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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Yazdani A, von Oppen F, Halperin BI, Yacoby A. Hunting for Majoranas. Science 2023; 380:eade0850. [PMID: 37347870 DOI: 10.1126/science.ade0850] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/25/2022] [Accepted: 05/22/2023] [Indexed: 06/24/2023]
Abstract
Over the past decade, there have been considerable efforts to observe non-abelian quasiparticles in novel quantum materials and devices. These efforts are motivated by the goals of demonstrating quantum statistics of quasiparticles beyond those of fermions and bosons and of establishing the underlying science for the creation of topologically protected quantum bits. In this Review, we focus on efforts to create topological superconducting phases that host Majorana zero modes. We consider the lessons learned from existing experimental efforts, which are motivating both improvements to present platforms and the exploration of new approaches. Although the experimental detection of non-abelian quasiparticles remains challenging, the knowledge gained thus far and the opportunities ahead offer high potential for discovery and advances in this exciting area of quantum physics.
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Affiliation(s)
- Ali Yazdani
- Joseph Henry Laboratories and Department of Physics, Princeton University, Princeton, NJ 08540, USA
| | - Felix von Oppen
- Dahlem Center for Complex Quantum Systems and Fachbereich Physik, Freie Universität Berlin, 14195 Berlin, Germany
| | | | - Amir Yacoby
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
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3
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Vekris A, Estrada Saldaña JC, Kanne T, Hvid-Olsen T, Marnauza M, Olsteins D, Wauters MM, Burrello M, Nygård J, Grove-Rasmussen K. Electronic Transport in Double-Nanowire Superconducting Islands with Multiple Terminals. NANO LETTERS 2022; 22:5765-5772. [PMID: 35833741 DOI: 10.1021/acs.nanolett.2c01161] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/15/2023]
Abstract
We characterize in situ grown parallel nanowires bridged by a superconducting island. The magnetic-field and temperature dependence of Coulomb blockade peaks measured across different pairs of nanowire ends suggest the presence of a subgap state extended over the hybrid parallel-nanowire island. Being gate-tunable, accessible by multiple terminals, and free of quasiparticle poisoning, these nanowires show promise for the implementation of several proposals that rely on parallel nanowire platforms.
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Affiliation(s)
- Alexandros Vekris
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark
- Sino-Danish Center for Education and Research (SDC) SDC Building, Yanqihu Campus, University of Chinese Academy of Sciences, 380 Huaibeizhuang, Huairou District, 101408 Beijing, China
| | | | - Thomas Kanne
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark
| | - Thor Hvid-Olsen
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark
| | - Mikelis Marnauza
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark
| | - Dags Olsteins
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark
| | - Matteo M Wauters
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark
- Niels Bohr International Academy, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark
| | - Michele Burrello
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark
- Niels Bohr International Academy, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark
| | - Jesper Nygård
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark
| | - Kasper Grove-Rasmussen
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark
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4
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Nielsen IE, Flensberg K, Egger R, Burrello M. Readout of Parafermionic States by Transport Measurements. PHYSICAL REVIEW LETTERS 2022; 129:037703. [PMID: 35905364 DOI: 10.1103/physrevlett.129.037703] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/13/2021] [Accepted: 05/12/2022] [Indexed: 06/15/2023]
Abstract
Recent experiments have demonstrated the possibility of inducing superconducting pairing into counterpropagating fractional quantum Hall edge modes. This paves the way for the realization of localized parafermionic modes, non-Abelian anyons that share fractional charges in a nonlocal way. We show that, for a pair of isolated parafermions, this joint degree of freedom can be read by conductance measurements across standard metallic electrodes. We propose two complementary setups. We investigate first the transport through a grounded superconductor hosting two interacting parafermions. In the low-energy limit, its conductance peaks reveal their shared fractional charge yielding a three-state telegraph noise for weak quasiparticle poisoning. We then examine the two-terminal electron conductance of a blockaded fractional topological superconductor, which displays a characteristic e/3 periodicity of its zero-bias peaks in the deep topological regime, thus signaling the presence of parafermionic modes.
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Affiliation(s)
- Ida E Nielsen
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, DK-2100 Copenhagen, Denmark
- Niels Bohr International Academy, University of Copenhagen, DK-2100 Copenhagen, Denmark
| | - Karsten Flensberg
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, DK-2100 Copenhagen, Denmark
| | - Reinhold Egger
- Institut für Theoretische Physik, Heinrich Heine Universität, D-40225 Düsseldorf, Germany
| | - Michele Burrello
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, DK-2100 Copenhagen, Denmark
- Niels Bohr International Academy, University of Copenhagen, DK-2100 Copenhagen, Denmark
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5
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Zhou T, Dartiailh MC, Sardashti K, Han JE, Matos-Abiague A, Shabani J, Žutić I. Fusion of Majorana bound states with mini-gate control in two-dimensional systems. Nat Commun 2022; 13:1738. [PMID: 35365644 PMCID: PMC8976011 DOI: 10.1038/s41467-022-29463-6] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/21/2021] [Accepted: 03/16/2022] [Indexed: 11/09/2022] Open
Abstract
A hallmark of topological superconductivity is the non-Abelian statistics of Majorana bound states (MBS), its chargeless zero-energy emergent quasiparticles. The resulting fractionalization of a single electron, stored nonlocally as a two spatially-separated MBS, provides a powerful platform for implementing fault-tolerant topological quantum computing. However, despite intensive efforts, experimental support for MBS remains indirect and does not probe their non-Abelian statistics. Here we propose how to overcome this obstacle in mini-gate controlled planar Josephson junctions (JJs) and demonstrate non-Abelian statistics through MBS fusion, detected by charge sensing using a quantum point contact, based on dynamical simulations. The feasibility of preparing, manipulating, and fusing MBS in two-dimensional (2D) systems is supported in our experiments which demonstrate the gate control of topological transition and superconducting properties with five mini gates in InAs/Al-based JJs. While we focus on this well-established platform, where the topological superconductivity was already experimentally detected, our proposal to identify elusive non-Abelian statistics motivates also further MBS studies in other gate-controlled 2D systems.
