1
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Khokhlov DA, Akzyanov RS, Kapranov AV. Magnetisation control of the nematicity direction and nodal points in a superconducting doped topological insulator. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2024; 36:455601. [PMID: 39134024 DOI: 10.1088/1361-648x/ad6e49] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/24/2024] [Accepted: 08/12/2024] [Indexed: 08/24/2024]
Abstract
We study the effects of magnetisation on the properties of the doped topological insulator of theBi2Se3family with nematic superconductivity. We found that the direction of the in-plane magnetisation fixes the direction of the nematicity in the system. The chiral state is more favourable than the nematic state for large values of out-of-plane magnetisation. Overall, the critical temperature of the nematic superconductivity is robust against magnetisation. We explore in detail the spectrum of the system with the pinned direction of the nematic order parameterΔy. Without magnetisation, there is a full gap in the spectrum because of finite hexagonal warping. At an out-of-planemzor orthogonal in-planemxmagnetisation that is strong enough, the spectrum is closed at the nodal points that are split by the magnetisation. Flat Majorana surface states connect such split bulk nodal points. Parallel magnetisationmylifts the nodal points and opens a full gap in the spectrum. We discuss relevant experiments and propose experimental verifications of our theory.
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Affiliation(s)
| | - R S Akzyanov
- Dukhov Research Institute of Automatics, Moscow 127055, Russia
- Moscow Institute of Physics and Technology, Dolgoprudny, Moscow Region 141700, Russia
- Institute for Theoretical and Applied Electrodynamics, Russian Academy of Sciences, Moscow 125412, Russia
| | - A V Kapranov
- Dukhov Research Institute of Automatics, Moscow 127055, Russia
- Moscow Institute of Physics and Technology, Dolgoprudny, Moscow Region 141700, Russia
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2
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Máthé L, Kovács-Krausz Z, Botiz I, Grosu I, El Anouz K, El Allati A, Zârbo LP. Phonon-Assisted Tunneling through Quantum Dot Systems Connected to Majorana Bound States. NANOMATERIALS (BASEL, SWITZERLAND) 2023; 13:nano13101616. [PMID: 37242032 DOI: 10.3390/nano13101616] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/08/2023] [Revised: 05/05/2023] [Accepted: 05/08/2023] [Indexed: 05/28/2023]
Abstract
We theoretically analyze phonon-assisted tunneling transport in a quantum dot side connected to a Majorana bound state in a topological superconducting nanowire. We investigate the behavior of the current through the dot, for a range of experimentally relevant parameters, in the presence of one long-wave optical phonon mode. We consider the current-gate voltage, the current-bias voltage and the current-dot-Majorana coupling characteristics under the influence of the electron-phonon coupling. In the absence of electron-phonon interaction, the Majorana bound states suppress the current when the gate voltage matches the Fermi level, but the increase in the bias voltage counteracts this effect. In the presence of electron-phonon coupling, the current behaves similarly as a function of the renormalized gate voltage. As an added feature at large bias voltages, it presents a dip or a plateau, depending on the size of the dot-Majorana coupling. Lastly, we show that the currents are most sensitive to, and depend non-trivially on the parameters of the Majorana circuit element, in the regime of low temperatures combined with low voltages. Our results provide insights into the complex physics of quantum dot devices used to probe Majorana bound states.
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Affiliation(s)
- Levente Máthé
- Center of Advanced Research and Technologies for Alternative Energies, National Institute for R & D of Isotopic and Molecular Technologies, 67-103 Donat, 400293 Cluj-Napoca, Romania
- Faculty of Physics, Babeș-Bolyai University, 1 Kogălniceanu, 400084 Cluj-Napoca, Romania
| | - Zoltán Kovács-Krausz
- Department of Physics, Institute of Physics, Budapest University of Technology and Economics, Műegyetem rkp. 3, H-1111 Budapest, Hungary
| | - Ioan Botiz
- Faculty of Physics, Babeș-Bolyai University, 1 Kogălniceanu, 400084 Cluj-Napoca, Romania
- Interdisciplinary Research Institute in Bio-Nano-Sciences, Babeș-Bolyai University, 42 Treboniu Laurian, 400271 Cluj-Napoca, Romania
| | - Ioan Grosu
- Faculty of Physics, Babeș-Bolyai University, 1 Kogălniceanu, 400084 Cluj-Napoca, Romania
| | - Khadija El Anouz
- Laboratory of R & D in Engineering Sciences, Faculty of Sciences and Techniques Al-Hoceima, Abdelmalek Essaadi University, Tetouan 93000, Morocco
| | - Abderrahim El Allati
- Laboratory of R & D in Engineering Sciences, Faculty of Sciences and Techniques Al-Hoceima, Abdelmalek Essaadi University, Tetouan 93000, Morocco
| | - Liviu P Zârbo
- Center of Advanced Research and Technologies for Alternative Energies, National Institute for R & D of Isotopic and Molecular Technologies, 67-103 Donat, 400293 Cluj-Napoca, Romania
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3
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Thamm M, Rosenow B. Machine Learning Optimization of Majorana Hybrid Nanowires. PHYSICAL REVIEW LETTERS 2023; 130:116202. [PMID: 37001061 DOI: 10.1103/physrevlett.130.116202] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/09/2022] [Accepted: 02/21/2023] [Indexed: 06/19/2023]
Abstract
As the complexity of quantum systems such as quantum bit arrays increases, efforts to automate expensive tuning are increasingly worthwhile. We investigate machine learning based tuning of gate arrays using the covariance matrix adaptation evolution strategy algorithm for the case study of Majorana wires with strong disorder. We find that the algorithm is able to efficiently improve the topological signatures, learn intrinsic disorder profiles, and completely eliminate disorder effects. For example, with only 20 gates, it is possible to fully recover Majorana zero modes destroyed by disorder by optimizing gate voltages.
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Affiliation(s)
- Matthias Thamm
- Institut für Theoretische Physik, Universität Leipzig, Brüderstrasse 16, 04103 Leipzig, Germany
| | - Bernd Rosenow
- Institut für Theoretische Physik, Universität Leipzig, Brüderstrasse 16, 04103 Leipzig, Germany
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4
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Zou WK, Wang Q, Zhao HK. Dynamic heat and charge transports through double-quantum-dot-interferometer modulated by Majorana bound states and time-oscillating Aharonov-Bohm flux. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2023; 35:165303. [PMID: 36796103 DOI: 10.1088/1361-648x/acbcb9] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/02/2022] [Accepted: 02/16/2023] [Indexed: 06/18/2023]
Abstract
Dynamic properties of Majorana bound states (MBSs) coupled double-quantum-dot (DQD) interferometer threaded with ac magnetic flux are investigated, and the time-averaged thermal current formulas are derived. Photon-assisted local and nonlocal Andreev reflections contribute efficiently to the charge and heat transports. The modifications of source-drain electric, electric-thermal, thermal conductances (G,ξ,κe), Seebeck coefficient (Sc), and thermoelectric figure of merit (ZT) versus AB phase have been calculated numerically. These coefficients exhibit the shift of oscillation period from 2πto 4πdistinctly due to attaching MBSs. The applied ac flux enhances the magnitudes ofG,ξ,κeobviously, and the detailed enhancing behaviors are relevant to the energy levels of DQD. The enhancements ofScandZTare generated due to the coupling of MBSs, while the application of ac flux suppresses the resonant oscillations. The investigation provides a clue for detecting MBSs through measuring the photon-assistedScandZTversus AB phase oscillations.
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Affiliation(s)
- Wei-Ke Zou
- School of Physics, Beijing Institute of Technology, Beijing 100081, People's Republic of China
- School of Physics and New Energy, Xuzhou University of Technology, Xuzhou 221018, People's Republic of China
| | - Qing Wang
- School of Physics, Beijing Institute of Technology, Beijing 100081, People's Republic of China
| | - Hong-Kang Zhao
- School of Physics, Beijing Institute of Technology, Beijing 100081, People's Republic of China
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5
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Liu L, Sun S, Huo Y, Li S, Han T. Current through a hybrid four-terminal Josephson junction with Majorana nanowires. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2022; 34:395302. [PMID: 35835089 DOI: 10.1088/1361-648x/ac8131] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/03/2022] [Accepted: 07/14/2022] [Indexed: 06/15/2023]
Abstract
We investigate the current through a hybrid four-terminal Josephson junction with semiconductor nanowires, in which the junction is connected with two superconducting electrodes and two normal electrodes. The semiconductor nanowire, which is subject to an external magnetic field with Rashba spin-orbit coupling and proximity-induced superconductivity, can host Majorana bound states. When all the nanowires lie in topological nontrivial region, a 4π-periodic current can be observed through the normal terminal and a 2π-periodic current through the superconducting terminal. When a rotating magnetic field is applied to the junction, the supercurrent through different terminals varies with the variation of the magnetic field direction. Only when the magnetic field is applied at certain angles, we find that the 4π-periodic current will appear through the normal terminal.
