-spin electrons, thus achieving triplet correlations between the quantum dots. Importantly, the exceptionally large spin-orbit interaction in our 2DEGs results in a strong triplet component, comparable in amplitude to the singlet pairing. The demonstration of CPS in a scalable and flexible platform provides a credible route to study on-chip entanglement and topological superconductivity in the form of artificial Kitaev chains.
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Affiliation(s)
- Qingzhen Wang
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology, Delft, 2600 GA, The Netherlands
| | - Sebastiaan L D Ten Haaf
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology, Delft, 2600 GA, The Netherlands
| | - Ivan Kulesh
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology, Delft, 2600 GA, The Netherlands
| | - Di Xiao
- Department of Physics and Astronomy, Purdue University, West Lafayette, 47907, IN, USA
| | - Candice Thomas
- Department of Physics and Astronomy, Purdue University, West Lafayette, 47907, IN, USA
| | - Michael J Manfra
- Department of Physics and Astronomy, Purdue University, West Lafayette, 47907, IN, USA
- Elmore School of Electrical and Computer Engineering, Purdue University, West Lafayette, 47907, IN, USA
- School of Materials Engineering, Purdue University, West Lafayette, 47907, IN, USA
- Microsoft Quantum Lab, West Lafayette, 47907, IN, USA
| | - Srijit Goswami
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology, Delft, 2600 GA, The Netherlands.
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6
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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: 9] [Impact Index Per Article: 9.0] [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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7
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Golubev DS, Zaikin AD. Cooper pair splitting controlled by a temperature gradient. BEILSTEIN JOURNAL OF NANOTECHNOLOGY 2023; 14:61-67. [PMID: 36761676 PMCID: PMC9843233 DOI: 10.3762/bjnano.14.7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 10/01/2022] [Accepted: 12/23/2022] [Indexed: 06/18/2023]
Abstract
Electrons in two different normal metallic electrodes attached to a sufficiently thin superconducting island may become entangled due to the effect of Cooper pair splitting. This phenomenon is of fundamental importance and may also have serious implications for developing quantum communication technologies. One way to identify Cooper pair splitting is to analyze long-range cross correlations of fluctuating currents in three-terminal hybrid normal-superconducting-normal nanostructures. Here, we theoretically investigate non-trivial behavior of cross-correlated non-local shot noise in the presence of a temperature gradient. We suggest that applying a temperature gradient may serve as an extra tool to control the phenomenon of Cooper pair splitting.
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Affiliation(s)
- Dmitry S Golubev
- QTF Centre of Excellence, Department of Applied Physics, Aalto University, FI-00076 Aalto, Finland
| | - Andrei D Zaikin
- I.E. Tamm Department of Theoretical Physics, P.N. Lebedev Physical Institute, 119991 Moscow, Russia
- National Research University Higher School of Economics, 101000 Moscow, Russia
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8
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Liu CX, Wang G, Dvir T, Wimmer M. Tunable Superconducting Coupling of Quantum Dots via Andreev Bound States in Semiconductor-Superconductor Nanowires. PHYSICAL REVIEW LETTERS 2022; 129:267701. [PMID: 36608192 DOI: 10.1103/physrevlett.129.267701] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/03/2022] [Revised: 05/18/2022] [Accepted: 11/23/2022] [Indexed: 06/17/2023]
Abstract
Semiconductor quantum dots have proven to be a useful platform for quantum simulation in the solid state. However, implementing a superconducting coupling between quantum dots mediated by a Cooper pair has so far suffered from limited tunability and strong suppression. This has limited applications such as Cooper pair splitting and quantum dot simulation of topological Kitaev chains. In this Letter, we propose how to mediate tunable effective couplings via Andreev bound states in a semiconductor-superconductor nanowire connecting two quantum dots. We show that in this way it is possible to individually control both the coupling mediated by Cooper pairs and by single electrons by changing the properties of the Andreev bound states with easily accessible experimental parameters. In addition, the problem of coupling suppression is greatly mitigated. We also propose how to experimentally extract the coupling strengths from resonant current in a three-terminal junction. Our proposal will enable future experiments that have not been possible so far.
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Affiliation(s)
- Chun-Xiao Liu
- Qutech and Kavli Institute of Nanoscience, Delft University of Technology, Delft 2600 GA, Netherlands
| | - Guanzhong Wang
- Qutech and Kavli Institute of Nanoscience, Delft University of Technology, Delft 2600 GA, Netherlands
| | - Tom Dvir
- Qutech and Kavli Institute of Nanoscience, Delft University of Technology, Delft 2600 GA, Netherlands
| | - Michael Wimmer
- Qutech and Kavli Institute of Nanoscience, Delft University of Technology, Delft 2600 GA, Netherlands
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9
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Singlet and triplet Cooper pair splitting in hybrid superconducting nanowires. Nature 2022; 612:448-453. [PMID: 36418399 DOI: 10.1038/s41586-022-05352-2] [Citation(s) in RCA: 8] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/17/2022] [Accepted: 09/15/2022] [Indexed: 11/25/2022]
Abstract
In most naturally occurring superconductors, electrons with opposite spins form Cooper pairs. This includes both conventional s-wave superconductors such as aluminium, as well as high-transition-temperature, d-wave superconductors. Materials with intrinsic p-wave superconductivity, hosting Cooper pairs made of equal-spin electrons, have not been conclusively identified, nor synthesized, despite promising progress1-3. Instead, engineered platforms where s-wave superconductors are brought into contact with magnetic materials have shown convincing signatures of equal-spin pairing4-6. Here we directly measure equal-spin pairing between spin-polarized quantum dots. This pairing is proximity-induced from an s-wave superconductor into a semiconducting nanowire with strong spin-orbit interaction. We demonstrate such pairing by showing that breaking a Cooper pair can result in two electrons with equal spin polarization. Our results demonstrate controllable detection of singlet and triplet pairing between the quantum dots. Achieving such triplet pairing in a sequence of quantum dots will be required for realizing an artificial Kitaev chain7-9.
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10
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Bordoloi A, Zannier V, Sorba L, Schönenberger C, Baumgartner A. Spin cross-correlation experiments in an electron entangler. Nature 2022; 612:454-458. [PMID: 36424409 DOI: 10.1038/s41586-022-05436-z] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/15/2022] [Accepted: 10/10/2022] [Indexed: 11/27/2022]
Abstract
Correlations are fundamental in describing many-body systems. However, in experiments, correlations are notoriously difficult to assess on a microscopic scale, especially for electron spins. Even though it is firmly established theoretically that the electrons in a Cooper pair1 of a superconductor form maximally spin-entangled singlet states with opposite spin projections2-4, no spin correlation experiments have been demonstrated so far. Here we report the direct measurement of the spin cross-correlations between the currents of a Cooper pair splitter5-13, an electronic device that emits electrons originating from Cooper pairs. We use ferromagnetic split-gates14,15, compatible with nearby superconducting structures, to individually spin polarize the transmissions of the quantum dots in the two electronic paths, which act as tunable spin filters. The signals are detected in standard transport and in highly sensitive transconductance experiments. We find that the spin cross-correlation is negative, consistent with spin singlet emission, and deviates from the ideal value mostly due to the overlap of the Zeeman split quantum dot states. Our results demonstrate a new route to perform spin correlation experiments in nano-electronic devices, especially suitable for those relying on magnetic field sensitive superconducting elements, like triplet or topologically non-trivial superconductors16-18, or to perform Bell tests with massive particles19,20.
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Affiliation(s)
- Arunav Bordoloi
- Department of Physics, University of Basel, Basel, Switzerland. .,Department of Physics, University of Maryland, College Park, MD, USA.
| | - Valentina Zannier
- NEST, Istituto Nanoscienze-CNR and Scuola Normale Superiore, Pisa, Italy
| | - Lucia Sorba
- NEST, Istituto Nanoscienze-CNR and Scuola Normale Superiore, Pisa, Italy
| | - Christian Schönenberger
- Department of Physics, University of Basel, Basel, Switzerland.,Swiss Nanoscience Institute, University of Basel, Basel, Switzerland
| | - Andreas Baumgartner
- Department of Physics, University of Basel, Basel, Switzerland. .,Swiss Nanoscience Institute, University of Basel, Basel, Switzerland.
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11
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Luo W, Geng H, Xing DY, Blatter G, Chen W. Entanglement of Nambu Spinors and Bell Inequality Test without Beam Splitters. PHYSICAL REVIEW LETTERS 2022; 129:120507. [PMID: 36179172 DOI: 10.1103/physrevlett.129.120507] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/30/2021] [Accepted: 09/06/2022] [Indexed: 06/16/2023]
Abstract
The identification of electronic entanglement in solids remains elusive so far, which is owed to the difficulty of implementing spinor-selective beam splitters with tunable polarization direction. Here, we propose to overcome this obstacle by producing and detecting a particular type of entanglement encoded in the Nambu spinor or electron-hole components of quasiparticles excited in quantum Hall edge states. Because of the opposite charge of electrons and holes, the detection of the Nambu spinor translates into a charge-current measurement, which eliminates the need for beam splitters and assures a high detection rate. Conveniently, the spinor correlation function at fixed effective polarizations derives from a single current-noise measurement, with the polarization directions of the detector easily adjusted by coupling the edge states to a voltage gate and a superconductor, both having been realized in experiments. We show that the violation of Bell inequality occurs in a large parameter region. Our Letter opens a new route for probing quasiparticle entanglement in solid-state physics exempt from traditional beam splitters.