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Affiliation(s)
- Tong Zhou
- Department of Physics, University at Buffalo, State University of New York, Buffalo, NY, 14260, USA.
| | - Matthieu C Dartiailh
- Center for Quantum Phenomena, Department of Physics, New York University, New York, NY, 10003, USA
| | - Kasra Sardashti
- Center for Quantum Phenomena, Department of Physics, New York University, New York, NY, 10003, USA
| | - Jong E Han
- Department of Physics, University at Buffalo, State University of New York, Buffalo, NY, 14260, USA
| | - Alex Matos-Abiague
- Department of Physics and Astronomy, Wayne State University, Detroit, MI, 48201, USA
| | - Javad Shabani
- Center for Quantum Phenomena, Department of Physics, New York University, New York, NY, 10003, USA
| | - Igor Žutić
- Department of Physics, University at Buffalo, State University of New York, Buffalo, NY, 14260, USA.
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6
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Marra P, Nigro A. Majorana/Andreev crossover and the fate of the topological phase transition in inhomogeneous nanowires. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2022; 34:124001. [PMID: 34929683 DOI: 10.1088/1361-648x/ac44d2] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/31/2021] [Accepted: 12/20/2021] [Indexed: 06/14/2023]
Abstract
Majorana bound states (MBS) and Andreev bound states (ABS) in realistic Majorana nanowires setups have similar experimental signatures which make them hard to distinguishing one from the other. Here, we characterize the continuous Majorana/Andreev crossover interpolating between fully-separated, partially-separated, and fully-overlapping Majorana modes, in terms of global and local topological invariants, fermion parity, quasiparticle densities, Majorana pseudospin and spin polarizations, density overlaps and transition probabilities between opposite Majorana components. We found that in inhomogeneous wires, the transition between fully-overlapping trivial ABS and nontrivial MBS does not necessarily mandate the closing of the bulk gap of quasiparticle excitations, but a simple parity crossing of partially-separated Majorana modes (ps-MM) from trivial to nontrivial regimes. We demonstrate that fully-separated and fully-overlapping Majorana modes correspond to the two limiting cases at the opposite sides of a continuous crossover: the only distinction between the two can be obtained by estimating the degree of separations of the Majorana components. This result does not contradict the bulk-edge correspondence: indeed, the field inhomogeneities driving the Majorana/Andreev crossover have a length scale comparable with the nanowire length, and therefore correspond to a nonlocal perturbation which breaks the topological protection of the MBS.
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Affiliation(s)
- Pasquale Marra
- Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro, Tokyo 153-8914, Japan
- Department of Physics, and Research and Education Center for Natural Sciences, Keio University, 4-1-1 Hiyoshi, Yokohama, Kanagawa 223-8521, Japan
| | - Angela Nigro
- Dipartimento di Fisica 'E. R. Caianiello', Università degli Studi di Salerno, 84084 Fisciano (Salerno), Italy
- Consiglio Nazionale delle Ricerche CNR-SPIN, UOS Salerno, 84084 Fisciano (Salerno), Italy
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7
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Garnier R, Mathieu-Huart A, Ronga-Pezeret S, Nouyrigat E, Benoit P, Goullé JP, Granon C, Manel J, Manouchehri N, Nisse P, Normand JC, Roulet A, Simon F, Gabach P, Tournoud C. Exposition de la population française à l’arsenic inorganique. Identification de valeurs toxicologiques de référence. TOXICOLOGIE ANALYTIQUE ET CLINIQUE 2020. [DOI: 10.1016/j.toxac.2020.05.004] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
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8
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Impact of ionizing radiation on superconducting qubit coherence. Nature 2020; 584:551-556. [DOI: 10.1038/s41586-020-2619-8] [Citation(s) in RCA: 66] [Impact Index Per Article: 16.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/25/2020] [Accepted: 06/05/2020] [Indexed: 11/09/2022]
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9
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Qin J, Zhao C, Xia B, Wang Z, Liu Y, Guan D, Wang S, Li Y, Zheng H, Liu C, Jia J. Coupling of superconductivity and Coulomb blockade in Sn nanoparticles. NANOTECHNOLOGY 2020; 31:305708. [PMID: 32259801 DOI: 10.1088/1361-6528/ab8763] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
Low dimensional superconductors have many unusual properties. When 0-dimensional superconductors reach the nanometer scale, the superconducting energy gap can be enhanced due to the shell effect. At the same time, the single electron Coulomb blockade effect can also be observed on metal nanoparticles if they are weakly coupled to the environment. So, if a superconducting nanoparticle is isolated well from the environment, the superconducting gap and the Coulomb gap would couple together, making the tunneling spectrum more complicated and interesting. Here Sn nanoparticles were deposited on the surface of STO (111). The charging energy of a nanoparticle mainly depends on its size and is comparable to the superconducting gap when the isolated particle is large enough. The superconducting energy gap can be deduced from the coupling tunneling spectrum and the shell effect is observed. The method to deduce the superconducting gap here is simpler than when fit using the Dynes density of states. Owing to the increased superconducting gap and critical field, the studied nanoparticles may find applications in studies of the properties of Majorana fermions.