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Affiliation(s)
- Long Liu
- Hebei College of Industry and Technology, Shijiazhuang, Hebei, 050091, People's Republic of China
| | - Sutao Sun
- School of Mathmatics and Science, Hebei GEO University, Shijiazhuang 050031, People's Republic of China
| | - Yunchang Huo
- Hebei College of Industry and Technology, Shijiazhuang, Hebei, 050091, People's Republic of China
| | - Shuang Li
- Hebei College of Industry and Technology, Shijiazhuang, Hebei, 050091, People's Republic of China
| | - Tiwen Han
- Hebei College of Industry and Technology, Shijiazhuang, Hebei, 050091, People's Republic of China
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6
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McLauchlan CK, Béri B. Fermion-Parity-Based Computation and Its Majorana-Zero-Mode Implementation. PHYSICAL REVIEW LETTERS 2022; 128:180504. [PMID: 35594115 DOI: 10.1103/physrevlett.128.180504] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/27/2021] [Accepted: 03/29/2022] [Indexed: 06/15/2023]
Abstract
Majorana zero modes (MZMs) promise a platform for topologically protected fermionic quantum computation. However, creating multiple MZMs and generating (directly or via measurements) the requisite transformations (e.g., braids) pose significant challenges. We introduce fermion-parity-based computation (FPBC): a measurement-based scheme, modeled on Pauli-based computation, that uses efficient classical processing to virtually increase the number of available MZMs and which, given magic state inputs, operates without transformations. FPBC requires all MZM parities to be measurable, but this conflicts with constraints in proposed MZM hardware. We thus introduce a design in which all parities are directly measurable and which is hence well suited for FPBC. While developing FPBC, we identify the "logical braid group" as the fermionic analog of the Clifford group.
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Affiliation(s)
| | - Benjamin Béri
- DAMTP, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
- T.C.M. Group, Cavendish Laboratory, University of Cambridge, J.J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom
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7
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Liu D, Zhang G, Cao Z, Zhang H, Liu DE. Universal Conductance Scaling of Andreev Reflections Using a Dissipative Probe. PHYSICAL REVIEW LETTERS 2022; 128:076802. [PMID: 35244417 DOI: 10.1103/physrevlett.128.076802] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/02/2021] [Accepted: 01/25/2022] [Indexed: 06/14/2023]
Abstract
The Majorana search is caught up in an extensive debate about the false-positive signals from nontopological Andreev bound states. We introduce a remedy using the dissipative probe to generate electron-boson interaction. We theoretically show that the interaction-induced renormalization leads to significantly distinct universal zero-bias conductance behaviors, i.e., distinct characteristic power law in temperature, for different types of Andreev reflections, that show a sharp contrast to that of a Majorana zero mode. Various specific cases have been studied, including the cases in which two charges involved in an Andreev reflection process maintain or lose coherence, and the cases for multiple Andreev bound states with or without a Majorana. A transparent list of conductance features in each case is provided to help distinguish the observed subgap states in experiments, which also promotes the identification of Majorana zero modes.
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Affiliation(s)
- Donghao Liu
- State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, China
| | - Gu Zhang
- Beijing Academy of Quantum Information Sciences, Beijing 100193, China
| | - Zhan Cao
- Beijing Academy of Quantum Information Sciences, Beijing 100193, China
| | - Hao Zhang
- State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, China
- Beijing Academy of Quantum Information Sciences, Beijing 100193, China
- Frontier Science Center for Quantum Information, Beijing 100184, China
| | - Dong E Liu
- State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, China
- Beijing Academy of Quantum Information Sciences, Beijing 100193, China
- Frontier Science Center for Quantum Information, Beijing 100184, China
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8
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Topological Superconducting Transition Characterized by a Modified Real-Space-Pfaffian Method and Mobility Edges in a One-Dimensional Quasiperiodic Lattice. Symmetry (Basel) 2022. [DOI: 10.3390/sym14020371] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022] Open
Abstract
A modified real-space-Pfaffian method is applied to characterize the topological superconducting transition of a one-dimensional p-wave superconductor with quasiperiodic potentials. We found that the Majorana zero-energy mode exists in the topological non-trivial phase, and its spatial distribution is localized at ends of the system, whereas in the topological trivial phase, there is no Majorana zero mode. Furthermore, we numerically found that due to the competition between the localized quasi-disorder and the extended p-wave pairing, there are mobility edges in the energy spectra. Our theoretical work enriches the research on the quasiperiodic p-wave superconducting models.
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9
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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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10
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Nanoresonator Enhancement of Majorana-Fermion-Induced Slow Light in Superconducting Iron Chains. MICROMACHINES 2021; 12:mi12121435. [PMID: 34945284 PMCID: PMC8705128 DOI: 10.3390/mi12121435] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 11/08/2021] [Revised: 11/21/2021] [Accepted: 11/21/2021] [Indexed: 11/17/2022]
Abstract
We theoretically investigate Fano resonance in the absorption spectrum of a quantum dot (QD) based on a hybrid QD-nanomechanical resonator (QD-NR) system mediated by Majorana fermions (MFs) in superconducting iron (Fe) chains. The absorption spectra exhibit a series of asymmetric Fano line shapes, which are accompanied by the rapid normal phase dispersion and induce the optical propagation properties such as the slow light effect under suitable parametric regimes. The results indicated that the slow light induced by MFs can be obtained under different coupling regimes and different detuning regimes. Moreover, we also investigated the role of the NR, and the NR behaving as a phonon cavity enhances the slow light effect.
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11
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Stefański P. Sub-gap Fano resonances in a topological superconducting wire with on-site Coulomb interactions. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2021; 33:465602. [PMID: 34388745 DOI: 10.1088/1361-648x/ac1d6d] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/12/2021] [Accepted: 08/13/2021] [Indexed: 06/13/2023]
Abstract
We consider theoretically a 1D-semiconducting wire with strong Rashba interaction in proximity withs-wave superconductor, driven into topological phase by external magnetic field. Additionally, we take into account on-site Coulomb interactions inside the wire. The system is modelled by a tight binding Hamiltonian with Rashba hopping term and induceds-wave superconductivity. Calculations are performed utilizing recursive Green's function method, and Coulomb interactions are treated selfconsistently within Hubbard I approximation. For the Hubbard levels residing withinp-wave superconducting gap, particle-hole symmetric four-resonance structure develops in the density of states, apart from Majorana resonance. One pair of particle-hole symmetric resonances is created by the discrete II-Hubbard levels of the particular site, and the second pair of Hubbard sub-bands originates from recursive summation over the sites of the wire. Quantum interference between both types of pairs of states creates in-gap charge-conjugated Fano resonances with opposite asymmetry factors. We demonstrate that when quantum interference is dominated by two-particle tunneling, the Majorana resonance is strongly diminished, while it is not altered when single-particle tunneling dominates in interference process. We also discuss some consequences for experimental distinction of true Majorana states, and show that on-site Coulomb interactions support the appearance of topological phase.
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Affiliation(s)
- Piotr Stefański
- Institute of Molecular Physics of the Polish Academy of Sciences, ul. Smoluchowskiego 17, 60-179 Poznań, Poland
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12
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Heedt S, Quintero-Pérez M, Borsoi F, Fursina A, van Loo N, Mazur GP, Nowak MP, Ammerlaan M, Li K, Korneychuk S, Shen J, van de Poll MAY, Badawy G, Gazibegovic S, de Jong N, Aseev P, van Hoogdalem K, Bakkers EPAM, Kouwenhoven LP. Shadow-wall lithography of ballistic superconductor-semiconductor quantum devices. Nat Commun 2021; 12:4914. [PMID: 34389705 PMCID: PMC8363628 DOI: 10.1038/s41467-021-25100-w] [Citation(s) in RCA: 21] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/14/2020] [Accepted: 07/19/2021] [Indexed: 11/09/2022] Open
Abstract
The realization of hybrid superconductor-semiconductor quantum devices, in particular a topological qubit, calls for advanced techniques to readily and reproducibly engineer induced superconductivity in semiconductor nanowires. Here, we introduce an on-chip fabrication paradigm based on shadow walls that offers substantial advances in device quality and reproducibility. It allows for the implementation of hybrid quantum devices and ultimately topological qubits while eliminating fabrication steps such as lithography and etching. This is critical to preserve the integrity and homogeneity of the fragile hybrid interfaces. The approach simplifies the reproducible fabrication of devices with a hard induced superconducting gap and ballistic normal-/superconductor junctions. Large gate-tunable supercurrents and high-order multiple Andreev reflections manifest the exceptional coherence of the resulting nanowire Josephson junctions. Our approach enables the realization of 3-terminal devices, where zero-bias conductance peaks emerge in a magnetic field concurrently at both boundaries of the one-dimensional hybrids.