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Affiliation(s)
- Wei Luo
- National Laboratory of Solid State Microstructures, School of Physics, and Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China
- School of Science, Jiangxi University of Science and Technology, Ganzhou 341000, China
| | - Hao Geng
- National Laboratory of Solid State Microstructures, School of Physics, and Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China
| | - D Y Xing
- National Laboratory of Solid State Microstructures, School of Physics, and Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China
| | - G Blatter
- Institute for Theoretical Physics, ETH Zurich, 8093 Zurich, Switzerland
| | - Wei Chen
- National Laboratory of Solid State Microstructures, School of Physics, and Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China
- Institute for Theoretical Physics, ETH Zurich, 8093 Zurich, Switzerland
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12
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Denisov A, Bubis A, Piatrusha S, Titova N, Nasibulin A, Becker J, Treu J, Ruhstorfer D, Koblmüller G, Tikhonov E, Khrapai V. Heat-Mode Excitation in a Proximity Superconductor. NANOMATERIALS (BASEL, SWITZERLAND) 2022; 12:1461. [PMID: 35564170 PMCID: PMC9101060 DOI: 10.3390/nano12091461] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 03/23/2022] [Revised: 04/14/2022] [Accepted: 04/16/2022] [Indexed: 11/25/2022]
Abstract
Mesoscopic superconductivity deals with various quasiparticle excitation modes, only one of them-the charge-mode-being directly accessible for conductance measurements due to the imbalance in populations of quasi-electron and quasihole excitation branches. Other modes carrying heat or even spin, valley etc. currents populate the branches equally and are charge-neutral, which makes them much harder to control. This noticeable gap in the experimental studies of mesoscopic non-equilibrium superconductivity can be filled by going beyond the conventional DC transport measurements and exploiting spontaneous current fluctuations. Here, we perform such an experiment and investigate the transport of heat in an open hybrid device based on a superconductor proximitized InAs nanowire. Using shot noise measurements, we investigate sub-gap Andreev heat guiding along the superconducting interface and fully characterize it in terms of the thermal conductance on the order of Gth∼e2/h, tunable by a back gate voltage. Understanding of the heat-mode also uncovers its implicit signatures in the non-local charge transport. Our experiments open a direct pathway to probe generic charge-neutral excitations in superconducting hybrids.
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Affiliation(s)
- Artem Denisov
- Osipyan Institute of Solid State Physics, Russian Academy of Sciences, 142432 Chernogolovka, Russia; (A.D.); (A.B.); (S.P.); (E.T.)
- Department of Physics, Princeton University, Princeton, NJ 08544, USA
| | - Anton Bubis
- Osipyan Institute of Solid State Physics, Russian Academy of Sciences, 142432 Chernogolovka, Russia; (A.D.); (A.B.); (S.P.); (E.T.)
- Skolkovo Institute of Science and Technology, Nobel Street 3, 121205 Moscow, Russia;
| | - Stanislau Piatrusha
- Osipyan Institute of Solid State Physics, Russian Academy of Sciences, 142432 Chernogolovka, Russia; (A.D.); (A.B.); (S.P.); (E.T.)
| | - Nadezhda Titova
- Institute of Physics, Technology, and Informational Systems, Moscow Pedagogical State University, 29 Malaya Pirogovskaya St, 119435 Moscow, Russia;
| | - Albert Nasibulin
- Skolkovo Institute of Science and Technology, Nobel Street 3, 121205 Moscow, Russia;
| | - Jonathan Becker
- Center for Nanotechnology and Nanomaterials, Walter Schottky Institut and Physik Department, Technische Universität München, Am Coulombwall 4, 85748 Garching, Germany; (J.B.); (J.T.); (D.R.); (G.K.)
| | - Julian Treu
- Center for Nanotechnology and Nanomaterials, Walter Schottky Institut and Physik Department, Technische Universität München, Am Coulombwall 4, 85748 Garching, Germany; (J.B.); (J.T.); (D.R.); (G.K.)
| | - Daniel Ruhstorfer
- Center for Nanotechnology and Nanomaterials, Walter Schottky Institut and Physik Department, Technische Universität München, Am Coulombwall 4, 85748 Garching, Germany; (J.B.); (J.T.); (D.R.); (G.K.)
| | - Gregor Koblmüller
- Center for Nanotechnology and Nanomaterials, Walter Schottky Institut and Physik Department, Technische Universität München, Am Coulombwall 4, 85748 Garching, Germany; (J.B.); (J.T.); (D.R.); (G.K.)
| | - Evgeny Tikhonov
- Osipyan Institute of Solid State Physics, Russian Academy of Sciences, 142432 Chernogolovka, Russia; (A.D.); (A.B.); (S.P.); (E.T.)
| | - Vadim Khrapai
- Osipyan Institute of Solid State Physics, Russian Academy of Sciences, 142432 Chernogolovka, Russia; (A.D.); (A.B.); (S.P.); (E.T.)
- Faculty of Physics, National Research University Higher School of Economics, 20 Myasnitskaya Street, 101000 Moscow, Russia
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13
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Brange F, Prech K, Flindt C. Dynamic Cooper Pair Splitter. PHYSICAL REVIEW LETTERS 2021; 127:237701. [PMID: 34936782 DOI: 10.1103/physrevlett.127.237701] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/09/2021] [Accepted: 11/08/2021] [Indexed: 06/14/2023]
Abstract
Cooper pair splitters are promising candidates for generating spin-entangled electrons. However, the splitting of Cooper pairs is a random and noisy process, which hinders further synchronized operations on the entangled electrons. To circumvent this problem, we here propose and analyze a dynamic Cooper pair splitter that produces a noiseless and regular flow of spin-entangled electrons. The Cooper pair splitter is based on a superconductor coupled to quantum dots, whose energy levels are tuned in and out of resonance to control the splitting process. We identify the optimal operating conditions for which exactly one Cooper pair is split per period of the external drive and the flow of entangled electrons becomes noiseless. To characterize the regularity of the Cooper pair splitter in the time domain, we analyze the g^{(2)} function of the output currents and the distribution of waiting times between split Cooper pairs. Our proposal is feasible using current technology, and it paves the way for dynamic quantum information processing with spin-entangled electrons.
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Affiliation(s)
- Fredrik Brange
- Department of Applied Physics, Aalto University, 00076 Aalto, Finland
| | - Kacper Prech
- Department of Applied Physics, Aalto University, 00076 Aalto, Finland
- School of Physics and Astronomy, University of Glasgow, Glasgow G12 8QQ, United Kingdom
| | - Christian Flindt
- Department of Applied Physics, Aalto University, 00076 Aalto, Finland
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14
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Ranni A, Brange F, Mannila ET, Flindt C, Maisi VF. Real-time observation of Cooper pair splitting showing strong non-local correlations. Nat Commun 2021; 12:6358. [PMID: 34737273 PMCID: PMC8569201 DOI: 10.1038/s41467-021-26627-8] [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: 02/20/2021] [Accepted: 10/17/2021] [Indexed: 12/01/2022] Open
Abstract
Controlled generation and detection of quantum entanglement between spatially separated particles constitute an essential prerequisite both for testing the foundations of quantum mechanics and for realizing future quantum technologies. Splitting of Cooper pairs from a superconductor provides entangled electrons at separate locations. However, experimentally accessing the individual split Cooper pairs constitutes a major unresolved issue as they mix together with electrons from competing processes. Here, we overcome this challenge with the first real-time observation of the splitting of individual Cooper pairs, enabling direct access to the time-resolved statistics of Cooper pair splitting. We determine the correlation statistics arising from two-electron processes and find a pronounced peak that is two orders of magnitude larger than the background. Our experiment thereby allows to unambiguously pinpoint and select split Cooper pairs with 99% fidelity. These results open up an avenue for performing experiments that tap into the spin-entanglement of split Cooper pairs. The splitting of Cooper pairs in superconductors has been challenging to detect experimentally. Here, the authors observe the real-time splitting of individual Cooper pairs in a superconducting device.
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Affiliation(s)
- Antti Ranni
- NanoLund and Solid State Physics, Lund University, Box 118, 22100, Lund, Sweden.
| | - Fredrik Brange
- Department of Applied Physics, Aalto University, 00076, Aalto, Finland
| | - Elsa T Mannila
- Department of Applied Physics, Aalto University, 00076, Aalto, Finland
| | - Christian Flindt
- Department of Applied Physics, Aalto University, 00076, Aalto, Finland
| | - Ville F Maisi
- NanoLund and Solid State Physics, Lund University, Box 118, 22100, Lund, Sweden.
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15
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Kürtössy O, Scherübl Z, Fülöp G, Lukács IE, Kanne T, Nygård J, Makk P, Csonka S. Andreev Molecule in Parallel InAs Nanowires. NANO LETTERS 2021; 21:7929-7937. [PMID: 34538054 PMCID: PMC8517978 DOI: 10.1021/acs.nanolett.1c01956] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 05/19/2021] [Indexed: 06/13/2023]
Abstract
Coupling individual atoms fundamentally changes the state of matter: electrons bound to atomic cores become delocalized turning an insulating state to a metallic one. A chain of atoms could lead to more exotic states if the tunneling takes place via the superconducting vacuum and can induce topologically protected excitations like Majorana or parafermions. Although coupling a single atom to a superconductor is well studied, the hybridization of two sites with individual tunability was not reported yet. The peculiar vacuum of the Bardeen-Cooper-Schrieffer (BCS) condensate opens the way to annihilate or generate two electrons from the bulk resulting in a so-called Andreev molecular state. By employing parallel nanowires with an Al shell, two artificial atoms were created at a minimal distance with an epitaxial superconducting link between. Hybridization via the BCS vacuum was observed and the spectrum of an Andreev molecule as a function of level positions was explored for the first time.
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Affiliation(s)
- Olivér Kürtössy
- Department
of Physics and Nanoelectronics “Momentum” Research Group
of the Hungarian Academy of Sciences, Budapest
University of Technology and Economics, Budafoki út 8, 1111 Budapest, Hungary
| | - Zoltán Scherübl
- Department
of Physics and Nanoelectronics “Momentum” Research Group
of the Hungarian Academy of Sciences, Budapest
University of Technology and Economics, Budafoki út 8, 1111 Budapest, Hungary
- University
of Grenoble Alpes, CEA, Grenoble INP, IRIG, PHELIQS, 38000 Grenoble, France
| | - Gergö Fülöp
- Department
of Physics and Nanoelectronics “Momentum” Research Group
of the Hungarian Academy of Sciences, Budapest
University of Technology and Economics, Budafoki út 8, 1111 Budapest, Hungary
| | - István Endre Lukács
- Center
for Energy Research, Institute of Technical
Physics and Material Science, Konkoly-Thege Miklós út 29-33, H-1121, Budapest, Hungary
| | - Thomas Kanne
- Center
for Quantum Devices, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark
| | - Jesper Nygård
- Center
for Quantum Devices, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark
| | - Péter Makk
- Department
of Physics and Nanoelectronics “Momentum” Research Group
of the Hungarian Academy of Sciences, Budapest
University of Technology and Economics, Budafoki út 8, 1111 Budapest, Hungary
| | - Szabolcs Csonka
- Department
of Physics and Nanoelectronics “Momentum” Research Group
of the Hungarian Academy of Sciences, Budapest
University of Technology and Economics, Budafoki út 8, 1111 Budapest, Hungary
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16
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Jakobsen MF, Brataas A, Qaiumzadeh A. Electrically Controlled Crossed Andreev Reflection in Two-Dimensional Antiferromagnets. PHYSICAL REVIEW LETTERS 2021; 127:017701. [PMID: 34270309 DOI: 10.1103/physrevlett.127.017701] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/15/2021] [Accepted: 06/03/2021] [Indexed: 06/13/2023]
Abstract
We report generic and tunable crossed Andreev reflection (CAR) in a superconductor sandwiched between two antiferromagnetic layers. We consider recent examples of two-dimensional magnets with hexagonal lattices, where gate voltages control the carrier type and density, and predict a robust signature of perfect CAR in the nonlocal differential conductance with one electron-doped and one hole-doped antiferromagnetic lead. The magnetic field-free and spin-degenerate CAR signal is electrically controlled and visible over a large voltage range, showing promise for solid-state quantum entanglement applications.