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Affiliation(s)
- Jin Qin
- Key Laboratory of Artificial Structures and Quantum Control (Ministry of Education), School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, People's Republic of China
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10
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Zhou T, Dartiailh MC, Mayer W, Han JE, Matos-Abiague A, Shabani J, Žutić I. Phase Control of Majorana Bound States in a Topological X Junction. PHYSICAL REVIEW LETTERS 2020; 124:137001. [PMID: 32302171 DOI: 10.1103/physrevlett.124.137001] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/08/2019] [Accepted: 02/19/2020] [Indexed: 06/11/2023]
Abstract
Topological superconductivity supports exotic Majorana bound states (MBS) which are chargeless zero-energy emergent quasiparticles. With their non-Abelian exchange statistics and fractionalization of a single electron stored nonlocally as a spatially separated MBS, they are particularly suitable for implementing fault-tolerant topological quantum computing. While realizing MBS has focused on one-dimensional systems, the onset of topological superconductivity requires delicate parameter tuning and geometric constraints pose significant challenges for their control and demonstration of non-Abelian statistics. To overcome these challenges, building on recent experiments in planar Josephson junctions (JJs), we propose a MBS platform of X-shaped JJs. This versatile implementation reveals how external flux control of the superconducting phase difference can generate and manipulate multiple MBS pairs to probe non-Abelian statistics. The underlying topological superconductivity exists over a large parameter space, consistent with materials used in our fabrication of such X junctions, as an important step towards scalable topological quantum computing.
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Affiliation(s)
- Tong Zhou
- Department of Physics, University at Buffalo, State University of New York, Buffalo, New York 14260, USA
| | - Matthieu C Dartiailh
- Center for Quantum Phenomena, Department of Physics, New York University, New York, New York 10003, USA
| | - William Mayer
- Center for Quantum Phenomena, Department of Physics, New York University, New York, New York 10003, USA
| | - Jong E Han
- Department of Physics, University at Buffalo, State University of New York, Buffalo, New York 14260, USA
| | - Alex Matos-Abiague
- Department of Physics and Astronomy, Wayne State University, Detroit, Michigan 48201, USA
| | - Javad Shabani
- Center for Quantum Phenomena, Department of Physics, New York University, New York, New York 10003, USA
| | - Igor Žutić
- Department of Physics, University at Buffalo, State University of New York, Buffalo, New York 14260, USA
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11
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Danon J, Hellenes AB, Hansen EB, Casparis L, Higginbotham AP, Flensberg K. Nonlocal Conductance Spectroscopy of Andreev Bound States: Symmetry Relations and BCS Charges. PHYSICAL REVIEW LETTERS 2020; 124:036801. [PMID: 32031855 DOI: 10.1103/physrevlett.124.036801] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/02/2019] [Indexed: 06/10/2023]
Abstract
Two-terminal conductance spectroscopy of superconducting devices is a common tool for probing Andreev and Majorana bound states. Here, we study theoretically a three-terminal setup, with two normal leads coupled to a grounded superconducting terminal. Using a single-electron scattering matrix, we derive the subgap conductance matrix for the normal leads and discuss its symmetries. In particular, we show that the local and the nonlocal elements of the conductance matrix have pairwise identical antisymmetric components. Moreover, we find that the nonlocal elements are directly related to the local BCS charges of the bound states close to the normal probes and we show how the BCS charge of overlapping Majorana bound states can be extracted from experiments.
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Affiliation(s)
- Jeroen Danon
- Center for Quantum Spintronics, Department of Physics, Norwegian University of Science and Technology, NO-7491 Trondheim, Norway
| | - Anna Birk Hellenes
- Center for Quantum Devices, Niels Bohr Institute, 2100 Copenhagen, Denmark
| | - Esben Bork Hansen
- Center for Quantum Devices, Niels Bohr Institute, 2100 Copenhagen, Denmark
| | - Lucas Casparis
- Center for Quantum Devices, Niels Bohr Institute, 2100 Copenhagen, Denmark
- Microsoft Quantum-Copenhagen, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark
| | - Andrew P Higginbotham
- Center for Quantum Devices, Niels Bohr Institute, 2100 Copenhagen, Denmark
- Microsoft Quantum-Copenhagen, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark
| | - Karsten Flensberg
- Center for Quantum Devices, Niels Bohr Institute, 2100 Copenhagen, Denmark
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12
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Ridderbos J, Brauns M, de Vries FK, Shen J, Li A, Kölling S, Verheijen MA, Brinkman A, van der Wiel WG, Bakkers EPAM, Zwanenburg FA. Hard Superconducting Gap and Diffusion-Induced Superconductors in Ge-Si Nanowires. NANO LETTERS 2020; 20:122-130. [PMID: 31771328 PMCID: PMC6953474 DOI: 10.1021/acs.nanolett.9b03438] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/21/2019] [Revised: 11/19/2019] [Indexed: 05/28/2023]
Abstract
We show a hard superconducting gap in a Ge-Si nanowire Josephson transistor up to in-plane magnetic fields of 250 mT, an important step toward creating and detecting Majorana zero modes in this system. A hard gap requires a highly homogeneous tunneling heterointerface between the superconducting contacts and the semiconducting nanowire. This is realized by annealing devices at 180 °C during which aluminum interdiffuses and replaces the germanium in a section of the nanowire. Next to Al, we find a superconductor with lower critical temperature (TC = 0.9 K) and a higher critical field (BC = 0.9-1.2 T). We can therefore selectively switch either superconductor to the normal state by tuning the temperature and the magnetic field and observe that the additional superconductor induces a proximity supercurrent in the semiconducting part of the nanowire even when the Al is in the normal state. In another device where the diffusion of Al rendered the nanowire completely metallic, a superconductor with a much higher critical temperature (TC = 2.9 K) and critical field (BC = 3.4 T) is found. The small size of these diffusion-induced superconductors inside nanowires may be of special interest for applications requiring high magnetic fields in arbitrary direction.