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Affiliation(s)
- Sebastian Heedt
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology, Delft, The Netherlands. .,Microsoft Quantum Lab Delft, Delft, The Netherlands.
| | | | - Francesco Borsoi
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology, Delft, The Netherlands
| | | | - Nick van Loo
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology, Delft, The Netherlands
| | - Grzegorz P Mazur
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology, Delft, The Netherlands
| | - Michał P Nowak
- AGH University of Science and Technology, Academic Centre for Materials and Nanotechnology, Krakow, Poland
| | - Mark Ammerlaan
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology, Delft, The Netherlands
| | - Kongyi Li
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology, Delft, The Netherlands
| | - Svetlana Korneychuk
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology, Delft, The Netherlands
| | - Jie Shen
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology, Delft, The Netherlands
| | - May An Y van de Poll
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology, Delft, The Netherlands
| | - Ghada Badawy
- Department of Applied Physics, Eindhoven University of Technology, Eindhoven, The Netherlands
| | - Sasa Gazibegovic
- Department of Applied Physics, Eindhoven University of Technology, Eindhoven, The Netherlands
| | - Nick de Jong
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology, Delft, The Netherlands.,Netherlands Organisation for Applied Scientific Research (TNO), Delft, The Netherlands
| | - Pavel Aseev
- Microsoft Quantum Lab Delft, Delft, The Netherlands
| | | | - Erik P A M Bakkers
- Department of Applied Physics, Eindhoven University of Technology, Eindhoven, The Netherlands
| | - Leo P Kouwenhoven
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology, Delft, The Netherlands.,Microsoft Quantum Lab Delft, Delft, The Netherlands
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13
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Wang Z, Cheng S, Liu X, Jiang H. Topological kink states in graphene. NANOTECHNOLOGY 2021; 32:402001. [PMID: 34161935 DOI: 10.1088/1361-6528/ac0dd8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/18/2021] [Accepted: 06/23/2021] [Indexed: 06/13/2023]
Abstract
Due to the unique band structure, graphene exhibits a number of exotic electronic properties that have not been observed in other materials. Among them, it has been demonstrated that there exist the one-dimensional valley-polarized topological kink states localized in the vicinity of the domain wall of graphene systems, where a bulk energy gap opens due to the inversion symmetry breaking. Notably, the valley-momentum locking nature makes the topological kink states attractive to the property manipulation in valleytronics. This paper systematically reviews both the theoretical research and experimental progress on topological kink states in monolayer graphene, bilayer graphene and graphene-like classical wave systems. Besides, various applications of topological kink states, including the valley filter, current partition, current manipulation, Majorana zero modes and etc, are also introduced.
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Affiliation(s)
- Zibo Wang
- College of Physics and Electronic Engineering, Sichuan Normal University, Chengdu 610068, People's Republic of China
- Center for Computational Sciences, Sichuan Normal University, Chengdu 610068, People's Republic of China
| | - Shuguang Cheng
- Department of Physics, Northwest University, Xi'an 710069, People's Republic of China
| | - Xiao Liu
- School of Physical Science and Technology, Soochow University, Suzhou 215006, People's Republic of China
| | - Hua Jiang
- School of Physical Science and Technology, Soochow University, Suzhou 215006, People's Republic of China
- Institute for Advanced Study of Soochow University, Suzhou 215006, People's Republic of China
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14
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Pendharkar M, Zhang B, Wu H, Zarassi A, Zhang P, Dempsey CP, Lee JS, Harrington SD, Badawy G, Gazibegovic S, Op Het Veld RLM, Rossi M, Jung J, Chen AH, Verheijen MA, Hocevar M, Bakkers EPAM, Palmstrøm CJ, Frolov SM. Parity-preserving and magnetic field-resilient superconductivity in InSb nanowires with Sn shells. Science 2021; 372:508-511. [PMID: 33858990 DOI: 10.1126/science.aba5211] [Citation(s) in RCA: 21] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/12/2019] [Accepted: 03/13/2021] [Indexed: 11/02/2022]
Abstract
Improving materials used to make qubits is crucial to further progress in quantum information processing. Of particular interest are semiconductor-superconductor heterostructures that are expected to form the basis of topological quantum computing. We grew semiconductor indium antimonide nanowires that were coated with shells of tin of uniform thickness. No interdiffusion was observed at the interface between Sn and InSb. Tunnel junctions were prepared by in situ shadowing. Despite the lack of lattice matching between Sn and InSb, a 15-nanometer-thick shell of tin was found to induce a hard superconducting gap, with superconductivity persisting in magnetic field up to 4 teslas. A small island of Sn-InSb exhibits the two-electron charging effect. These findings suggest a less restrictive approach to fabricating superconducting and topological quantum circuits.
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Affiliation(s)
- M Pendharkar
- Electrical and Computer Engineering, University of California, Santa Barbara, CA 93106, USA
| | - B Zhang
- Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, PA 15260, USA
| | - H Wu
- Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, PA 15260, USA
| | - A Zarassi
- Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, PA 15260, USA
| | - P Zhang
- Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, PA 15260, USA
| | - C P Dempsey
- Electrical and Computer Engineering, University of California, Santa Barbara, CA 93106, USA
| | - J S Lee
- California NanoSystems Institute, University of California, Santa Barbara, CA 93106, USA
| | - S D Harrington
- Materials Department, University of California, Santa Barbara, CA 93106, USA
| | - G Badawy
- Eindhoven University of Technology, 5600 MB Eindhoven, Netherlands
| | - S Gazibegovic
- Eindhoven University of Technology, 5600 MB Eindhoven, Netherlands
| | | | - M Rossi
- Eindhoven University of Technology, 5600 MB Eindhoven, Netherlands
| | - J Jung
- Eindhoven University of Technology, 5600 MB Eindhoven, Netherlands
| | - A-H Chen
- Univ. Grenoble Alpes, CNRS, Grenoble INP, Institut Néel, 38000 Grenoble, France
| | - M A Verheijen
- Eindhoven University of Technology, 5600 MB Eindhoven, Netherlands
| | - M Hocevar
- Univ. Grenoble Alpes, CNRS, Grenoble INP, Institut Néel, 38000 Grenoble, France
| | - E P A M Bakkers
- Eindhoven University of Technology, 5600 MB Eindhoven, Netherlands
| | - C J Palmstrøm
- Electrical and Computer Engineering, University of California, Santa Barbara, CA 93106, USA.,California NanoSystems Institute, University of California, Santa Barbara, CA 93106, USA.,Materials Department, University of California, Santa Barbara, CA 93106, USA
| | - S M Frolov
- Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, PA 15260, USA.
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15
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Khan SA, Lampadaris C, Cui A, Stampfer L, Liu Y, Pauka SJ, Cachaza ME, Fiordaliso EM, Kang JH, Korneychuk S, Mutas T, Sestoft JE, Krizek F, Tanta R, Cassidy MC, Jespersen TS, Krogstrup P. Highly Transparent Gatable Superconducting Shadow Junctions. ACS NANO 2020; 14:14605-14615. [PMID: 32396328 DOI: 10.1021/acsnano.0c02979] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
Gate-tunable junctions are key elements in quantum devices based on hybrid semiconductor-superconductor materials. They serve multiple purposes ranging from tunnel spectroscopy probes to voltage-controlled qubit operations in gatemon and topological qubits. Common to all is that junction transparency plays a critical role. In this study, we grow single-crystalline InAs, InSb, and InAs1-xSbx semiconductor nanowires with epitaxial Al, Sn, and Pb superconductors and in situ shadowed junctions in a single-step molecular beam epitaxy process. We investigate correlations between fabrication parameters, junction morphologies, and electronic transport properties of the junctions and show that the examined in situ shadowed junctions are of significantly higher quality than the etched junctions. By varying the edge sharpness of the shadow junctions, we show that the sharpest edges yield the highest junction transparency for all three examined semiconductors. Further, critical supercurrent measurements reveal an extraordinarily high ICRN, close to the KO-2 limit. This study demonstrates a promising engineering path toward reliable gate-tunable superconducting qubits.