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Affiliation(s)
- Martin F Jakobsen
- Center for Quantum Spintronics, Department of Physics, Norwegian University of Science and Technology, NO-7491 Trondheim, Norway
| | - Arne Brataas
- Center for Quantum Spintronics, Department of Physics, Norwegian University of Science and Technology, NO-7491 Trondheim, Norway
| | - Alireza Qaiumzadeh
- Center for Quantum Spintronics, Department of Physics, Norwegian University of Science and Technology, NO-7491 Trondheim, Norway
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17
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Pandey P, Danneau R, Beckmann D. Ballistic Graphene Cooper Pair Splitter. PHYSICAL REVIEW LETTERS 2021; 126:147701. [PMID: 33891452 DOI: 10.1103/physrevlett.126.147701] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/19/2020] [Accepted: 03/05/2021] [Indexed: 06/12/2023]
Abstract
We report an experimental study of a Cooper pair splitter based on ballistic graphene multiterminal junctions. In a two transverse junction geometry, namely the superconductor-graphene-superconductor and the normal metal-graphene-normal metal, we observe clear signatures of Cooper pair splitting in the local as well as nonlocal electronic transport measurements. Our experimental data can be very well described by our beam splitter model. These results open up possibilities to design new entangled state detection experiments using ballistic Cooper pair splitters.
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Affiliation(s)
- P Pandey
- Institute of Nanotechnology, Karlsruhe Institute of Technology, Karlsruhe D-76021, Germany
| | - R Danneau
- Institute for Quantum Materials and Technologies, Karlsruhe Institute of Technology, Karlsruhe D-76021, Germany
| | - D Beckmann
- Institute for Quantum Materials and Technologies, Karlsruhe Institute of Technology, Karlsruhe D-76021, Germany
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18
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Tan ZB, Laitinen A, Kirsanov NS, Galda A, Vinokur VM, Haque M, Savin A, Golubev DS, Lesovik GB, Hakonen PJ. Thermoelectric current in a graphene Cooper pair splitter. Nat Commun 2021; 12:138. [PMID: 33420055 PMCID: PMC7794233 DOI: 10.1038/s41467-020-20476-7] [Citation(s) in RCA: 18] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/06/2020] [Accepted: 11/29/2020] [Indexed: 11/17/2022] Open
Abstract
Generation of electric voltage in a conductor by applying a temperature gradient is a fundamental phenomenon called the Seebeck effect. This effect and its inverse is widely exploited in diverse applications ranging from thermoelectric power generators to temperature sensing. Recently, a possibility of thermoelectricity arising from the interplay of the non-local Cooper pair splitting and the elastic co-tunneling in the hybrid normal metal-superconductor-normal metal structures was predicted. Here, we report the observation of the non-local Seebeck effect in a graphene-based Cooper pair splitting device comprising two quantum dots connected to an aluminum superconductor and present a theoretical description of this phenomenon. The observed non-local Seebeck effect offers an efficient tool for producing entangled electrons. Thermoelectricity due to the interplay of the nonlocal Cooper pair splitting and the elastic co-tunneling in normal metal-superconductor-normal metal structure is predicted. Here, the authors observe the non-local Seebeck effect in a graphene-based Cooper pair splitting device.
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Affiliation(s)
- Z B Tan
- Low Temperature Laboratory, Department of Applied Physics, Aalto University, Espoo, Finland.,Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen, 518055, China
| | - A Laitinen
- Low Temperature Laboratory, Department of Applied Physics, Aalto University, Espoo, Finland
| | - N S Kirsanov
- Low Temperature Laboratory, Department of Applied Physics, Aalto University, Espoo, Finland.,Terra Quantum AG, St. Gallerstrasse 16A, 9400, Rorschach, Switzerland.,Moscow Institute of Physics and Technology, Institutskii Per. 9, Dolgoprudny, Moscow Distr., 141700, Russian Federation.,Consortium for Advanced Science and Engineering (CASE), University of Chicago, 5801 S Ellis Avenue, Chicago, IL, 60637, USA
| | - A Galda
- James Franck Institute, University of Chicago, Chicago, IL, 60637, USA.,Materials Science Division, Argonne National Laboratory, 9700 S. Cass Avenue, Argonne, IL, 60439, USA
| | - V M Vinokur
- Consortium for Advanced Science and Engineering (CASE), University of Chicago, 5801 S Ellis Avenue, Chicago, IL, 60637, USA.,Materials Science Division, Argonne National Laboratory, 9700 S. Cass Avenue, Argonne, IL, 60439, USA
| | - M Haque
- Low Temperature Laboratory, Department of Applied Physics, Aalto University, Espoo, Finland
| | - A Savin
- Low Temperature Laboratory, Department of Applied Physics, Aalto University, Espoo, Finland
| | - D S Golubev
- QTF Centre of Excellence, Department of Applied Physics, Aalto University, FI-00076, Aalto, Finland
| | - G B Lesovik
- Terra Quantum AG, St. Gallerstrasse 16A, 9400, Rorschach, Switzerland.,Moscow Institute of Physics and Technology, Institutskii Per. 9, Dolgoprudny, Moscow Distr., 141700, Russian Federation
| | - P J Hakonen
- Low Temperature Laboratory, Department of Applied Physics, Aalto University, Espoo, Finland. .,QTF Centre of Excellence, Department of Applied Physics, Aalto University, FI-00076, Aalto, Finland.
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19
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Large spatial extension of the zero-energy Yu-Shiba-Rusinov state in a magnetic field. Nat Commun 2020; 11:1834. [PMID: 32286260 PMCID: PMC7156378 DOI: 10.1038/s41467-020-15322-9] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/19/2019] [Accepted: 03/03/2020] [Indexed: 11/30/2022] Open
Abstract
Various promising qubit concepts have been put forward recently based on engineered superconductor subgap states like Andreev bound states, Majorana zero modes or the Yu-Shiba-Rusinov (Shiba) states. The coupling of these subgap states via a superconductor strongly depends on their spatial extension and is an essential next step for future quantum technologies. Here we investigate the spatial extension of a Shiba state in a semiconductor quantum dot coupled to a superconductor. With detailed transport measurements and numerical renormalization group calculations we find a remarkable more than 50 nm extension of the zero energy Shiba state, much larger than the one observed in very recent scanning tunneling microscopy measurements. Moreover, we demonstrate that its spatial extension increases substantially in a magnetic field. Local magnetic moments coupled to superconductors can form subgap Yu-Shiba-Rusinov states. Here the authors show that Shiba states made with an InAs nanowire quantum dot have large spatial extent, which is beneficial for making Shiba chains that are predicted to host Majorana zero modes.
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20
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Park GH, Watanabe K, Taniguchi T, Lee GH, Lee HJ. Engineering Crossed Andreev Reflection in Double-Bilayer Graphene. NANO LETTERS 2019; 19:9002-9007. [PMID: 31738553 DOI: 10.1021/acs.nanolett.9b03981] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
Crossed Andreev reflection (CAR) is a nonlocal process that converts an incoming electron (hole) from one normal electrode to an out-going hole (electron) in another normal electrode through a superconductor (SC). CAR corresponds to the inverse process of Cooper pair splitting, which generates a quantum-entangled electron pair with spatial separation. Here, we fabricated vertically stacked double bilayer graphene (BLG) connected via a superconducting electrode and achieved a spacing between BLG sheets of ∼14 nm, which is far shorter than the superconducting coherence length. We confirm the highly efficient CAR effect by observing strong negative differential resistance in a nonlocal configuration and demonstrate that the competing processes against the CAR can be effectively suppressed by separately tuning the chemical potential of each BLG. The dependence of nonlocal signals on bias voltage, temperature, and chemical potential is consistent with the predicted CAR process. Our results provide a new pathway to a novel SC-based quantum entangler with the in situ tunability of the correlated-pair-splitting efficiency.
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Affiliation(s)
- Geon-Hyoung Park
- Department of Physics , Pohang University of Science and Technology , Pohang 37673 , Korea
| | - Kenji Watanabe
- National Institute for Material Science , Tsukuba 305-0044 , Japan
| | | | - Gil-Ho Lee
- Department of Physics , Pohang University of Science and Technology , Pohang 37673 , Korea
| | - Hu-Jong Lee
- Department of Physics , Pohang University of Science and Technology , Pohang 37673 , Korea
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21
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Ueda K, Matsuo S, Kamata H, Baba S, Sato Y, Takeshige Y, Li K, Jeppesen S, Samuelson L, Xu H, Tarucha S. Dominant nonlocal superconducting proximity effect due to electron-electron interaction in a ballistic double nanowire. SCIENCE ADVANCES 2019; 5:eaaw2194. [PMID: 31620554 PMCID: PMC6777966 DOI: 10.1126/sciadv.aaw2194] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 11/30/2018] [Accepted: 09/08/2019] [Indexed: 06/10/2023]
Abstract
Cooper pair splitting (CPS) can induce nonlocal correlation between two normal conductors that are coupled to a superconductor. CPS in a double one-dimensional electron gas is an appropriate platform for extracting a large number of entangled electron pairs and is one of the key ingredients for engineering Majorana fermions with no magnetic field. In this study, we investigated CPS by using a Josephson junction of a gate-tunable ballistic InAs double nanowire. The measured switching current into the two nanowires is significantly larger than the sum of the switching current into the respective nanowires, indicating that interwire superconductivity is dominant compared with intrawire superconductivity. From its dependence on the number of propagating channels in the nanowires, the observed CPS is assigned to one-dimensional electron-electron interaction. Our results will pave the way for the utilization of one-dimensional electron-electron interaction to reveal the physics of high-efficiency CPS and to engineer Majorana fermions in double nanowire systems via CPS.