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Affiliation(s)
- Joost Ridderbos
- MESA
+ Institute for Nanotechnology, University
of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands
| | - Matthias Brauns
- QuTech
and Kavli Institute of Nanoscience, Delft
University of Technology, 2600 GA Delft, The Netherlands
| | - Folkert K. de Vries
- MESA
+ Institute for Nanotechnology, University
of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands
| | - Jie Shen
- QuTech
and Kavli Institute of Nanoscience, Delft
University of Technology, 2600 GA Delft, The Netherlands
| | - Ang Li
- Department
of Applied Physics, Eindhoven University
of Technology, Postbox 513, 5600 MB Eindhoven, The Netherlands
| | - Sebastian Kölling
- Department
of Applied Physics, Eindhoven University
of Technology, Postbox 513, 5600 MB Eindhoven, The Netherlands
| | - Marcel A. Verheijen
- Department
of Applied Physics, Eindhoven University
of Technology, Postbox 513, 5600 MB Eindhoven, The Netherlands
| | - Alexander Brinkman
- MESA
+ Institute for Nanotechnology, University
of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands
| | - Wilfred G. van der Wiel
- MESA
+ Institute for Nanotechnology, University
of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands
| | - Erik P. A. M. Bakkers
- Department
of Applied Physics, Eindhoven University
of Technology, Postbox 513, 5600 MB Eindhoven, The Netherlands
| | - Floris A. Zwanenburg
- MESA
+ Institute for Nanotechnology, University
of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands
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13
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Cao Z, Zhang H, Lü HF, He WX, Lu HZ, Xie XC. Decays of Majorana or Andreev Oscillations Induced by Steplike Spin-Orbit Coupling. PHYSICAL REVIEW LETTERS 2019; 122:147701. [PMID: 31050472 DOI: 10.1103/physrevlett.122.147701] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/07/2018] [Indexed: 06/09/2023]
Abstract
The Majorana zero mode in the semiconductor-superconductor nanowire is one of the promising candidates for topological quantum computing. Recently, in islands of nanowires, subgap-state energies have been experimentally observed to oscillate as a function of the magnetic field, showing a signature of overlapped Majorana bound states. However, the oscillation amplitude either dies away after an overshoot or decays, sharply opposite to the theoretically predicted enhanced oscillations for Majorana bound states. We reveal that a steplike distribution of spin-orbit coupling in realistic devices can induce the decaying Majorana oscillations, resulting from the coupling-induced energy repulsion between the quasiparticle spectra on the two sides of the step. This steplike spin-orbit coupling can also lead to decaying oscillations in the spectrum of the Andreev bound states. For Coulomb-blockade peaks mediated by the Majorana bound states, the peak spacings have been predicted to correlate with peak heights by a π/2 phase shift, which was ambiguous in recent experiments and may be explained by the steplike spin-orbit coupling. Our work will inspire more works to reexamine effects of the nonuniform spin-orbit coupling, which is generally present in experimental devices.
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Affiliation(s)
- Zhan Cao
- Shenzhen Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China
- School of Physics, Southeast University, Nanjing 211189, China
- Peng Cheng Laboratory, Shenzhen 518055, China
- Shenzhen Key Laboratory of Quantum Science and Engineering, Shenzhen 518055, China
| | - Hao Zhang
- State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, China
- Beijing Academy of Quantum Information Sciences, Beijing 100193, China
| | - Hai-Feng Lü
- School of Physics, University of Electronic Science and Technology of China, Chengdu 610054, China
| | - Wan-Xiu He
- Center for Interdisciplinary Studies and Key Laboratory for Magnetism and Magnetic Materials of the Ministry of Education, Lanzhou University, Lanzhou 730000, China
| | - Hai-Zhou Lu
- Shenzhen Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China
- Peng Cheng Laboratory, Shenzhen 518055, China
- Shenzhen Key Laboratory of Quantum Science and Engineering, Shenzhen 518055, China
| | - X C Xie
- Beijing Academy of Quantum Information Sciences, Beijing 100193, China
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
- CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences, Beijing 100190, China
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14
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O'Farrell ECT, Drachmann ACC, Hell M, Fornieri A, Whiticar AM, Hansen EB, Gronin S, Gardner GC, Thomas C, Manfra MJ, Flensberg K, Marcus CM, Nichele F. Hybridization of Subgap States in One-Dimensional Superconductor-Semiconductor Coulomb Islands. PHYSICAL REVIEW LETTERS 2018; 121:256803. [PMID: 30608825 DOI: 10.1103/physrevlett.121.256803] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/25/2018] [Indexed: 06/09/2023]
Abstract
We present measurements of one-dimensional superconductor-semiconductor Coulomb islands, fabricated by gate confinement of a two-dimensional InAs heterostructure with an epitaxial Al layer. When tuned via electrostatic side gates to regimes without subgap states, Coulomb blockade reveals Cooper-pair mediated transport. When subgap states are present, Coulomb peak positions and heights oscillate in a correlated way with magnetic field and gate voltage, as predicted theoretically, with (anti)crossings in (parallel) transverse magnetic field indicating Rashba-type spin-orbit coupling. Overall results are consistent with a picture of overlapping Majorana zero modes in finite wires.