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Affiliation(s)
- Sabbir A Khan
- Microsoft Quantum Materials Lab Copenhagen, 2800 Lyngby, Denmark
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark
| | - Charalampos Lampadaris
- Microsoft Quantum Materials Lab Copenhagen, 2800 Lyngby, Denmark
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark
| | - Ajuan Cui
- Microsoft Quantum Materials Lab Copenhagen, 2800 Lyngby, Denmark
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark
| | - Lukas Stampfer
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark
| | - Yu Liu
- Microsoft Quantum Materials Lab Copenhagen, 2800 Lyngby, Denmark
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark
| | - Sebastian J Pauka
- Microsoft Quantum Sydney, The University of Sydney, Sydney, NSW 2006, Australia
| | - Martin E Cachaza
- Microsoft Quantum Materials Lab Copenhagen, 2800 Lyngby, Denmark
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark
| | | | - Jung-Hyun Kang
- Microsoft Quantum Materials Lab Copenhagen, 2800 Lyngby, Denmark
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark
| | - Svetlana Korneychuk
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology, 2600 GA Delft, The Netherlands
| | - Timo Mutas
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark
| | - Joachim E Sestoft
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark
| | - Filip Krizek
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark
| | - Rawa Tanta
- Microsoft Quantum Materials Lab Copenhagen, 2800 Lyngby, Denmark
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark
| | - Maja C Cassidy
- Microsoft Quantum Sydney, The University of Sydney, Sydney, NSW 2006, Australia
| | - Thomas S Jespersen
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark
| | - Peter Krogstrup
- Microsoft Quantum Materials Lab Copenhagen, 2800 Lyngby, Denmark
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark
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16
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Ottar Klausen K, Sitek A, Erlingsson SI, Manolescu A. Majorana zero modes in nanowires with combined triangular and hexagonal geometry. NANOTECHNOLOGY 2020; 31:354001. [PMID: 32408282 DOI: 10.1088/1361-6528/ab932e] [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
The effects of geometry on the hosting of Majorana zero modes are explored in core-shell nanowires with a hexagonal core and a triangular shell, and vice versa. The energy interval separating electronic states localized in the corners from states localized on the sides of the shell is shown to be larger for a triangular nanowire with a hexagonal core, than a triangular one. We build the topological phase diagram for both cases and compare them to earlier work on prismatic nanowires with matching core and shell geometry. We suggest that a dual core nanowire is needed to allow for braiding operations of Majorana zero modes at the nanowire end plane.
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Affiliation(s)
- Kristjan Ottar Klausen
- Department of Engineering, Reykjavik University, Menntavegur 1, IS-101 Reykjavik, Iceland
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17
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Liu N, Xie Y, Liu G, Sohn S, Raj A, Han G, Wu B, Cha JJ, Liu Z, Schroers J. General Nanomolding of Ordered Phases. PHYSICAL REVIEW LETTERS 2020; 124:036102. [PMID: 32031828 DOI: 10.1103/physrevlett.124.036102] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/04/2019] [Indexed: 06/10/2023]
Abstract
Large-scale, controlled fabrication of ordered phases is challenging at the nanoscale, yet highly demanded as their well-ordered structure and chemistry is the key for advanced functionality. Here, we demonstrate a general nanomolding process of ordered phases based on atomic diffusion. Resulting nanowires are single crystals and maintain their composition and structure throughout their length, which we explain by a self-ordering process originating from their narrow Gibbs free energy. The versatility, control, and precision of this thermomechanical nanomolding method of ordered phases provides new insights into single crystal growth and suggest itself as a technology to enable wide spread usage for nanoscale and quantum devices.
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Affiliation(s)
- Naijia Liu
- Department of Mechanical Engineering and Materials Science, Yale University, New Haven, Connecticut 06511, USA
| | - Yujun Xie
- Department of Mechanical Engineering and Materials Science, Yale University, New Haven, Connecticut 06511, USA
- Energy Sciences Institute, Yale West Campus, West Haven, Connecticut 06516, USA
| | - Guannan Liu
- Department of Mechanical Engineering and Materials Science, Yale University, New Haven, Connecticut 06511, USA
| | - Sungwoo Sohn
- Department of Mechanical Engineering and Materials Science, Yale University, New Haven, Connecticut 06511, USA
| | - Arindam Raj
- Department of Mechanical Engineering and Materials Science, Yale University, New Haven, Connecticut 06511, USA
| | - Guoxing Han
- Department of Engineering Mechanics, School of Civil Engineering, Wuhan University, Wuhan, Hubei 430072, China
| | - Bozhao Wu
- Department of Engineering Mechanics, School of Civil Engineering, Wuhan University, Wuhan, Hubei 430072, China
| | - Judy J Cha
- Department of Mechanical Engineering and Materials Science, Yale University, New Haven, Connecticut 06511, USA
- Energy Sciences Institute, Yale West Campus, West Haven, Connecticut 06516, USA
| | - Ze Liu
- Department of Engineering Mechanics, School of Civil Engineering, Wuhan University, Wuhan, Hubei 430072, China
| | - Jan Schroers
- Department of Mechanical Engineering and Materials Science, Yale University, New Haven, Connecticut 06511, USA
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18
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Ménard GC, Anselmetti GLR, Martinez EA, Puglia D, Malinowski FK, Lee JS, Choi S, Pendharkar M, Palmstrøm CJ, Flensberg K, Marcus CM, Casparis L, Higginbotham AP. Conductance-Matrix Symmetries of a Three-Terminal Hybrid Device. PHYSICAL REVIEW LETTERS 2020; 124:036802. [PMID: 32031865 DOI: 10.1103/physrevlett.124.036802] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/02/2019] [Indexed: 06/10/2023]
Abstract
We present conductance-matrix measurements of a three-terminal superconductor-semiconductor hybrid device consisting of two normal leads and one superconducting lead. Using a symmetry decomposition of the conductance, we find that antisymmetric components of pairs of local and nonlocal conductances qualitatively match at energies below the superconducting gap, and we compare this finding with symmetry relations based on a noninteracting scattering matrix approach. Further, the local charge character of Andreev bound states is extracted from the symmetry-decomposed conductance data and is found to be similar at both ends of the device and tunable with gate voltage. Finally, we measure the conductance matrix as a function of magnetic field and identify correlated splittings in low-energy features, demonstrating how conductance-matrix measurements can complement traditional single-probe measurements in the search for Majorana zero modes.
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Affiliation(s)
- G C Ménard
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
- Microsoft Quantum-Copenhagen, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
| | - G L R Anselmetti
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
- Microsoft Quantum-Copenhagen, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
| | - E A Martinez
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
- Microsoft Quantum-Copenhagen, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
| | - D Puglia
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
- Microsoft Quantum-Copenhagen, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
| | - F K Malinowski
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
- Microsoft Quantum-Copenhagen, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
| | - J S Lee
- California NanoSystems Institute, University of California, Santa Barbara, California 93106, USA
| | - S Choi
- Department of Electrical Engineering, University of California, Santa Barbara, California 93106, USA
| | - M Pendharkar
- Department of Electrical Engineering, University of California, Santa Barbara, California 93106, USA
| | - C J Palmstrøm
- California NanoSystems Institute, University of California, Santa Barbara, California 93106, USA
- Department of Electrical Engineering, University of California, Santa Barbara, California 93106, USA
- Materials Department, University of California, Santa Barbara, California 93106, USA
| | - K Flensberg
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
| | - C M Marcus
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
- Microsoft Quantum-Copenhagen, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
| | - L Casparis
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
- Microsoft Quantum-Copenhagen, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
| | - A P Higginbotham
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
- Microsoft Quantum-Copenhagen, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
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19
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Awoga OA, Cayao J, Black-Schaffer AM. Supercurrent Detection of Topologically Trivial Zero-Energy States in Nanowire Junctions. PHYSICAL REVIEW LETTERS 2019; 123:117001. [PMID: 31573272 DOI: 10.1103/physrevlett.123.117001] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/08/2019] [Indexed: 06/10/2023]
Abstract
We report the emergence of zero-energy states in the trivial phase of a short nanowire junction with a strong spin-orbit coupling and magnetic field, formed by strong coupling between the nanowire and two superconductors. The zero-energy states appear in the junction when the superconductors induce a large energy shift in the nanowire, such that the junction naturally forms a quantum dot, a process that is highly tunable by the superconductor width. Most importantly, we demonstrate that the zero-energy states produce a π shift in the phase-biased supercurrent, which can be used as a simple tool for their unambiguous detection, ruling out any Majorana-like interpretation.