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Affiliation(s)
- Kento Ueda
- Department of Applied Physics, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan
| | - Sadashige Matsuo
- Department of Applied Physics, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan
- Center for Emergent Matter Science, RIKEN, 2-1 Hirosawa, Wako-shi, Saitama 351-0198, Japan
- JST, PRESTO, 4-1-8 Honcho, Kawaguchi-shi, Saitama 332-0012, Japan
| | - Hiroshi Kamata
- Department of Applied Physics, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan
- Center for Emergent Matter Science, RIKEN, 2-1 Hirosawa, Wako-shi, Saitama 351-0198, Japan
| | - Shoji Baba
- Department of Applied Physics, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan
| | - Yosuke Sato
- Department of Applied Physics, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan
| | - Yuusuke Takeshige
- Department of Applied Physics, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan
| | - Kan Li
- Beijing Key Laboratory of Quantum Devices, Key Laboratory for the Physics and Chemistry of Nanodevices and Department of Electronics, Peking University, Beijing 100871, China
| | - Sören Jeppesen
- Division of Solid State Physics, Lund University, Box 118, SE-221 00 Lund, Sweden
| | - Lars Samuelson
- Division of Solid State Physics, Lund University, Box 118, SE-221 00 Lund, Sweden
| | - Hongqi Xu
- Beijing Key Laboratory of Quantum Devices, Key Laboratory for the Physics and Chemistry of Nanodevices and Department of Electronics, Peking University, Beijing 100871, China
- Division of Solid State Physics, Lund University, Box 118, SE-221 00 Lund, Sweden
- Beijing Academy of Quantum Information Sciences, Beijing 100193, China
| | - Seigo Tarucha
- Department of Applied Physics, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan
- Center for Emergent Matter Science, RIKEN, 2-1 Hirosawa, Wako-shi, Saitama 351-0198, Japan
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22
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Zhang SB, Trauzettel B. Perfect Crossed Andreev Reflection in Dirac Hybrid Junctions in the Quantum Hall Regime. PHYSICAL REVIEW LETTERS 2019; 122:257701. [PMID: 31347857 DOI: 10.1103/physrevlett.122.257701] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/30/2019] [Indexed: 06/10/2023]
Abstract
Perfect crossed Andreev reflection (CAR) is striking for high-efficiency Cooper pair splitting, which bears promising applications in quantum communication. Recent experimental advances have disclosed the way to explore CAR in Dirac fermion systems under ultrastrong magnetic fields. We develop a scattering approach to study quantum-Hall-superconductor-quantum-Hall junctions formed by a two-dimensional time-reversal symmetric Dirac semimetal. We propose two different setups of the hybrid junction in the quantum limit, where only zeroth Landau levels are involved in transport to exploit perfect CAR. In both setups, the CAR probability can reach unity without applying bias voltage and is controllable by the magnetic field strength, the junction width, the length, and the doping of the superconductor. CAR dominates the nonlocal transport and is directly measurable by the differential conductances. We also identify a quantized spin injection per CAR event in one of the two setups. Our proposal is experimentally feasible and will be helpful for exploring high-efficiency Cooper pair splitting and spin injection in Dirac materials.
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Affiliation(s)
- Song-Bo Zhang
- Institute for Theoretical Physics and Astrophysics, University of Würzburg, D-97074 Würzburg, Germany
| | - Björn Trauzettel
- Institute for Theoretical Physics and Astrophysics, University of Würzburg, D-97074 Würzburg, Germany
- Würzburg-Dresden Cluster of Excellence ct.qmat, Germany
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23
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Zhan H, Vanević M, Belzig W. Continuous-Variable Entanglement Test in Driven Quantum Contacts. PHYSICAL REVIEW LETTERS 2019; 122:236801. [PMID: 31298914 DOI: 10.1103/physrevlett.122.236801] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/12/2018] [Revised: 03/17/2019] [Indexed: 06/10/2023]
Abstract
The standard entanglement test using the Clauser-Horne-Shimony-Holt inequality is known to fail in mesoscopic junctions at finite temperatures. Since this is due to the bidirectional particle flow, a similar failure is expected to occur in an ac-driven contact. We develop a continuous-variable entanglement test suitable for electrons and holes that are created by the ac drive. At low enough temperatures the generalized Bell inequality is violated in junctions with low conductance or a small number of transport channels and with ac voltages which create few electron-hole pairs per cycle. Our ac-entanglement test depends on the total number of electron-hole pairs and on the distribution of probabilities of pair creations similar to the Fano factor.
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Affiliation(s)
- Hongxin Zhan
- Fachbereich Physik, Universität Konstanz, D-78457 Konstanz, Germany
| | - Mihajlo Vanević
- Department of Physics, University of Belgrade, 11158 Belgrade, Serbia
| | - Wolfgang Belzig
- Fachbereich Physik, Universität Konstanz, D-78457 Konstanz, Germany
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24
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Scherübl Z, Pályi A, Csonka S. Transport signatures of an Andreev molecule in a quantum dot-superconductor-quantum dot setup. BEILSTEIN JOURNAL OF NANOTECHNOLOGY 2019; 10:363-378. [PMID: 30800576 PMCID: PMC6369982 DOI: 10.3762/bjnano.10.36] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 09/25/2018] [Accepted: 01/03/2019] [Indexed: 06/09/2023]
Abstract
Hybrid devices combining quantum dots with superconductors are important building blocks of conventional and topological quantum-information experiments. A requirement for the success of such experiments is to understand the various tunneling-induced non-local interaction mechanisms that are present in the devices, namely crossed Andreev reflection, elastic co-tunneling, and direct interdot tunneling. Here, we provide a theoretical study of a simple device that consists of two quantum dots and a superconductor tunnel-coupled to the dots, often called a Cooper-pair splitter. We study the three special cases where one of the three non-local mechanisms dominates, and calculate measurable ground-state properties, as well as the zero-bias and finite-bias differential conductance characterizing electron transport through this device. We describe how each non-local mechanism controls the measurable quantities, and thereby find experimental fingerprints that allow one to identify and quantify the dominant non-local mechanism using experimental data. Finally, we study the triplet blockade effect and the associated negative differential conductance in the Cooper-pair splitter, and show that they can arise regardless of the nature of the dominant non-local coupling mechanism. Our results should facilitate the characterization of hybrid devices, and their optimization for various quantum-information-related experiments and applications.
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Affiliation(s)
- Zoltán Scherübl
- Department of Physics and MTA-BME Momentum Nanoelectronics Research Group, Budapest University of Technology and Economics, Budafoki út 8., 1111 Budapest, Hungary
| | - András Pályi
- Department of Theoretical Physics and MTA-BME Exotic Quantum Phases ”Momentum” Research Group, Budapest University of Technology and Economics, 1111 Budapest, Hungary
| | - Szabolcs Csonka
- Department of Physics and MTA-BME Momentum Nanoelectronics Research Group, Budapest University of Technology and Economics, Budafoki út 8., 1111 Budapest, Hungary
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25
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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.
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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
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26
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Trocha P, Wrześniewski K. Cross-correlations in a quantum dot Cooper pair splitter with ferromagnetic leads. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2018; 30:305303. [PMID: 29911660 DOI: 10.1088/1361-648x/aacd24] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
We investigate Andreev transport through a quantum dot attached to two external ferromagnetic leads and one superconducting electrode. The transport properties of the system are studied by means of the real-time diagrammatic technique in the sequential tunneling regime. To distinguish various contributions to Andreev current we calculate the current cross-correlations, i.e. correlations between currents flowing through two junctions with normal leads. We analyze dependence of current cross-correlations on various parameters of the considered model, both in linear and nonlinear transport regimes. The processes and mechanisms leading to enhancement, suppression or sign change of current cross-correlations are examined and discussed. Interestingly, our results show that for specific transport regimes splitted Cooper pair results in two uncorrelated electrons. However, utilizing ferromagnetic leads instead of non-magnetic electrodes can result in positive current cross-correlations.
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Affiliation(s)
- Piotr Trocha
- Faculty of Physics, Adam Mickiewicz University, 61-614 Poznań, Poland
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27
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Nonlocal supercurrent of quartets in a three-terminal Josephson junction. Proc Natl Acad Sci U S A 2018; 115:6991-6994. [PMID: 29915041 DOI: 10.1073/pnas.1800044115] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
A novel nonlocal supercurrent, carried by quartets, each consisting of four electrons, is expected to appear in a voltage-biased three-terminal Josephson junction. This supercurrent results from a nonlocal Andreev bound state (ABS), formed among three superconducting terminals. While in a two-terminal Josephson junction the usual ABS, and thus the dc Josephson current, exists only in equilibrium, the ABS, which gives rise to the quartet supercurrent, persists in the nonlinear regime. In this work, we report such resonance in a highly coherent three-terminal Josephson junction made in an InAs nanowire in proximity to an aluminum superconductor. In addition to nonlocal conductance measurements, cross-correlation measurements of current fluctuations provided a distinctive signature of the quartet supercurrent. Multiple device geometries had been tested, allowing us to rule out competing mechanisms and to establish the underlying microscopic origin of this coherent nondissipative current.