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Affiliation(s)
- E C T O'Farrell
- Center for Quantum Devices and Station Q Copenhagen, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
| | - A C C Drachmann
- Center for Quantum Devices and Station Q Copenhagen, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
| | - M Hell
- Center for Quantum Devices and Station Q Copenhagen, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
- Division of Solid State Physics and NanoLund, Lund University, Box 118, S-22100 Lund, Sweden
| | - A Fornieri
- Center for Quantum Devices and Station Q Copenhagen, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
| | - A M Whiticar
- Center for Quantum Devices and Station Q Copenhagen, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
| | - E B Hansen
- Center for Quantum Devices and Station Q Copenhagen, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
| | - S Gronin
- Department of Physics and Astronomy and Station Q Purdue, Purdue University, West Lafayette, Indiana 47907, USA
- Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907, USA
| | - G C Gardner
- Department of Physics and Astronomy and Station Q Purdue, Purdue University, West Lafayette, Indiana 47907, USA
- Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907, USA
| | - C Thomas
- Department of Physics and Astronomy and Station Q Purdue, Purdue University, West Lafayette, Indiana 47907, USA
- Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907, USA
| | - M J Manfra
- Department of Physics and Astronomy and Station Q Purdue, Purdue University, West Lafayette, Indiana 47907, USA
- Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907, USA
- School of Materials Engineering, Purdue University, West Lafayette, Indiana 47907, USA
- School of Electrical and Computer Engineering, Purdue University, West Lafayette, Indiana 47907, USA
| | - K Flensberg
- Center for Quantum Devices and Station Q Copenhagen, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
| | - C M Marcus
- Center for Quantum Devices and Station Q Copenhagen, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
| | - F Nichele
- Center for Quantum Devices and Station Q Copenhagen, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
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15
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Shen J, Heedt S, Borsoi F, van Heck B, Gazibegovic S, Op Het Veld RLM, Car D, Logan JA, Pendharkar M, Ramakers SJJ, Wang G, Xu D, Bouman D, Geresdi A, Palmstrøm CJ, Bakkers EPAM, Kouwenhoven LP. Parity transitions in the superconducting ground state of hybrid InSb-Al Coulomb islands. Nat Commun 2018; 9:4801. [PMID: 30442935 PMCID: PMC6237907 DOI: 10.1038/s41467-018-07279-7] [Citation(s) in RCA: 38] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/03/2018] [Accepted: 10/22/2018] [Indexed: 12/03/2022] Open
Abstract
The number of electrons in small metallic or semiconducting islands is quantised. When tunnelling is enabled via opaque barriers this number can change by an integer. In superconductors the addition is in units of two electron charges (2e), reflecting that the Cooper pair condensate must have an even parity. This ground state (GS) is foundational for all superconducting qubit devices. Here, we study a hybrid superconducting–semiconducting island and find three typical GS evolutions in a parallel magnetic field: a robust 2e-periodic even-parity GS, a transition to a 2e-periodic odd-parity GS, and a transition from a 2e- to a 1e-periodic GS. The 2e-periodic odd-parity GS persistent in gate-voltage occurs when a spin-resolved subgap state crosses zero energy. For our 1e-periodic GSs we explicitly show the origin being a single zero-energy state gapped from the continuum, i.e., compatible with an Andreev bound states stabilized at zero energy or the presence of Majorana zero modes. Understanding the ground state (GS) phase transitions in the quantum tunneling regime of a superconducting system is important for future qubit devices. Here, Shen, Heedt and Borsoi et al. report distinct types of fermion parity GS transitions as a function of magnetic field and gate voltages in a Coulomb-blockaded InSb–Al island.