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Affiliation(s)
- Oladunjoye A Awoga
- Department of Physics and Astronomy, Uppsala University, Box 516, S-751 20 Uppsala, Sweden
| | - Jorge Cayao
- Department of Physics and Astronomy, Uppsala University, Box 516, S-751 20 Uppsala, Sweden
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20
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Chen J, Woods BD, Yu P, Hocevar M, Car D, Plissard SR, Bakkers EPAM, Stanescu TD, Frolov SM. Ubiquitous Non-Majorana Zero-Bias Conductance Peaks in Nanowire Devices. PHYSICAL REVIEW LETTERS 2019; 123:107703. [PMID: 31573319 DOI: 10.1103/physrevlett.123.107703] [Citation(s) in RCA: 20] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/08/2019] [Indexed: 06/10/2023]
Abstract
We perform tunneling measurements on indium antimonide nanowire-superconductor hybrid devices fabricated for the studies of Majorana bound states. At finite magnetic field, resonances that strongly resemble Majorana bound states, including zero-bias pinning, become common to the point of ubiquity. Since Majorana bound states are predicted in only a limited parameter range in nanowire devices, we seek an alternative explanation for the observed zero-bias peaks. With the help of a self-consistent Poission-Schrödinger multiband model developed in parallel, we identify several families of trivial subgap states that overlap and interact, giving rise to a crowded spectrum near zero energy and zero-bias conductance peaks in experiments. These findings advance the search for Majorana bound states through improved understanding of broader phenomena found in superconductor-semiconductor systems.
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Affiliation(s)
- J Chen
- Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA
- Department of Electrical and Computer Engineering and Peterson Institute of NanoScience and Engineering, University of Pittsburgh, Pittsburgh, Pennsylvania 15261, USA
| | - B D Woods
- Department of Physics and Astronomy, West Virginia University, Morgantown, West Virginia 26506, USA
| | - P Yu
- Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA
| | - M Hocevar
- Univ. Grenoble Alpes, CNRS, Grenoble INP, Institut Néel, 38000 Grenoble, France
| | - D Car
- Eindhoven University of Technology, 5600 MB, Eindhoven, Netherlands
| | - S R Plissard
- LAAS CNRS, Université de Toulouse, 31031 Toulouse, France
| | - E P A M Bakkers
- Eindhoven University of Technology, 5600 MB, Eindhoven, Netherlands
| | - T D Stanescu
- Department of Physics and Astronomy, West Virginia University, Morgantown, West Virginia 26506, USA
| | - S M Frolov
- Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA
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21
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Estrada Saldaña JC, Žitko R, Cleuziou JP, Lee EJH, Zannier V, Ercolani D, Sorba L, Aguado R, De Franceschi S. Charge localization and reentrant superconductivity in a quasi-ballistic InAs nanowire coupled to superconductors. SCIENCE ADVANCES 2019; 5:eaav1235. [PMID: 31281880 PMCID: PMC6611689 DOI: 10.1126/sciadv.aav1235] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 08/16/2018] [Accepted: 05/29/2019] [Indexed: 06/09/2023]
Abstract
A semiconductor nanowire with strong spin-orbit coupling in proximity to a superconductor is predicted to display Majorana edge states emerging under a properly oriented magnetic field. The experimental investigation of these exotic states requires assessing the one-dimensional (1D) character of the nanowire and understanding the superconducting proximity effect in the presence of a magnetic field. Here, we explore the quasi-ballistic 1D transport regime of an InAs nanowire with Ta contacts. Fine-tuned by means of local gates, the observed plateaus of approximately quantized conductance hide the presence of a localized electron, giving rise to a lurking Coulomb blockade effect and Kondo physics. When Ta becomes superconducting, this local charge causes an unusual, reentrant magnetic field dependence of the supercurrent, which we ascribe to a 0 - π transition. Our results underline the relevant role of unintentional charge localization in the few-channel regime where helical subbands and Majorana quasi-particles are expected to arise.
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Affiliation(s)
| | - R. Žitko
- Jožef Stefan Institute, Jamova 39, Ljubljana, Slovenia
- Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, Ljubljana, Slovenia
| | - J. P. Cleuziou
- Université Grenoble Alpes, CEA, INAC-PHELIQS, 38000 Grenoble, France
| | - E. J. H. Lee
- Université Grenoble Alpes, CEA, INAC-PHELIQS, 38000 Grenoble, France
| | - V. Zannier
- NEST–Istituto Nanoscienze–CNR and Scuola Normale Superiore, Piazza S. Silvestro 12, 56127 Pisa, Italy
| | - D. Ercolani
- NEST–Istituto Nanoscienze–CNR and Scuola Normale Superiore, Piazza S. Silvestro 12, 56127 Pisa, Italy
| | - L. Sorba
- NEST–Istituto Nanoscienze–CNR and Scuola Normale Superiore, Piazza S. Silvestro 12, 56127 Pisa, Italy
| | - R. Aguado
- Materials Science Factory, Instituto de Ciencia de Materiales de Madrid (ICMM), Consejo Superior de Investigaciones Científicas (CSIC), Sor Juana Inés de la Cruz 3, 28049 Madrid, Spain
| | - S. De Franceschi
- Université Grenoble Alpes, CEA, INAC-PHELIQS, 38000 Grenoble, France
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22
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Gao Z, Sun J, Han M, Yin Y, Gu Y, Yang ZX, Zeng H. Recent advances in Sb-based III-V nanowires. NANOTECHNOLOGY 2019; 30:212002. [PMID: 30708362 DOI: 10.1088/1361-6528/ab03ee] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
Owing to the high mobility, narrow bandgap, strong spin-orbit coupling and large g-factor, Sb-based III-V nanowires (NWs) attracted significant interests in high speed electronics, long-wavelength photodetectors and quantum superconductivity in the past decade. In this review, we aim to give an integrated summarization about the recent advances in binary as well as ternary Sb-based III-V NWs, starting from the fundamental properties, NWs growth mechanism, typical synthetic methods to their applications in transistors, photodetectors, and Majorana fermions detection. Up to now, famous NWs growth techniques of solid-source chemical vapor deposition (CVD), molecular beam epitaxy, metal organic vapor phase epitaxy and metal organic CVD etc have been adopted and developed for the controllable growth of Sb-based III-V NWs. Several parameters including heating temperature, III/V ratio of source materials, growth temperature, catalyst size and kinds, and growth substrate play important roles on the morphology, position, diameter distribution, growth orientation and crystal phase of Sb-based III-V NWs. Furthermore, we discuss the photoelectrical applications of Sb-based III-V NWs such as field-effect-transistors, tunnel diode, low-power inverter, and infrared detectors etc. Importantly, due to the strongest spin-orbit interaction and giant g-factor among all III-V semiconductors, InSb with the geometry of one-dimension NW is considered as the most promising candidate for the detection of Majorana fermions. In the end, we also summarize the main challenges remaining in the field and put forward some suggestions for the future development of Sb-based III-V NWs.
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Affiliation(s)
- Zhaofeng Gao
- Shenzhen Research Institute of Shandong University, Shenzhen, 518057, People's Republic of China. School of Microelectronics, Shandong University, Jinan, 250100, People's Republic of China
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23
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Yip S, Shen L, Ho JC. Recent advances in III-Sb nanowires: from synthesis to applications. NANOTECHNOLOGY 2019; 30:202003. [PMID: 30625448 DOI: 10.1088/1361-6528/aafcce] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/28/2023]
Abstract
The excellent properties of III-V semiconductors make them intriguing candidates for next-generation electronics and optoelectronics. Their nanowire (NW) counterparts further provide interesting geometry and a quantum confinement effect which benefits various applications. Among the many members of all the III-V semiconductors, III-antimonide NWs have attracted significant research interest due to their narrow, direct bandgap and high carrier mobility. However, due to the difficulty of NW fabrication, the development of III-antimonide NWs and their corresponding applications are always a step behind the other III-V semiconductors. Until recent years, because of advances in understanding and fabrication techniques, electronic and optoelectronic devices based on III-antimonide NWs with novel performance have been fabricated. In this review, we will focus on the development of the synthesis of III-antimonide NWs using different techniques and strategies for fine-tuning the crystal structure and composition as well as fabricating their corresponding heterostructures. With such development, the recent progress in the applications of III-antimonide NWs in electronics and optoelectronics is also surveyed. All these discussions provide valuable guidelines for the design of III-antimonide NWs for next-generation device utilization.