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28
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Cottet A, Dartiailh MC, Desjardins MM, Cubaynes T, Contamin LC, Delbecq M, Viennot JJ, Bruhat LE, Douçot B, Kontos T. Cavity QED with hybrid nanocircuits: from atomic-like physics to condensed matter phenomena. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2017; 29:433002. [PMID: 28925381 DOI: 10.1088/1361-648x/aa7b4d] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
Circuit QED techniques have been instrumental in manipulating and probing with exquisite sensitivity the quantum state of superconducting quantum bits coupled to microwave cavities. Recently, it has become possible to fabricate new devices in which the superconducting quantum bits are replaced by hybrid mesoscopic circuits combining nanoconductors and metallic reservoirs. This mesoscopic QED provides a new experimental playground to study the light-matter interaction in electronic circuits. Here, we present the experimental state of the art of mesoscopic QED and its theoretical description. A first class of experiments focuses on the artificial atom limit, where some quasiparticles are trapped in nanocircuit bound states. In this limit, the circuit QED techniques can be used to manipulate and probe electronic degrees of freedom such as confined charges, spins, or Andreev pairs. A second class of experiments uses cavity photons to reveal the dynamics of electron tunneling between a nanoconductor and fermionic reservoirs. For instance, the Kondo effect, the charge relaxation caused by grounded metallic contacts, and the photo-emission caused by voltage-biased reservoirs have been studied. The tunnel coupling between nanoconductors and fermionic reservoirs also enable one to obtain split Cooper pairs, or Majorana bound states. Cavity photons represent a qualitatively new tool to study these exotic condensed matter states.
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Affiliation(s)
- Audrey Cottet
- Laboratoire Pierre Aigrain, Ecole Normale Supérieure, CNRS UMR 8551, Laboratoire associé aux universités Pierre et Marie Curie et Denis Diderot, 24, rue Lhomond, 75231 Paris Cedex 05, France
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29
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Ota T, Hashisaka M, Muraki K, Fujisawa T. Negative and positive cross-correlations of current noises in quantum Hall edge channels at bulk filling factor [Formula: see text]. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2017; 29:225302. [PMID: 28401878 DOI: 10.1088/1361-648x/aa6cc0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
Cross-correlation noise in electrical currents generated from a series connection of two quantum point contacts (QPCs), the injector and the detector, is described for investigating energy relaxation in quantum Hall edge channels at bulk filling factor [Formula: see text]. We address the importance of tuning the energy bias across the detector for this purpose. For a long channel with a macroscopic floating ohmic contact that thermalizes the electrons, the cross-correlation turns from negative values to the maximally positive value (identical noise in the two currents) by tuning the effective energy bias to zero. This can be understood by considering competition between the low-frequency charge fluctuation generated at the injector, which contributes positive correlation, and the partition noise at the detector, which gives negative correlation. Strikingly, even for a short channel without intentional thermalization, significantly large positive correlation is observed in contrast to negative values expected for coherent transport between the two QPCs.
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Affiliation(s)
- T Ota
- Department of Physics, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro, Tokyo, 152-8551, Japan
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30
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Wrześniewski K, Trocha P, Weymann I. Current cross-correlations in double quantum dot based Cooper pair splitters with ferromagnetic leads. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2017; 29:195302. [PMID: 28379841 DOI: 10.1088/1361-648x/aa682d] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
We investigate the current cross-correlations in a double quantum dot based Cooper pair splitter coupled to one superconducting and two ferromagnetic electrodes. The analysis is performed by assuming a weak coupling between the double dot and ferromagnetic leads, while the coupling to the superconductor is arbitrary. Employing the perturbative real-time diagrammatic technique, we study the Andreev transport properties of the device, focusing on the Andreev current cross-correlations, for various parameters of the model, both in the linear and nonlinear response regimes. Depending on parameters and transport regime, we find both positive and negative current cross-correlations. Enhancement of the former type of cross-correlations indicates transport regimes, in which the device works with high Cooper pair splitting efficiency, contrary to the latter type of correlations, which imply negative influence on the splitting. The processes and mechanisms leading to both types of current cross-correlations are thoroughly examined and discussed, giving a detailed insight into the Andreev transport properties of the considered device.
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31
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Gooth J, Borg M, Schmid H, Schaller V, Wirths S, Moselund K, Luisier M, Karg S, Riel H. Ballistic One-Dimensional InAs Nanowire Cross-Junction Interconnects. NANO LETTERS 2017; 17:2596-2602. [PMID: 28334529 DOI: 10.1021/acs.nanolett.7b00400] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
Coherent interconnection of quantum bits remains an ongoing challenge in quantum information technology. Envisioned hardware to achieve this goal is based on semiconductor nanowire (NW) circuits, comprising individual NW devices that are linked through ballistic interconnects. However, maintaining the sensitive ballistic conduction and confinement conditions across NW intersections is a nontrivial problem. Here, we go beyond the characterization of a single NW device and demonstrate ballistic one-dimensional (1D) quantum transport in InAs NW cross-junctions, monolithically integrated on Si. Characteristic 1D conductance plateaus are resolved in field-effect measurements across up to four NW-junctions in series. The 1D ballistic transport and sub-band splitting is preserved for both crossing-directions. We show that the 1D modes of a single injection terminal can be distributed into multiple NW branches. We believe that NW cross-junctions are well-suited as cross-directional communication links for the reliable transfer of quantum information as required for quantum computational systems.
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Affiliation(s)
- Johannes Gooth
- IBM Research - Zurich , Säumerstrasse 4, 8803 Rüschlikon, Switzerland
| | - Mattias Borg
- IBM Research - Zurich , Säumerstrasse 4, 8803 Rüschlikon, Switzerland
| | - Heinz Schmid
- IBM Research - Zurich , Säumerstrasse 4, 8803 Rüschlikon, Switzerland
| | - Vanessa Schaller
- IBM Research - Zurich , Säumerstrasse 4, 8803 Rüschlikon, Switzerland
| | - Stephan Wirths
- IBM Research - Zurich , Säumerstrasse 4, 8803 Rüschlikon, Switzerland
| | - Kirsten Moselund
- IBM Research - Zurich , Säumerstrasse 4, 8803 Rüschlikon, Switzerland
| | - Mathieu Luisier
- ETH Zurich, Integrated Systems Laboratory , Gloriastrasse 35, 8092 Zurich, Switzerland
| | - Siegfried Karg
- IBM Research - Zurich , Säumerstrasse 4, 8803 Rüschlikon, Switzerland
| | - Heike Riel
- IBM Research - Zurich , Säumerstrasse 4, 8803 Rüschlikon, Switzerland
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32
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Car D, Conesa-Boj S, Zhang H, Op Het Veld RLM, de Moor MWA, Fadaly EMT, Gül Ö, Kölling S, Plissard SR, Toresen V, Wimmer MT, Watanabe K, Taniguchi T, Kouwenhoven LP, Bakkers EPAM. InSb Nanowires with Built-In Ga xIn 1-xSb Tunnel Barriers for Majorana Devices. NANO LETTERS 2017; 17:721-727. [PMID: 28173706 DOI: 10.1021/acs.nanolett.6b03835] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
Majorana zero modes (MZMs), prime candidates for topological quantum bits, are detected as zero bias conductance peaks (ZBPs) in tunneling spectroscopy measurements. Implementation of a narrow and high tunnel barrier in the next generation of Majorana devices can help to achieve the theoretically predicted quantized height of the ZBP. We propose a material-oriented approach to engineer a sharp and narrow tunnel barrier by synthesizing a thin axial segment of GaxIn1-xSb within an InSb nanowire. By varying the precursor molar fraction and the growth time, we accurately control the composition and the length of the barriers. The height and the width of the GaxIn1-xSb tunnel barrier are extracted from the Wentzel-Kramers-Brillouin (WKB) fits to the experimental I-V traces.
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Affiliation(s)
- Diana Car
- Department of Applied Physics, Eindhoven University of Technology , P.O. Box 513, 5600 MB Eindhoven, The Netherlands
| | - Sonia Conesa-Boj
- Kavli Institute of Nanoscience, Delft University of Technology , 2628CJ Delft, The Netherlands
| | - Hao Zhang
- Kavli Institute of Nanoscience, Delft University of Technology , 2628CJ Delft, The Netherlands
| | - Roy L M Op Het Veld
- Kavli Institute of Nanoscience, Delft University of Technology , 2628CJ Delft, The Netherlands
| | - Michiel W A de Moor
- Kavli Institute of Nanoscience, Delft University of Technology , 2628CJ Delft, The Netherlands
| | - Elham M T Fadaly
- Kavli Institute of Nanoscience, Delft University of Technology , 2628CJ Delft, The Netherlands
| | - Önder Gül
- Kavli Institute of Nanoscience, Delft University of Technology , 2628CJ Delft, The Netherlands
| | - Sebastian Kölling
- Department of Applied Physics, Eindhoven University of Technology , P.O. Box 513, 5600 MB Eindhoven, The Netherlands
| | | | - Vigdis Toresen
- Kavli Institute of Nanoscience, Delft University of Technology , 2628CJ Delft, The Netherlands
| | - Michael T Wimmer
- Kavli Institute of Nanoscience, Delft University of Technology , 2628CJ Delft, The Netherlands
| | - Kenji Watanabe
- Advanced Materials Laboratory, National Institute for Materials Science , 1-1 Namiki, Tsukuba 305-0044, Japan
| | - Takashi Taniguchi
- Advanced Materials Laboratory, National Institute for Materials Science , 1-1 Namiki, Tsukuba 305-0044, Japan
| | - Leo P Kouwenhoven
- Kavli Institute of Nanoscience, Delft University of Technology , 2628CJ Delft, The Netherlands
| | - Erik P A M Bakkers
- Department of Applied Physics, Eindhoven University of Technology , P.O. Box 513, 5600 MB Eindhoven, The Netherlands
- Kavli Institute of Nanoscience, Delft University of Technology , 2628CJ Delft, The Netherlands
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33
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Brange F, Malkoc O, Samuelsson P. Minimal Entanglement Witness from Electrical Current Correlations. PHYSICAL REVIEW LETTERS 2017; 118:036804. [PMID: 28157375 DOI: 10.1103/physrevlett.118.036804] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/19/2016] [Indexed: 06/06/2023]
Abstract
Despite great efforts, an unambiguous demonstration of entanglement of mobile electrons in solid state conductors is still lacking. Investigating theoretically a generic entangler-detector setup, we here show that a witness of entanglement between two flying electron qubits can be constructed from only two current cross correlation measurements, for any nonzero detector efficiencies and noncollinear polarization vectors. We find that all entangled pure states, but not all mixed ones, can be detected with only two measurements, except the maximally entangled states, which require three. Moreover, detector settings for optimal entanglement witnessing are presented.