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Affiliation(s)
- Jie Shen
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology, 2600 GA, Delft, The Netherlands.
| | - Sebastian Heedt
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology, 2600 GA, Delft, The Netherlands
| | - Francesco Borsoi
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology, 2600 GA, Delft, The Netherlands
| | - Bernard van Heck
- Microsoft Quantum, Microsoft Station Q, University of California Santa Barbara, Santa Barbara, CA, 93106, USA
| | - Sasa Gazibegovic
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology, 2600 GA, Delft, The Netherlands.,Department of Applied Physics, Eindhoven University of Technology, 5600 MB, Eindhoven, The Netherlands
| | - Roy L M Op Het Veld
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology, 2600 GA, Delft, The Netherlands.,Department of Applied Physics, Eindhoven University of Technology, 5600 MB, Eindhoven, The Netherlands
| | - Diana Car
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology, 2600 GA, Delft, The Netherlands.,Department of Applied Physics, Eindhoven University of Technology, 5600 MB, Eindhoven, The Netherlands
| | - John A Logan
- Materials Department, University of California Santa Barbara, Santa Barbara, CA, 93106, USA
| | - Mihir Pendharkar
- Electrical and Computer Engineering, University of California Santa Barbara, Santa Barbara, CA, 93106, USA
| | - Senja J J Ramakers
- 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
| | - Di Xu
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology, 2600 GA, Delft, The Netherlands
| | - Daniël Bouman
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology, 2600 GA, Delft, The Netherlands
| | - Attila Geresdi
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology, 2600 GA, Delft, The Netherlands
| | - Chris J Palmstrøm
- Materials Department, University of California Santa Barbara, Santa Barbara, CA, 93106, USA.,Electrical and Computer Engineering, University of California Santa Barbara, Santa Barbara, CA, 93106, USA
| | - Erik P A M Bakkers
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology, 2600 GA, 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, 2600 GA, Delft, The Netherlands. .,Microsoft Station Q at Delft University of Technology, 2600 GA, Delft, The Netherlands.
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16
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Serniak K, Hays M, de Lange G, Diamond S, Shankar S, Burkhart LD, Frunzio L, Houzet M, Devoret MH. Hot Nonequilibrium Quasiparticles in Transmon Qubits. PHYSICAL REVIEW LETTERS 2018; 121:157701. [PMID: 30362798 DOI: 10.1103/physrevlett.121.157701] [Citation(s) in RCA: 28] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/02/2018] [Revised: 07/27/2018] [Indexed: 06/08/2023]
Abstract
Nonequilibrium quasiparticle excitations degrade the performance of a variety of superconducting circuits. Understanding the energy distribution of these quasiparticles will yield insight into their generation mechanisms, the limitations they impose on superconducting devices, and how to efficiently mitigate quasiparticle-induced qubit decoherence. To probe this energy distribution, we systematically correlate qubit relaxation and excitation with charge-parity switches in an offset-charge-sensitive transmon qubit, and find that quasiparticle-induced excitation events are the dominant mechanism behind the residual excited-state population in our samples. By itself, the observed quasiparticle distribution would limit T_{1} to ≈200 μs, which indicates that quasiparticle loss in our devices is on equal footing with all other loss mechanisms. Furthermore, the measured rate of quasiparticle-induced excitation events is greater than that of relaxation events, which signifies that the quasiparticles are more energetic than would be predicted from a thermal distribution describing their apparent density.
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Affiliation(s)
- K Serniak
- Department of Applied Physics, Yale University, New Haven, Connecticut 06520, USA
| | - M Hays
- Department of Applied Physics, Yale University, New Haven, Connecticut 06520, USA
| | - G de Lange
- Department of Applied Physics, Yale University, New Haven, Connecticut 06520, USA
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology, 2600 GA Delft, Netherlands
| | - S Diamond
- Department of Applied Physics, Yale University, New Haven, Connecticut 06520, USA
| | - S Shankar
- Department of Applied Physics, Yale University, New Haven, Connecticut 06520, USA
| | - L D Burkhart
- Department of Applied Physics, Yale University, New Haven, Connecticut 06520, USA
| | - L Frunzio
- Department of Applied Physics, Yale University, New Haven, Connecticut 06520, USA
| | - M Houzet
- Univ. Grenoble Alpes, CEA, INAC-Pheliqs, F-38000 Grenoble, France
| | - M H Devoret
- Department of Applied Physics, Yale University, New Haven, Connecticut 06520, USA
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17
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Ren C, Wu Y, Sun M, Wang S, Tian H. Manifestation of topological transitions in a multi-terminal Josephson junction. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2018; 30:385503. [PMID: 30124432 DOI: 10.1088/1361-648x/aadb6f] [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 study nonequilibrium (NE) transport in four-terminal (three-terminal) topological superconductor (SC)-quantum dot (QD) topological superconductor junctions, where the QD is connected via tunneling barriers to the two TS leads and two (one) normal leads (N), respectively. For the four-terminal junction, we find that when increasing the Zeeman field from 0 to a critical value, the supercurrent profile evolves from a typical s-wave pattern to a pure p-wave pattern. In addition, by analyzing the zero-phase difference supercurrent as a function of voltage [Formula: see text] applied to the normal leads and the Zeeman field h applied to the SC, the low-momentum gap [Formula: see text] can be inferred by utilizing the fact that the emergence of a tunneling-induced current should be satisfied under the condition [Formula: see text]. For the three-terminal junction, the NE supercurrent can reveal the quasi-Andreev bound state by exploiting the Andreev reflection process-induced current occurring between the N and SC. Our findings provide an arguably easier route for manifesting the topological phase transition by observing the gap collapse and then reopening as the Zeeman field increases through multi-terminal NE transport.