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Affiliation(s)
- SenPo Yip
- Department of Materials Science and Engineering, City University of Hong Kong, Hong Kong Special Administrative Region of China, People's Republic of China. Shenzhen Research Institute, City University of Hong Kong, Shenzhen 518057, People's Republic of China
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24
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Grivnin A, Bor E, Heiblum M, Oreg Y, Shtrikman H. Concomitant opening of a bulk-gap with an emerging possible Majorana zero mode. Nat Commun 2019; 10:1940. [PMID: 31036841 PMCID: PMC6488617 DOI: 10.1038/s41467-019-09771-0] [Citation(s) in RCA: 44] [Impact Index Per Article: 8.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/06/2018] [Accepted: 03/20/2019] [Indexed: 11/23/2022] Open
Abstract
Majorana quasiparticles are generally detected in a 1D topological superconductor by tunneling electrons into its edge, with an emergent zero-bias conductance peak (ZBCP). However, such a ZBCP can also result from other mechanisms, hence, additional verifications are required. Since the emergence of a Majorana must be accompanied by an opening of a topological gap in the bulk, two simultaneous measurements are performed: one in the bulk and another at the edge of a 1D InAs nanowire coated with epitaxial aluminum. Only under certain experimental parameters, a closing of the superconducting bulk-gap that is followed by its reopening, appears simultaneously with a ZBCP at the edge. Such events suggest the occurrence of a topologically non-trivial phase. Yet, we also find that ZBCPs are observed under different tuning parameters without simultaneous reopening of a bulk-gap. This demonstrates the importance of simultaneous probing of bulk and edge in the identification of Majorana edge-states.
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Affiliation(s)
- Anna Grivnin
- Braun Center for Submicron Research, Weizmann Institute of Science, Rehovot, 76100, Israel
- Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot, 76100, Israel
| | - Ella Bor
- Braun Center for Submicron Research, Weizmann Institute of Science, Rehovot, 76100, Israel
- Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot, 76100, Israel
| | - Moty Heiblum
- Braun Center for Submicron Research, Weizmann Institute of Science, Rehovot, 76100, Israel.
- Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot, 76100, Israel.
| | - Yuval Oreg
- Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot, 76100, Israel
| | - Hadas Shtrikman
- Braun Center for Submicron Research, Weizmann Institute of Science, Rehovot, 76100, Israel
- Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot, 76100, Israel
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25
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Ren H, Pientka F, Hart S, Pierce AT, Kosowsky M, Lunczer L, Schlereth R, Scharf B, Hankiewicz EM, Molenkamp LW, Halperin BI, Yacoby A. Topological superconductivity in a phase-controlled Josephson junction. Nature 2019; 569:93-98. [PMID: 31019296 DOI: 10.1038/s41586-019-1148-9] [Citation(s) in RCA: 62] [Impact Index Per Article: 12.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/05/2018] [Accepted: 02/14/2019] [Indexed: 11/09/2022]
Abstract
Topological superconductors can support localized Majorana states at their boundaries1-5. These quasi-particle excitations obey non-Abelian statistics that can be used to encode and manipulate quantum information in a topologically protected manner6,7. Although signatures of Majorana bound states have been observed in one-dimensional systems, there is an ongoing effort to find alternative platforms that do not require fine-tuning of parameters and can be easily scaled to large numbers of states8-21. Here we present an experimental approach towards a two-dimensional architecture of Majorana bound states. Using a Josephson junction made of a HgTe quantum well coupled to thin-film aluminium, we are able to tune the transition between a trivial and a topological superconducting state by controlling the phase difference across the junction and applying an in-plane magnetic field22. We determine the topological state of the resulting superconductor by measuring the tunnelling conductance at the edge of the junction. At low magnetic fields, we observe a minimum in the tunnelling spectra near zero bias, consistent with a trivial superconductor. However, as the magnetic field increases, the tunnelling conductance develops a zero-bias peak, which persists over a range of phase differences that expands systematically with increasing magnetic field. Our observations are consistent with theoretical predictions for this system and with full quantum mechanical numerical simulations performed on model systems with similar dimensions and parameters. Our work establishes this system as a promising platform for realizing topological superconductivity and for creating and manipulating Majorana modes and probing topological superconducting phases in two-dimensional systems.
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Affiliation(s)
- Hechen Ren
- Department of Physics, Harvard University, Cambridge, MA, USA.,Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, CA, USA
| | - Falko Pientka
- Department of Physics, Harvard University, Cambridge, MA, USA.,Max-Planck-Institut für Physik komplexer Systeme, Dresden, Germany
| | - Sean Hart
- Department of Physics, Harvard University, Cambridge, MA, USA.,IBM T. J. Watson Research Center, Yorktown Heights, NY, USA
| | - Andrew T Pierce
- Department of Physics, Harvard University, Cambridge, MA, USA
| | | | - Lukas Lunczer
- Physikalisches Institut (EP3) and Institute for Topological Insulators, Universität Würzburg, Würzburg, Germany
| | - Raimund Schlereth
- Physikalisches Institut (EP3) and Institute for Topological Insulators, Universität Würzburg, Würzburg, Germany
| | - Benedikt Scharf
- Institut für Theoretische Physik und Astrophysik and Würzburg-Dresden Cluster of Excellence ct.qmat, Universität Würzburg, Würzburg, Germany
| | - Ewelina M Hankiewicz
- Institut für Theoretische Physik und Astrophysik and Würzburg-Dresden Cluster of Excellence ct.qmat, Universität Würzburg, Würzburg, Germany
| | | | | | - Amir Yacoby
- Department of Physics, Harvard University, Cambridge, MA, USA.
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26
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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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Chen HJ, Wu HW. Rabi splitting and optical Kerr nonlinearity of quantum dot mediated by Majorana fermions. Sci Rep 2018; 8:17677. [PMID: 30518767 PMCID: PMC6281668 DOI: 10.1038/s41598-018-35680-1] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/21/2018] [Accepted: 11/09/2018] [Indexed: 11/22/2022] Open
Abstract
Majorana fermions (MFs), due to their significance in fundamental physics and potential applications in topological quantum computation based on solid-state devices, have drawn widespread attention. Here, we design a hybrid semiconductor/superconductor ring (S/SR) device and put forward an optical method for detecting a pair of MFs in the S/SR device with a quantum dot (QD) with the popular optical pump-probe scheme, which is very different from the present electrical method only considering one nearby MF coupled to the QD. The symmetric and unsymmetric Rabi splitting and optical Kerr nonlinear effect of QD mediated by MFs are investigated under uncoupled and coupled majorana modes, respectively. The coherent optical spectra indicate that a pair of MFs coupled to the QD induced remarkable splitting under different parameters regime and the physical origin of these phenomena are elaborated detailedly. Due to QD-MFs coupling, the probe absorption spectra present the phenomenon of Majorana modes induced transparency (MMIT) which will induce remarkable phenomena of slow light. The coherent optical spectra afford a potential supplement for probing MFs and support Majorana fermions-based topological quantum computation.
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Affiliation(s)
- Hua-Jun Chen
- School of Mechanics and Photoelectric Physics, Anhui University of Science and Technology, Huainan Anhui, 232001, China
| | - Hong-Wei Wu
- School of Mechanics and Photoelectric Physics, Anhui University of Science and Technology, Huainan Anhui, 232001, China.
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28
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Mi S, Burset P, Flindt C. Electron waiting times in hybrid junctions with topological superconductors. Sci Rep 2018; 8:16828. [PMID: 30442914 PMCID: PMC6237767 DOI: 10.1038/s41598-018-34776-y] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/18/2018] [Accepted: 10/22/2018] [Indexed: 11/09/2022] Open
Abstract
We investigate the waiting time distributions (WTDs) of superconducting hybrid junctions, considering both conventional and topologically nontrivial superconductors hosting Majorana bound states at their edges. To this end, we employ a scattering matrix formalism that allows us to evaluate the waiting times between the transmissions and reflections of electrons or holes. Specifically, we analyze normal-metal–superconductor (NIS) junctions and NISIN junctions, where Cooper pairs are spatially split into different leads. The distribution of waiting times is sensitive to the simultaneous reflection of electrons and holes, which is enhanced by the zero-energy state in topological superconductors. For the NISIN junctions, the WTDs of trivial superconductors feature a sharp dependence on the applied voltage, while for topological ones they are mostly independent of it. This particular voltage dependence is again connected to the presence of topological edge states, showing that WTDs are a promising tool for identifying topological superconductivity.