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Affiliation(s)
- F Brange
- Department of Physics, Lund University, Box 118, SE-221 00 Lund, Sweden
| | - O Malkoc
- Department of Physics, Lund University, Box 118, SE-221 00 Lund, Sweden
| | - P Samuelsson
- Department of Physics, Lund University, Box 118, SE-221 00 Lund, Sweden
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34
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Paul GC, Dutta P, Saha A. Transport and noise properties of a normal metal-superconductor-normal metal junction with mixed singlet and chiral triplet pairings. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2017; 29:015301. [PMID: 27830661 DOI: 10.1088/0953-8984/29/1/015301] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
We study transport and zero frequency shot noise properties of a normal metal-superconductor-normal metal (NSN) junction, with the superconductor having mixed singlet and chiral triplet pairings. We show that in the subgapped regime when the chiral triplet pairing amplitude dominates over that of the singlet, a resonance phenomena emerges out at zero energy where all the quantum mechanical scattering probabilities acquire a value of 0.25. At the resonance, crossed Andreev reflection mediating through such junction, acquires a zero energy peak. This reflects as a zero energy peak in the conductance as well depending on the doping concentration. We also investigate shot noise for this system and show that shot noise cross-correlation is negative in the subgapped regime when the triplet pairing dominates over the singlet one. The latter is in sharp contrast to the positive shot noise obtained when the singlet pairing is the dominating one.
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35
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Nieminen T, Lähteenmäki P, Tan Z, Cox D, Hakonen PJ. Low-noise correlation measurements based on software-defined-radio receivers and cooled microwave amplifiers. THE REVIEW OF SCIENTIFIC INSTRUMENTS 2016; 87:114706. [PMID: 27910622 DOI: 10.1063/1.4966971] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
We present a microwave correlation measurement system based on two low-cost USB-connected software defined radio dongles modified to operate as coherent receivers by using a common local oscillator. Existing software is used to obtain I/Q samples from both dongles simultaneously at a software tunable frequency. To achieve low noise, we introduce an easy low-noise solution for cryogenic amplification at 600-900 MHz based on single discrete HEMT with 21 dB gain and 7 K noise temperature. In addition, we discuss the quantization effects in a digital correlation measurement and determination of optimal integration time by applying Allan deviation analysis.
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Affiliation(s)
- Teemu Nieminen
- Low Temperature Laboratory, Department of Applied Physics, Aalto University School of Science, P.O. Box 15100, FI-00076 Aalto, Finland
| | - Pasi Lähteenmäki
- Low Temperature Laboratory, Department of Applied Physics, Aalto University School of Science, P.O. Box 15100, FI-00076 Aalto, Finland
| | - Zhenbing Tan
- Low Temperature Laboratory, Department of Applied Physics, Aalto University School of Science, P.O. Box 15100, FI-00076 Aalto, Finland
| | - Daniel Cox
- Low Temperature Laboratory, Department of Applied Physics, Aalto University School of Science, P.O. Box 15100, FI-00076 Aalto, Finland
| | - Pertti J Hakonen
- Low Temperature Laboratory, Department of Applied Physics, Aalto University School of Science, P.O. Box 15100, FI-00076 Aalto, Finland
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36
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Tikhonov ES, Shovkun DV, Snelder M, Stehno MP, Huang Y, Golden MS, Golubov AA, Brinkman A, Khrapai VS. Andreev Reflection in an s-Type Superconductor Proximized 3D Topological Insulator. PHYSICAL REVIEW LETTERS 2016; 117:147001. [PMID: 27740782 DOI: 10.1103/physrevlett.117.147001] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/31/2016] [Indexed: 06/06/2023]
Abstract
We investigate transport and shot noise in lateral normal-metal-3D topological-insulator-superconductor contacts, where the 3D topological insulator (TI) is based on Bi. In the normal state, the devices are in the elastic diffusive transport regime, as demonstrated by a nearly universal value of the shot noise Fano factor F_{N}≈1/3 in magnetic field and in a reference normal-metal contact. In the absence of magnetic field, we identify the Andreev reflection (AR) regime, which gives rise to the effective charge doubling in shot noise measurements. Surprisingly, the Fano factor F_{AR}≈0.22±0.02 is considerably reduced in the AR regime compared to F_{N}, in contrast to previous AR experiments in normal metals and semiconductors. We suggest that this effect is related to a finite thermal conduction of the proximized, superconducting TI owing to a residual density of states at low energies.
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Affiliation(s)
- E S Tikhonov
- Institute of Solid State Physics, Russian Academy of Sciences, 142432 Chernogolovka, Russian Federation
- Moscow Institute of Physics and Technology, Dolgoprudny, 141700 Russian Federation
| | - D V Shovkun
- Institute of Solid State Physics, Russian Academy of Sciences, 142432 Chernogolovka, Russian Federation
- Moscow Institute of Physics and Technology, Dolgoprudny, 141700 Russian Federation
| | - M Snelder
- MESA+ Institute for Nanotechnology, University of Twente, 7500 AE Enschede, The Netherlands
| | - M P Stehno
- MESA+ Institute for Nanotechnology, University of Twente, 7500 AE Enschede, The Netherlands
| | - Y Huang
- Van der Waals-Zeeman Institute, University of Amsterdam, 1098 XH Amsterdam, The Netherlands
| | - M S Golden
- Van der Waals-Zeeman Institute, University of Amsterdam, 1098 XH Amsterdam, The Netherlands
| | - A A Golubov
- Moscow Institute of Physics and Technology, Dolgoprudny, 141700 Russian Federation
- MESA+ Institute for Nanotechnology, University of Twente, 7500 AE Enschede, The Netherlands
| | - A Brinkman
- MESA+ Institute for Nanotechnology, University of Twente, 7500 AE Enschede, The Netherlands
| | - V S Khrapai
- Institute of Solid State Physics, Russian Academy of Sciences, 142432 Chernogolovka, Russian Federation
- Moscow Institute of Physics and Technology, Dolgoprudny, 141700 Russian Federation
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37
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Kammhuber J, Cassidy MC, Zhang H, Gül Ö, Pei F, de Moor MWA, Nijholt B, Watanabe K, Taniguchi T, Car D, Plissard SR, Bakkers EPAM, Kouwenhoven LP. Conductance Quantization at Zero Magnetic Field in InSb Nanowires. NANO LETTERS 2016; 16:3482-3486. [PMID: 27121534 DOI: 10.1021/acs.nanolett.6b00051] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
Ballistic electron transport is a key requirement for existence of a topological phase transition in proximitized InSb nanowires. However, measurements of quantized conductance as direct evidence of ballistic transport have so far been obscured due to the increased chance of backscattering in one-dimensional nanowires. We show that by improving the nanowire-metal interface as well as the dielectric environment we can consistently achieve conductance quantization at zero magnetic field. Additionally we study the contribution of orbital effects to the sub-band dispersion for different orientation of the magnetic field, observing a near-degeneracy between the second and third sub-bands.
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Affiliation(s)
- Jakob Kammhuber
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology , 2628 CJ Delft, The Netherlands
| | - Maja C Cassidy
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology , 2628 CJ Delft, The Netherlands
| | - Hao Zhang
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology , 2628 CJ Delft, The Netherlands
| | - Önder Gül
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology , 2628 CJ Delft, The Netherlands
| | - Fei Pei
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology , 2628 CJ Delft, The Netherlands
| | - Michiel W A de Moor
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology , 2628 CJ Delft, The Netherlands
| | - Bas Nijholt
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology , 2628 CJ Delft, The Netherlands
| | - Kenji Watanabe
- Advanced Materials Laboratory, National Institute for Materials Science , 1-1 Namiki, Tsukuba 305-0044, Japan
| | - Takashi Taniguchi
- Advanced Materials Laboratory, National Institute for Materials Science , 1-1 Namiki, Tsukuba 305-0044, Japan
| | - Diana Car
- Department of Applied Physics, Eindhoven University of Technology , 5600 MB Eindhoven, The Netherlands
| | - Sébastien R Plissard
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology , 2628 CJ Delft, The Netherlands
- Department of Applied Physics, Eindhoven University of Technology , 5600 MB Eindhoven, The Netherlands
| | - Erik P A M Bakkers
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology , 2628 CJ Delft, The Netherlands
- Department of Applied Physics, Eindhoven University of Technology , 5600 MB Eindhoven, The Netherlands
| | - Leo P Kouwenhoven
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology , 2628 CJ Delft, The Netherlands
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38
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Fülöp G, d'Hollosy S, Hofstetter L, Baumgartner A, Nygård J, Schönenberger C, Csonka S. Wet etch methods for InAs nanowire patterning and self-aligned electrical contacts. NANOTECHNOLOGY 2016; 27:195303. [PMID: 27040175 DOI: 10.1088/0957-4484/27/19/195303] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
Advanced synthesis of semiconductor nanowires (NWs) enables their application in diverse fields, notably in chemical and electrical sensing, photovoltaics, or quantum electronic devices. In particular, indium arsenide (InAs) NWs are an ideal platform for quantum devices, e.g. they may host topological Majorana states. While the synthesis has been continously perfected, only a few techniques have been developed to tailor individual NWs after growth. Here we present three wet chemical etch methods for the post-growth morphological engineering of InAs NWs on the sub-100 nm scale. The first two methods allow the formation of self-aligned electrical contacts to etched NWs, while the third method results in conical shaped NW profiles ideal for creating smooth electrical potential gradients and shallow barriers. Low temperature experiments show that NWs with etched segments have stable transport characteristics and can serve as building blocks of quantum electronic devices. As an example we report the formation of a single electrically stable quantum dot between two etched NW segments.