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Affiliation(s)
- Chongdan Ren
- Department of Physics, Zunyi Normal University, Kweichow 563002, People's Republic of China
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18
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Zhao X, Hu X. Toward high-fidelity coherent electron spin transport in a GaAs double quantum dot. Sci Rep 2018; 8:13968. [PMID: 30228299 PMCID: PMC6143546 DOI: 10.1038/s41598-018-31879-4] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/06/2018] [Accepted: 08/14/2018] [Indexed: 11/18/2022] Open
Abstract
In this paper, we investigate how to achieve high-fidelity electron spin transport in a GaAs double quantum dot. Our study examines fidelity loss in spin transport from multiple perspectives. We first study incoherent fidelity loss due to hyperfine and spin-orbit interaction. We calculate fidelity loss due to the random Overhauser field from hyperfine interaction, and spin relaxation rate due to spin-orbit interaction in a wide range of experimental parameters with a focus on the occurrence of spin hot spots. A safe parameter regime is identified in order to avoid these spin hot spots. We then analyze systematic errors due to non-adiabatic transitions in the Landau-Zener process of sweeping the interdot detuning, and propose a scheme to take advantage of possible Landau-Zener-Stückelberg interference to achieve high-fidelity spin transport at a higher speed. At last, we study another systematic error caused by the correction to the electron g-factor from the double dot potential, which can lead to a notable phase error. In all, our results should provide a useful guidance for future experiments on coherent electron spin transport.
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Affiliation(s)
- Xinyu Zhao
- Department of Physics, University at Buffalo, SUNY, Buffalo, New York, 14260-1500, USA
| | - Xuedong Hu
- Department of Physics, University at Buffalo, SUNY, Buffalo, New York, 14260-1500, USA.
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19
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Hays M, de Lange G, Serniak K, van Woerkom DJ, Bouman D, Krogstrup P, Nygård J, Geresdi A, Devoret MH. Direct Microwave Measurement of Andreev-Bound-State Dynamics in a Semiconductor-Nanowire Josephson Junction. PHYSICAL REVIEW LETTERS 2018; 121:047001. [PMID: 30095962 DOI: 10.1103/physrevlett.121.047001] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/22/2017] [Indexed: 06/08/2023]
Abstract
The modern understanding of the Josephson effect in mesosopic devices derives from the physics of Andreev bound states, fermionic modes that are localized in a superconducting weak link. Recently, Josephson junctions constructed using semiconducting nanowires have led to the realization of superconducting qubits with gate-tunable Josephson energies. We have used a microwave circuit QED architecture to detect Andreev bound states in such a gate-tunable junction based on an aluminum-proximitized indium arsenide nanowire. We demonstrate coherent manipulation of these bound states, and track the bound-state fermion parity in real time. Individual parity-switching events due to nonequilibrium quasiparticles are observed with a characteristic timescale T_{parity}=160±10 μs. The T_{parity} of a topological nanowire junction sets a lower bound on the bandwidth required for control of Majorana bound states.
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Affiliation(s)
- M Hays
- Department of Applied Physics, Yale University, New Haven, Connecticut 06520, USA
| | - G de Lange
- Department of Applied Physics, Yale University, New Haven, Connecticut 06520, USA
- QuTech and Delft University of Technology, 2600 GA Delft, Netherlands
- Kavli Institute of Nanoscience, Delft University of Technology, 2600 GA Delft, Netherlands
| | - K Serniak
- Department of Applied Physics, Yale University, New Haven, Connecticut 06520, USA
| | - D J van Woerkom
- QuTech and Delft University of Technology, 2600 GA Delft, Netherlands
- Kavli Institute of Nanoscience, Delft University of Technology, 2600 GA Delft, Netherlands
| | - D Bouman
- QuTech and Delft University of Technology, 2600 GA Delft, Netherlands
- Kavli Institute of Nanoscience, Delft University of Technology, 2600 GA Delft, Netherlands
| | - P Krogstrup
- Center for Quantum Devices and Station Q Copenhagen, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
| | - J Nygård
- Center for Quantum Devices and Station Q Copenhagen, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
| | - A Geresdi
- QuTech and Delft University of Technology, 2600 GA Delft, Netherlands
- Kavli Institute of Nanoscience, Delft University of Technology, 2600 GA Delft, Netherlands
| | - M H Devoret
- Department of Applied Physics, Yale University, New Haven, Connecticut 06520, USA
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20
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Zazunov A, Iks A, Alvarado M, Levy Yeyati A, Egger R. Josephson effect in junctions of conventional and topological superconductors. BEILSTEIN JOURNAL OF NANOTECHNOLOGY 2018; 9:1659-1676. [PMID: 29977700 PMCID: PMC6009709 DOI: 10.3762/bjnano.9.158] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 01/30/2018] [Accepted: 04/27/2018] [Indexed: 06/08/2023]
Abstract
We present a theoretical analysis of the equilibrium Josephson current-phase relation in hybrid devices made of conventional s-wave spin-singlet superconductors (S) and topological superconductor (TS) wires featuring Majorana end states. Using Green's function techniques, the topological superconductor is alternatively described by the low-energy continuum limit of a Kitaev chain or by a more microscopic spinful nanowire model. We show that for the simplest S-TS tunnel junction, only the s-wave pairing correlations in a spinful TS nanowire model can generate a Josephson effect. The critical current is much smaller in the topological regime and exhibits a kink-like dependence on the Zeeman field along the wire. When a correlated quantum dot (QD) in the magnetic regime is present in the junction region, however, the Josephson current becomes finite also in the deep topological phase as shown for the cotunneling regime and by a mean-field analysis. Remarkably, we find that the S-QD-TS setup can support φ0-junction behavior, where a finite supercurrent flows at vanishing phase difference. Finally, we also address a multi-terminal S-TS-S geometry, where the TS wire acts as tunable parity switch on the Andreev bound states in a superconducting atomic contact.