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Affiliation(s)
- Shuo Mi
- Department of Applied Physics, Aalto University, 00076, Aalto, Finland. .,Univ. Grenoble Alpes, CEA, INAC-Pheliqs, 38000, Grenoble, France.
| | - Pablo Burset
- Department of Applied Physics, Aalto University, 00076, Aalto, Finland
| | - Christian Flindt
- Department of Applied Physics, Aalto University, 00076, Aalto, Finland
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29
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Wang Q, Liu CC, Lu YM, Zhang F. High-Temperature Majorana Corner States. PHYSICAL REVIEW LETTERS 2018; 121:186801. [PMID: 30444417 DOI: 10.1103/physrevlett.121.186801] [Citation(s) in RCA: 46] [Impact Index Per Article: 7.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/18/2018] [Revised: 09/26/2018] [Indexed: 06/09/2023]
Abstract
Majorana bound states often occur at the end of a 1D topological superconductor. Validated by a new bulk invariant and an intuitive edge argument, we show the emergence of one Majorana Kramers pair at each corner of a square-shaped 2D topological insulator proximitized by an s_{±}-wave (e.g., Fe-based) superconductor. We obtain a phase diagram that addresses the relaxation of crystal symmetry and edge orientation. We propose two experimental realizations in candidate materials. Our scheme offers a higher-order and higher-temperature route for exploring non-Abelian quasiparticles.
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Affiliation(s)
- Qiyue Wang
- Department of Physics, University of Texas at Dallas, Richardson, Texas 75080, USA
| | - Cheng-Cheng Liu
- School of Physics, Beijing Institute of Technology, Beijing 100081, China
| | - Yuan-Ming Lu
- Department of Physics, Ohio State University, Columbus, Ohio 43210, USA
| | - Fan Zhang
- Department of Physics, University of Texas at Dallas, Richardson, Texas 75080, USA
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30
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Avraham N, Reiner J, Kumar-Nayak A, Morali N, Batabyal R, Yan B, Beidenkopf H. Quasiparticle Interference Studies of Quantum Materials. ADVANCED MATERIALS (DEERFIELD BEACH, FLA.) 2018; 30:e1707628. [PMID: 29862584 DOI: 10.1002/adma.201707628] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/31/2017] [Revised: 03/13/2018] [Indexed: 06/08/2023]
Abstract
Exotic electronic states are realized in novel quantum materials. This field is revolutionized by the topological classification of materials. Such compounds necessarily host unique states on their boundaries. Scanning tunneling microscopy studies of these surface states have provided a wealth of spectroscopic characterization, with the successful cooperation of ab initio calculations. The method of quasiparticle interference imaging proves to be particularly useful for probing the dispersion relation of the surface bands. Herein, how a variety of additional fundamental electronic properties can be probed via this method is reviewed. It is demonstrated how quasiparticle interference measurements entail mesoscopic size quantization and the electronic phase coherence in semiconducting nanowires; helical spin protection and energy-momentum fluctuations in a topological insulator; and the structure of the Bloch wave function and the relative insusceptibility of topological electronic states to surface potential in a topological Weyl semimetal.
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Affiliation(s)
- Nurit Avraham
- Condensed Matter Department, Weizmann Institute of Science, Rehovot, 7610001, Israel
| | - Jonathan Reiner
- Condensed Matter Department, Weizmann Institute of Science, Rehovot, 7610001, Israel
| | - Abhay Kumar-Nayak
- Condensed Matter Department, Weizmann Institute of Science, Rehovot, 7610001, Israel
| | - Noam Morali
- Condensed Matter Department, Weizmann Institute of Science, Rehovot, 7610001, Israel
| | - Rajib Batabyal
- Condensed Matter Department, Weizmann Institute of Science, Rehovot, 7610001, Israel
| | - Binghai Yan
- Condensed Matter Department, Weizmann Institute of Science, Rehovot, 7610001, Israel
| | - Haim Beidenkopf
- Condensed Matter Department, Weizmann Institute of Science, Rehovot, 7610001, Israel
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31
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Su Z, Zarassi A, Hsu JF, San-Jose P, Prada E, Aguado R, Lee EJH, Gazibegovic S, Op Het Veld RLM, Car D, Plissard SR, Hocevar M, Pendharkar M, Lee JS, Logan JA, Palmstrøm CJ, Bakkers EPAM, Frolov SM. Mirage Andreev Spectra Generated by Mesoscopic Leads in Nanowire Quantum Dots. PHYSICAL REVIEW LETTERS 2018; 121:127705. [PMID: 30296125 DOI: 10.1103/physrevlett.121.127705] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/10/2018] [Indexed: 06/08/2023]
Abstract
We study transport mediated by Andreev bound states formed in InSb nanowire quantum dots. Two kinds of superconducting source and drain contacts are used: epitaxial Al/InSb devices exhibit a doubling of tunneling resonances, while, in NbTiN/InSb devices, Andreev spectra of the dot appear to be replicated multiple times at increasing source-drain bias voltages. In both devices, a mirage of a crowded spectrum is created. To describe the observations a model is developed that combines the effects of a soft induced gap and of additional Andreev bound states both in the quantum dot and in the finite regions of the nanowire adjacent to the quantum dot. Understanding of Andreev spectroscopy is important for the correct interpretation of Majorana experiments done on the same structures.
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Affiliation(s)
- Z Su
- Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA
| | - A Zarassi
- Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA
| | - J-F Hsu
- Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA
| | - P San-Jose
- Instituto de Ciencia de Materiales de Madrid (ICMM-CSIC), Cantoblanco, 28049 Madrid, Spain
| | - E Prada
- Departamento de Fisica de la Materia Condensada, Condensed Matter Physics Center (IFIMAC) and Instituto Nicolas Cabrera, Universidad Autonoma de Madrid, E-28049 Madrid, Spain
| | - R Aguado
- Instituto de Ciencia de Materiales de Madrid (ICMM-CSIC), Cantoblanco, 28049 Madrid, Spain
| | - E J H Lee
- Departamento de Fisica de la Materia Condensada, Condensed Matter Physics Center (IFIMAC) and Instituto Nicolas Cabrera, Universidad Autonoma de Madrid, E-28049 Madrid, Spain
| | - S Gazibegovic
- Eindhoven University of Technology, 5600 MB, Eindhoven, Netherlands
| | | | - D Car
- Eindhoven University of Technology, 5600 MB, Eindhoven, Netherlands
| | - S R Plissard
- LAAS CNRS, Université de Toulouse, 31031 Toulouse, France
| | - M Hocevar
- Univ. Grenoble Alpes, CNRS, Grenoble INP, Institut Néel, 38000 Grenoble, France
| | - M Pendharkar
- Electrical and Computer Engineering, University of California Santa Barbara, Santa Barbara, California 93106, USA
| | - J S Lee
- California NanoSystems Institute, University of California Santa Barbara, Santa Barbara, California 93106, USA
| | - J A Logan
- Materials Department, University of California, Santa Barbara, Santa Barbara, California 93106, USA
| | - C J Palmstrøm
- Electrical and Computer Engineering, University of California Santa Barbara, Santa Barbara, California 93106, USA
- California NanoSystems Institute, University of California Santa Barbara, Santa Barbara, California 93106, USA
- Materials Department, University of California, Santa Barbara, Santa Barbara, California 93106, USA
| | - E P A M Bakkers
- Eindhoven University of Technology, 5600 MB, Eindhoven, Netherlands
| | - S M Frolov
- Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA
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32
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Manesco ALR, Weber G, Rodrigues D. Hidden chiral symmetries in BDI multichannel Kitaev chains. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2018; 30:175401. [PMID: 29546849 DOI: 10.1088/1361-648x/aab722] [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
Realistic implementations of the Kitaev chain require, in general, the introduction of extra internal degrees of freedom. In the present work, we discuss the presence of hidden BDI symmetries for free Hamiltonians describing systems with an arbitrary number of internal degrees of freedom. We generalize results of a spinfull Kitaev chain to construct a Hamiltonian with n internal degrees of freedom and obtain the corresponding hidden chiral symmetry. As an explicit application of this generalized result, we exploit by analytical and numerical calculations the case of a spinful two-band Kitaev chain, which can host up to four Majorana bound states. We also observe the appearence of minigap states, when chiral symmetry is broken.