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Affiliation(s)
- G Fülöp
- Department of Physics, Budapest University of Technology and Economics, and Condensed Matter Research Group of the Hungarian Academy of Sciences, Budafoki út 8, 1111 Budapest, Hungary
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39
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High Efficiency CVD Graphene-lead (Pb) Cooper Pair Splitter. Sci Rep 2016; 6:23051. [PMID: 26971450 PMCID: PMC4789789 DOI: 10.1038/srep23051] [Citation(s) in RCA: 30] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/21/2015] [Accepted: 02/24/2016] [Indexed: 11/08/2022] Open
Abstract
Generation and manipulation of quantum entangled electrons is an important concept in quantum mechanics, and necessary for advances in quantum information processing; but not yet established in solid state systems. A promising device is a superconductor-two quantum dots Cooper pair splitter. Early nanowire based devices, while efficient, are limited in scalability and further electron manipulation. We demonstrate an optimized, high efficiency, CVD grown graphene-based Cooper pair splitter. Our device is designed to induce superconductivity in graphene via the proximity effect, resulting in both a large superconducting gap Δ = 0.5 meV, and coherence length ξ = 200 nm. The flat nature of the device lowers parasitic capacitance, increasing charging energy EC. Our design also eases geometric restrictions and minimizes output channel separation. As a result we measure a visibility of up to 86% and a splitting efficiency of up to 62%. This will pave the way towards near unity efficiencies, long distance splitting, and post-splitting electron manipulation.
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40
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Ronen Y, Cohen Y, Kang JH, Haim A, Rieder MT, Heiblum M, Mahalu D, Shtrikman H. Charge of a quasiparticle in a superconductor. Proc Natl Acad Sci U S A 2016; 113:1743-8. [PMID: 26831071 PMCID: PMC4763780 DOI: 10.1073/pnas.1515173113] [Citation(s) in RCA: 29] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
Nonlinear charge transport in superconductor-insulator-superconductor (SIS) Josephson junctions has a unique signature in the shuttled charge quantum between the two superconductors. In the zero-bias limit Cooper pairs, each with twice the electron charge, carry the Josephson current. An applied bias VSD leads to multiple Andreev reflections (MAR), which in the limit of weak tunneling probability should lead to integer multiples of the electron charge ne traversing the junction, with n integer larger than 2Δ/eVSD and Δ the superconducting order parameter. Exceptionally, just above the gap eVSD ≥ 2Δ, with Andreev reflections suppressed, one would expect the current to be carried by partitioned quasiparticles, each with energy-dependent charge, being a superposition of an electron and a hole. Using shot-noise measurements in an SIS junction induced in an InAs nanowire (with noise proportional to the partitioned charge), we first observed quantization of the partitioned charge q = e*/e = n, with n = 1-4, thus reaffirming the validity of our charge interpretation. Concentrating next on the bias region eVSD ~ 2Δ, we found a reproducible and clear dip in the extracted charge to q ~ 0.6, which, after excluding other possibilities, we attribute to the partitioned quasiparticle charge. Such dip is supported by numerical simulations of our SIS structure.
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Affiliation(s)
- Yuval Ronen
- Braun Center for Submicron Research, Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 76100, Israel
| | - Yonatan Cohen
- Braun Center for Submicron Research, Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 76100, Israel
| | - Jung-Hyun Kang
- Braun Center for Submicron Research, Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 76100, Israel
| | - Arbel Haim
- Braun Center for Submicron Research, Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 76100, Israel
| | - Maria-Theresa Rieder
- Braun Center for Submicron Research, Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 76100, Israel; Dahlem Center for Complex Quantum Systems, Freie University, 14195 Berlin, Germany
| | - Moty Heiblum
- Braun Center for Submicron Research, Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 76100, Israel;
| | - Diana Mahalu
- Braun Center for Submicron Research, Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 76100, Israel
| | - Hadas Shtrikman
- Braun Center for Submicron Research, Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 76100, Israel
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41
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Fülöp G, Domínguez F, d'Hollosy S, Baumgartner A, Makk P, Madsen MH, Guzenko VA, Nygård J, Schönenberger C, Levy Yeyati A, Csonka S. Magnetic Field Tuning and Quantum Interference in a Cooper Pair Splitter. PHYSICAL REVIEW LETTERS 2015; 115:227003. [PMID: 26650317 DOI: 10.1103/physrevlett.115.227003] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/03/2015] [Indexed: 06/05/2023]
Abstract
Cooper pair splitting (CPS) is a process in which the electrons of the naturally occurring spin-singlet pairs in a superconductor are spatially separated using two quantum dots. Here, we investigate the evolution of the conductance correlations in an InAs CPS device in the presence of an external magnetic field. In our experiments the gate dependence of the signal that depends on both quantum dots continuously evolves from a slightly asymmetric Lorentzian to a strongly asymmetric Fano-type resonance with increasing field. These experiments can be understood in a simple three-site model, which shows that the nonlocal CPS leads to symmetric line shapes, while the local transport processes can exhibit an asymmetric shape due to quantum interference. These findings demonstrate that the electrons from a Cooper pair splitter can propagate coherently after their emission from the superconductor and how a magnetic field can be used to optimize the performance of a CPS device. In addition, the model calculations suggest that the estimate of the CPS efficiency in the experiments is a lower bound for the actual efficiency.
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Affiliation(s)
- G Fülöp
- Department of Physics, Budapest University of Technology and Economics, and Condensed Matter Research Group of the Hungarian Academy of Sciences, Budafoki út 8, 1111 Budapest, Hungary
| | - F Domínguez
- Departamento de Física Teórica de la Materia Condensada, Condensed Matter Physics Center (IFIMAC), and Instituto Nicolás Cabrera, Universidad Autónoma de Madrid, E-28049 Madrid, Spain
| | - S d'Hollosy
- Department of Physics, University of Basel, Klingelbergstrasse 82, CH-4056 Basel, Switzerland
| | - A Baumgartner
- Department of Physics, University of Basel, Klingelbergstrasse 82, CH-4056 Basel, Switzerland
| | - P Makk
- Department of Physics, Budapest University of Technology and Economics, and Condensed Matter Research Group of the Hungarian Academy of Sciences, Budafoki út 8, 1111 Budapest, Hungary
- Department of Physics, University of Basel, Klingelbergstrasse 82, CH-4056 Basel, Switzerland
| | - M H Madsen
- Center for Quantum Devices & Nano-Science Center, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, DK-2100 Copenhagen, Denmark
| | - V A Guzenko
- Laboratory for Micro- and Nanotechnology, Paul Scherrer Institute, CH-5232 Villigen PSI, Switzerland
| | - J Nygård
- Center for Quantum Devices & Nano-Science Center, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, DK-2100 Copenhagen, Denmark
| | - C Schönenberger
- Department of Physics, University of Basel, Klingelbergstrasse 82, CH-4056 Basel, Switzerland
| | - A Levy Yeyati
- Departamento de Física Teórica de la Materia Condensada, Condensed Matter Physics Center (IFIMAC), and Instituto Nicolás Cabrera, Universidad Autónoma de Madrid, E-28049 Madrid, Spain
| | - S Csonka
- Department of Physics, Budapest University of Technology and Economics, and Condensed Matter Research Group of the Hungarian Academy of Sciences, Budafoki út 8, 1111 Budapest, Hungary
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d'Hollosy S, Jung M, Baumgartner A, Guzenko VA, Madsen MH, Nygård J, Schönenberger C. Gigahertz Quantized Charge Pumping in Bottom-Gate-Defined InAs Nanowire Quantum Dots. NANO LETTERS 2015; 15:4585-4590. [PMID: 26086240 DOI: 10.1021/acs.nanolett.5b01190] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
Semiconducting nanowires (NWs) are a versatile, highly tunable material platform at the heart of many new developments in nanoscale and quantum physics. Here, we demonstrate charge pumping, that is, the controlled transport of individual electrons through an InAs NW quantum dot (QD) device at frequencies up to 1.3 GHz. The QD is induced electrostatically in the NW by a series of local bottom gates in a state of the art device geometry. A periodic modulation of a single gate is enough to obtain a dc current proportional to the frequency of the modulation. The dc bias, the modulation amplitude and the gate voltages on the local gates can be used to control the number of charges conveyed per cycle. Charge pumping in InAs NWs is relevant not only in metrology as a current standard, but also opens up the opportunity to investigate a variety of exotic states of matter, for example, Majorana modes, by single electron spectroscopy and correlation experiments.
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Affiliation(s)
- S d'Hollosy
- †Institute of Physics, University of Basel, Klingelbergstrasse 82, CH-4056 Basel, Switzerland
| | - M Jung
- †Institute of Physics, University of Basel, Klingelbergstrasse 82, CH-4056 Basel, Switzerland
| | - A Baumgartner
- †Institute of Physics, University of Basel, Klingelbergstrasse 82, CH-4056 Basel, Switzerland
| | - V A Guzenko
- ‡Laboratory for Micro- and Nanotechnology, Paul Scherrer Institute, CH-5232 Villigen PSI, Switzerland
| | - M H Madsen
- §Center for Quantum Devices and Nano-Science Center, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, DK-2100 Copenhagen, Denmark
| | - J Nygård
- §Center for Quantum Devices and Nano-Science Center, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, DK-2100 Copenhagen, Denmark
| | - C Schönenberger
- †Institute of Physics, University of Basel, Klingelbergstrasse 82, CH-4056 Basel, Switzerland
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43
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Cooper pair splitting in parallel quantum dot Josephson junctions. Nat Commun 2015; 6:7446. [PMID: 26130172 PMCID: PMC4506998 DOI: 10.1038/ncomms8446] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/08/2014] [Accepted: 05/09/2015] [Indexed: 11/17/2022] Open
Abstract
Devices to generate on-demand non-local spin entangled electron pairs have potential application as solid-state analogues of the entangled photon sources used in quantum optics. Recently, Andreev entanglers that use two quantum dots as filters to adiabatically split and separate the quasi-particles of Cooper pairs have shown efficient splitting through measurements of the transport charge but the spin entanglement has not been directly confirmed. Here we report measurements on parallel quantum dot Josephson junction devices allowing a Josephson current to flow due to the adiabatic splitting and recombination of the Cooper pair between the dots. The evidence for this non-local transport is confirmed through study of the non-dissipative supercurrent while tuning independently the dots with local electrical gates. As the Josephson current arises only from processes that maintain the coherence, we can confirm that a current flows from the spatially separated entangled pair. Spin-entangled electron pairs are one possible resource for future solid-state quantum information processing systems. Here, the authors directly prove spin entanglement between two electrons that had previously been a Cooper pair in a superconducting lead but were split using two quantum dots.