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Affiliation(s)
- Alex Zazunov
- Institut für Theoretische Physik, Heinrich-Heine-Universität, D-40225 Düsseldorf, Germany
| | - Albert Iks
- Institut für Theoretische Physik, Heinrich-Heine-Universität, D-40225 Düsseldorf, Germany
| | - Miguel Alvarado
- Departamento de Física Teórica de la Materia Condensada C-V, Condensed Matter Physics Center (IFIMAC) and Instituto Nicolás Cabrera, Universidad Autónoma de Madrid, E-28049 Madrid, Spain
| | - Alfredo Levy Yeyati
- Departamento de Física Teórica de la Materia Condensada C-V, Condensed Matter Physics Center (IFIMAC) and Instituto Nicolás Cabrera, Universidad Autónoma de Madrid, E-28049 Madrid, Spain
| | - Reinhold Egger
- Institut für Theoretische Physik, Heinrich-Heine-Universität, D-40225 Düsseldorf, Germany
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21
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Ren JT, Lü HF, Ke SS, Guo Y, Zhang HW. Disorder-induced suppression of the zero-bias conductance peak splitting in topological superconducting nanowires. BEILSTEIN JOURNAL OF NANOTECHNOLOGY 2018; 9:1358-1369. [PMID: 29977670 PMCID: PMC6009613 DOI: 10.3762/bjnano.9.128] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 11/16/2017] [Accepted: 03/27/2018] [Indexed: 06/08/2023]
Abstract
We investigate the effect of three types of intrinsic disorder, including that in pairing energy, chemical potential, and hopping amplitude, on the transport properties through the superconducting nanowires with Majorana bound states (MBSs). The conductance and the noise Fano factor are calculated based on a tight-binding model by adopting a non-equilibrium Green's function method. It is found that the disorder can effectively lead to a reduction in the conductance peak spacings and significantly suppress the peak height. Remarkably, for a longer nanowire, the zero-bias peak could be reproduced by weak disorder for a finite Majorana energy splitting. It is interesting that the shot noise provides a signature to discriminate whether the zero-bias peak is induced by Majorana zero mode or disorder. For Majorana zero mode, the noise Fano factor approaches zero in the low bias voltage limit due to the resonant Andreev tunneling. However, the Fano factor is finite in the case of a disorder-induced zero-bias peak.
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Affiliation(s)
- Jun-Tong Ren
- State Key Laboratory of Electronic Thin Films and Integrated Devices and School of Physical Electronics, University of Electronic Science and Technology of China, Chengdu 610054, China
| | - Hai-Feng Lü
- State Key Laboratory of Electronic Thin Films and Integrated Devices and School of Physical Electronics, University of Electronic Science and Technology of China, Chengdu 610054, China
- Department of Physics and State Key Laboratory of Low-Dimensional Quantum Physics, Tsinghua University, Beijing 100084, China
| | - Sha-Sha Ke
- State Key Laboratory of Electronic Thin Films and Integrated Devices and School of Physical Electronics, University of Electronic Science and Technology of China, Chengdu 610054, China
| | - Yong Guo
- Department of Physics and State Key Laboratory of Low-Dimensional Quantum Physics, Tsinghua University, Beijing 100084, China
| | - Huai-Wu Zhang
- State Key Laboratory of Electronic Thin Films and Integrated Devices and School of Physical Electronics, University of Electronic Science and Technology of China, Chengdu 610054, China
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22
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Liu J, Yu T, Song J. Revealing the interference effect of Majorana fermions in a topological Josephson junction. BEILSTEIN JOURNAL OF NANOTECHNOLOGY 2018; 9:520-529. [PMID: 29527429 PMCID: PMC5827801 DOI: 10.3762/bjnano.9.50] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/04/2017] [Accepted: 01/12/2018] [Indexed: 06/09/2023]
Abstract
We study theoretically the local density of states (DOS) in a topological Josephson junction. We show that the well-known 4π Josephson effect originates from the interference effect between two Majorana fermions (MFs) that are localized at the Josephson junction. In addition, the DOS for electrons (holes) shows the 4π interference information along each parity conserved energy spectrum. The DOS displays a 2π period oscillation when two trivial states interfere with each other. This means that the DOS information may be used to distinguish the MFs from trivial localized states. We suggest that the interference effect and the DOS can be detected by using two STM leads or two normal leads. A single side lead can only detect the Andreev reflection tunneling process in the junction, which cannot reveal information about the interference effect in general. However, using two side leads, we can reveal information about the interference effect of the MFs as well as the DOS by combining Andreev reflection with the electron transmission process.
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Affiliation(s)
- Jie Liu
- Department of Applied Physics, School of Science, Xi’an Jiaotong University, Xi’an 710049, China
| | - Tiantian Yu
- Department of Applied Physics, School of Science, Xi’an Jiaotong University, Xi’an 710049, China
| | - Juntao Song
- Department of Physics and Hebei Advanced Thin Film Laboratory, Hebei Normal University, Shijiazhuang 050024, China
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