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44
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Robust electron pairing in the integer quantum hall effect regime. Nat Commun 2015; 6:7435. [DOI: 10.1038/ncomms8435] [Citation(s) in RCA: 30] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/29/2014] [Accepted: 05/08/2015] [Indexed: 11/08/2022] Open
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45
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Brange F, Malkoc O, Samuelsson P. Subdecoherence time generation and detection of orbital entanglement in quantum dots. PHYSICAL REVIEW LETTERS 2015; 114:176803. [PMID: 25978249 DOI: 10.1103/physrevlett.114.176803] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/16/2015] [Indexed: 06/04/2023]
Abstract
Recent experiments have demonstrated subdecoherence time control of individual single-electron orbital qubits. Here we propose a quantum-dot-based scheme for generation and detection of pairs of orbitally entangled electrons on a time scale much shorter than the decoherence time. The electrons are entangled, via two-particle interference, and transferred to the detectors during a single cotunneling event, making the scheme insensitive to charge noise. For sufficiently long detector dot lifetimes, cross-correlation detection of the dot charges can be performed with real-time counting techniques, providing for an unambiguous short-time Bell inequality test of orbital entanglement.
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Affiliation(s)
- F Brange
- Department of Physics, Lund University, Box 118, SE-221 00 Lund, Sweden
| | - O Malkoc
- Department of Physics, Lund University, Box 118, SE-221 00 Lund, Sweden
| | - P Samuelsson
- Department of Physics, Lund University, Box 118, SE-221 00 Lund, Sweden
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46
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Correlated spin currents generated by resonant-crossed Andreev reflections in topological superconductors. Nat Commun 2015; 5:3232. [PMID: 24492649 PMCID: PMC3926009 DOI: 10.1038/ncomms4232] [Citation(s) in RCA: 71] [Impact Index Per Article: 7.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/15/2013] [Accepted: 01/09/2014] [Indexed: 11/08/2022] Open
Abstract
Topological superconductors, which support Majorana fermion excitations, have been the subject of intense studies due to their novel transport properties and their potential applications in fault-tolerant quantum computations. Here we propose a new type of topological superconductors that can be used as a novel source of correlated spin currents. We show that inducing superconductivity on a AIII class topological insulator wire, which respects a chiral symmetry and supports protected fermionic end states, will result in a topological superconductor. This topological superconductor supports two topological phases with one or two Majorana fermion end states, respectively. In the phase with two Majorana fermions, the superconductor can split Cooper pairs efficiently into electrons in two spatially separated leads due to Majorana-induced resonant-crossed Andreev reflections. The resulting currents in the leads are correlated and spin-polarized. Importantly, the proposed topological superconductors can be realized using quantum anomalous Hall insulators in proximity to superconductors. Materials that exhibit topologically protected electronic structures are expected to enable the development of more efficient spintronic devices. He et al. suggest that combining a quantum anomalous Hall insulator with a superconductor could be used to generate correlated spin currents.
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47
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Tan ZB, Cox D, Nieminen T, Lähteenmäki P, Golubev D, Lesovik GB, Hakonen PJ. Cooper pair splitting by means of graphene quantum dots. PHYSICAL REVIEW LETTERS 2015; 114:096602. [PMID: 25793837 DOI: 10.1103/physrevlett.114.096602] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/06/2014] [Indexed: 05/21/2023]
Abstract
A split Cooper pair is a natural source for entangled electrons which is a basic ingredient for quantum information in the solid state. We report an experiment on a superconductor-graphene double quantum dot (QD) system, in which we observe Cooper pair splitting (CPS) up to a CPS efficiency of ∼10%. With bias on both QDs, we are able to detect a positive conductance correlation across the two distinctly decoupled QDs. Furthermore, with bias only on one QD, CPS and elastic cotunneling can be distinguished by tuning the energy levels of the QDs to be asymmetric or symmetric with respect to the Fermi level in the superconductor.
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Affiliation(s)
- Z B Tan
- Low Temperature Laboratory, Department of Applied Physics, Aalto University, P.O. Box 15100, FI-00076 Aalto, Finland
| | - D Cox
- Low Temperature Laboratory, Department of Applied Physics, Aalto University, P.O. Box 15100, FI-00076 Aalto, Finland
| | - T Nieminen
- Low Temperature Laboratory, Department of Applied Physics, Aalto University, P.O. Box 15100, FI-00076 Aalto, Finland
| | - P Lähteenmäki
- Low Temperature Laboratory, Department of Applied Physics, Aalto University, P.O. Box 15100, FI-00076 Aalto, Finland
| | - D Golubev
- Low Temperature Laboratory, Department of Applied Physics, Aalto University, P.O. Box 15100, FI-00076 Aalto, Finland
| | - G B Lesovik
- L.D. Landau Institute for Theoretical Physics RAS, Chernogolovka, 142432 Moscow Region, Russia
| | - P J Hakonen
- Low Temperature Laboratory, Department of Applied Physics, Aalto University, P.O. Box 15100, FI-00076 Aalto, Finland
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48
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Chen W, Shi DN, Xing DY. Long-range Cooper pair splitter with high entanglement production rate. Sci Rep 2015; 5:7607. [PMID: 25556521 PMCID: PMC5154587 DOI: 10.1038/srep07607] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/02/2014] [Accepted: 11/19/2014] [Indexed: 12/04/2022] Open
Abstract
Cooper pairs in the superconductor are a natural source of spin entanglement. The existing proposals of the Cooper pair splitter can only realize a low efficiency of entanglement production, and its size is constrained by the superconducting coherence length. Here we show that a long-range Cooper pair splitter can be implemented in a normal metal-superconductor-normal metal (NSN) junction by driving a supercurrent in the S. The supercurrent results in a band gap modification of the S, which significantly enhances the crossed Andreev reflection (CAR) of the NSN junction and simultaneously quenches its elastic cotunneling. Therefore, a high entanglement production rate close to its saturation value can be achieved by the inverse CAR. Interestingly, in addition to the conventional entangled electron states between opposite energy levels, novel entangled states with equal energy can also be induced in our proposal.
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Affiliation(s)
- Wei Chen
- College of Science, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
| | - D N Shi
- College of Science, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
| | - D Y Xing
- 1] National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University, Nanjing 210093, China [2] Collaborative Innovation Center of Advanced Microstructures
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49
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Ubbelohde N, Hohls F, Kashcheyevs V, Wagner T, Fricke L, Kästner B, Pierz K, Schumacher HW, Haug RJ. Partitioning of on-demand electron pairs. NATURE NANOTECHNOLOGY 2015; 10:46-49. [PMID: 25437747 DOI: 10.1038/nnano.2014.275] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/28/2014] [Accepted: 10/21/2014] [Indexed: 06/04/2023]
Abstract
The on-demand generation and separation of entangled photon pairs are key components of quantum information processing in quantum optics. In an electronic analogue, the decomposition of electron pairs represents an essential building block for using the quantum state of ballistic electrons in electron quantum optics. The scattering of electrons has been used to probe the particle statistics of stochastic sources in Hanbury Brown and Twiss experiments and the recent advent of on-demand sources further offers the possibility to achieve indistinguishability between multiple sources in Hong-Ou-Mandel experiments. Cooper pairs impinging stochastically at a mesoscopic beamsplitter have been successfully partitioned, as verified by measuring the coincidence of arrival. Here, we demonstrate the splitting of electron pairs generated on demand. Coincidence correlation measurements allow the reconstruction of the full counting statistics, revealing regimes of statistically independent, distinguishable or correlated partitioning, and have been envisioned as a source of information on the quantum state of the electron pair. The high pair-splitting fidelity opens a path to future on-demand generation of spin-entangled electron pairs from a suitably prepared two-electron quantum-dot ground state.
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Affiliation(s)
- Niels Ubbelohde
- Institut für Festkörperphysik, Leibniz Universität Hannover, 30167 Hannover, Germany
| | - Frank Hohls
- Physikalisch-Technische Bundesanstalt, 38116 Braunschweig, Germany
| | | | - Timo Wagner
- Institut für Festkörperphysik, Leibniz Universität Hannover, 30167 Hannover, Germany
| | - Lukas Fricke
- Physikalisch-Technische Bundesanstalt, 38116 Braunschweig, Germany
| | - Bernd Kästner
- Physikalisch-Technische Bundesanstalt, 38116 Braunschweig, Germany
| | - Klaus Pierz
- Physikalisch-Technische Bundesanstalt, 38116 Braunschweig, Germany
| | | | - Rolf J Haug
- Institut für Festkörperphysik, Leibniz Universität Hannover, 30167 Hannover, Germany
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50
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Schroer A, Braunecker B, Levy Yeyati A, Recher P. Detection of spin entanglement via spin-charge separation in crossed Tomonaga-Luttinger liquids. PHYSICAL REVIEW LETTERS 2014; 113:266401. [PMID: 25615359 DOI: 10.1103/physrevlett.113.266401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/17/2014] [Indexed: 06/04/2023]
Abstract
We investigate tunneling between two spinful Tomonaga-Luttinger liquids (TLLs) realized, e.g., as two crossed nanowires or quantum Hall edge states. When injecting into each TLL one electron of opposite spin, the dc current measured after the crossing differs for singlet, triplet, or product states. This is a striking new non-Fermi liquid feature because the (mean) current in a noninteracting beam splitter is insensitive to spin entanglement. It can be understood in terms of collective excitations subject to spin-charge separation. This behavior may offer an easier alternative to traditional entanglement detection schemes based on current noise, which we show to be suppressed by the interactions.
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Affiliation(s)
- Alexander Schroer
- Institut für Mathematische Physik, Technische Universität Braunschweig, D-38106 Braunschweig, Germany
| | - Bernd Braunecker
- Scottish Universities Physics Alliance, School of Physics and Astronomy, University of St Andrews, North Haugh, St Andrews KY16 9SS, United Kingdom
| | - Alfredo Levy Yeyati
- Departamento de Física Teórica de la Materia Condensada, Condensed Matter Physics Center (IFIMAC), and Instituto Nicolás Cabrera, Universidad Autónoma de Madrid, E-28049 Madrid, Spain
| | - Patrik Recher
- Institut für Mathematische Physik, Technische Universität Braunschweig, D-38106 Braunschweig, Germany and Interactive Research Center of Science, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro, Tokyo 152-8551, Japan
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