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Affiliation(s)
| | - Gabrielle Weber
- Lorena Engineering School, University of São Paulo Lorena, SP, Brazil
| | - Durval Rodrigues
- Lorena Engineering School, University of São Paulo Lorena, SP, Brazil
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33
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Gül Ö, Zhang H, Bommer JDS, de Moor MWA, Car D, Plissard SR, Bakkers EPAM, Geresdi A, Watanabe K, Taniguchi T, Kouwenhoven LP. Ballistic Majorana nanowire devices. NATURE NANOTECHNOLOGY 2018; 13:192-197. [PMID: 29335565 DOI: 10.1038/s41565-017-0032-8] [Citation(s) in RCA: 22] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/15/2017] [Accepted: 11/20/2017] [Indexed: 06/07/2023]
Abstract
Majorana modes are zero-energy excitations of a topological superconductor that exhibit non-Abelian statistics1-3. Following proposals for their detection in a semiconductor nanowire coupled to an s-wave superconductor4,5, several tunnelling experiments reported characteristic Majorana signatures6-11. Reducing disorder has been a prime challenge for these experiments because disorder can mimic the zero-energy signatures of Majoranas12-16, and renders the topological properties inaccessible17-20. Here, we show characteristic Majorana signatures in InSb nanowire devices exhibiting clear ballistic transport properties. Application of a magnetic field and spatial control of carrier density using local gates generates a zero bias peak that is rigid over a large region in the parameter space of chemical potential, Zeeman energy and tunnel barrier potential. The reduction of disorder allows us to resolve separate regions in the parameter space with and without a zero bias peak, indicating topologically distinct phases. These observations are consistent with the Majorana theory in a ballistic system 21 , and exclude the known alternative explanations that invoke disorder12-16 or a nonuniform chemical potential22,23.
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Affiliation(s)
- Önder Gül
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology, Delft, The Netherlands.
- Department of Physics, Harvard University, Cambridge, MA, USA.
| | - Hao Zhang
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology, Delft, The Netherlands.
| | - Jouri D S Bommer
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology, Delft, The Netherlands
| | - Michiel W A de Moor
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology, Delft, The Netherlands
| | - Diana Car
- Department of Applied Physics, Eindhoven University of Technology, Eindhoven, The Netherlands
| | - Sébastien R Plissard
- Department of Applied Physics, Eindhoven University of Technology, Eindhoven, The Netherlands
- CNRS-Laboratoire d'Analyse et d'Architecture des Systèmes (LAAS), Université de Toulouse, Toulouse, France
| | - Erik P A M Bakkers
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology, Delft, The Netherlands
- Department of Applied Physics, Eindhoven University of Technology, Eindhoven, The Netherlands
| | - Attila Geresdi
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology, Delft, The Netherlands
| | - Kenji Watanabe
- Advanced Materials Laboratory, National Institute for Materials Science, Tsukuba, Japan
| | - Takashi Taniguchi
- Advanced Materials Laboratory, National Institute for Materials Science, Tsukuba, Japan
| | - Leo P Kouwenhoven
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology, Delft, The Netherlands.
- Microsoft Station Q Delft, Delft, The Netherlands.
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34
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Stanescu TD, Sitek A, Manolescu A. Robust topological phase in proximitized core-shell nanowires coupled to multiple superconductors. BEILSTEIN JOURNAL OF NANOTECHNOLOGY 2018; 9:1512-1526. [PMID: 29977684 PMCID: PMC6009546 DOI: 10.3762/bjnano.9.142] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/03/2017] [Accepted: 04/13/2018] [Indexed: 05/05/2023]
Abstract
We consider core-shell nanowires with prismatic geometry contacted with two or more superconductors in the presence of a magnetic field applied parallel to the wire. In this geometry, the lowest energy states are localized on the outer edges of the shell, which strongly inhibits the orbital effects of the longitudinal magnetic field that are detrimental to Majorana physics. Using a tight-binding model of coupled parallel chains, we calculate the topological phase diagram of the hybrid system in the presence of non-vanishing transverse potentials and finite relative phases between the parent superconductors. We show that having finite relative phases strongly enhances the stability of the induced topological superconductivity over a significant range of chemical potentials and reduces the value of the critical field associated with the topological quantum phase transition.
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Affiliation(s)
- Tudor D Stanescu
- Department of Physics and Astronomy, West Virginia University, Morgantown, WV 26506, USA
| | - Anna Sitek
- Department of Theoretical Physics, Faculty of Fundamental Problems of Technology, Wroclaw University of Science and Technology, Wroclaw, 50-370, Poland
- School of Science and Engineering, Reykjavik University, Menntavegur 1, IS-101 Reykjavik, Iceland
| | - Andrei Manolescu
- School of Science and Engineering, Reykjavik University, Menntavegur 1, IS-101 Reykjavik, Iceland
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35
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Zuo K, Mourik V, Szombati DB, Nijholt B, van Woerkom DJ, Geresdi A, Chen J, Ostroukh VP, Akhmerov AR, Plissard SR, Car D, Bakkers EPAM, Pikulin DI, Kouwenhoven LP, Frolov SM. Supercurrent Interference in Few-Mode Nanowire Josephson Junctions. PHYSICAL REVIEW LETTERS 2017; 119:187704. [PMID: 29219554 DOI: 10.1103/physrevlett.119.187704] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/07/2017] [Indexed: 06/07/2023]
Abstract
Junctions created by coupling two superconductors via a semiconductor nanowire in the presence of high magnetic fields are the basis for the potential detection, fusion, and braiding of Majorana bound states. We study NbTiN/InSb nanowire/NbTiN Josephson junctions and find that the dependence of the critical current on the magnetic field exhibits gate-tunable nodes. This is in contrast with a well-known Fraunhofer effect, under which critical current nodes form a regular pattern with a period fixed by the junction area. Based on a realistic numerical model we conclude that the Zeeman effect induced by the magnetic field and the spin-orbit interaction in the nanowire are insufficient to explain the observed evolution of the Josephson effect. We find the interference between the few occupied one-dimensional modes in the nanowire to be the dominant mechanism responsible for the critical current behavior. We also report a strong suppression of critical currents at finite magnetic fields that should be taken into account when designing circuits based on Majorana bound states.
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Affiliation(s)
- Kun Zuo
- QuTech, Delft University of Technology, 2600 GA Delft, Netherlands
- Kavli Institute of Nanoscience, Delft University of Technology, 2600 GA Delft, Netherlands
| | - Vincent Mourik
- QuTech, Delft University of Technology, 2600 GA Delft, Netherlands
- Kavli Institute of Nanoscience, Delft University of Technology, 2600 GA Delft, Netherlands
- Centre for Quantum Computation and Communication Technologies, School of Electrical Engineering and Telecommunications, UNSW Sydney, Sydney, New South Wales 2052, Australia
| | - Daniel B Szombati
- QuTech, Delft University of Technology, 2600 GA Delft, Netherlands
- Kavli Institute of Nanoscience, Delft University of Technology, 2600 GA Delft, Netherlands
- Australian Research Council Centre of Excellence for Engineered Quantum Systems, St Lucia, Queensland 4072, Australia
- School of Mathematics and Physics, University of Queensland, St Lucia, Queensland 4072, Australia
| | - Bas Nijholt
- Kavli Institute of Nanoscience, Delft University of Technology, 2600 GA Delft, Netherlands
| | - David J van Woerkom
- QuTech, Delft University of Technology, 2600 GA Delft, Netherlands
- Kavli Institute of Nanoscience, Delft University of Technology, 2600 GA Delft, Netherlands
- Department of Physics, ETH Zurich, CH-8093 Zurich, Switzerland
| | - Attila Geresdi
- QuTech, Delft University of Technology, 2600 GA Delft, Netherlands
- Kavli Institute of Nanoscience, Delft University of Technology, 2600 GA Delft, Netherlands
| | - Jun Chen
- Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA
| | | | - Anton R Akhmerov
- Kavli Institute of Nanoscience, Delft University of Technology, 2600 GA Delft, Netherlands
| | - Sebastién R Plissard
- Kavli Institute of Nanoscience, Delft University of Technology, 2600 GA Delft, Netherlands
- Department of Applied Physics, Eindhoven University of Technology, 5600 MB Eindhoven, Netherlands
| | - Diana Car
- QuTech, Delft University of Technology, 2600 GA Delft, Netherlands
- Kavli Institute of Nanoscience, Delft University of Technology, 2600 GA Delft, Netherlands
- Department of Applied Physics, Eindhoven University of Technology, 5600 MB Eindhoven, Netherlands
| | - Erik P A M Bakkers
- QuTech, Delft University of Technology, 2600 GA Delft, Netherlands
- Kavli Institute of Nanoscience, Delft University of Technology, 2600 GA Delft, Netherlands
- Department of Applied Physics, Eindhoven University of Technology, 5600 MB Eindhoven, Netherlands
| | - Dmitry I Pikulin
- Station Q, Microsoft Research, Santa Barbara, California 93106-6105, USA
- Department of Physics and Astronomy, University of British Columbia, Vancouver British Columbia, Canada V6T 1Z1
- Quantum Matter Institute, University of British Columbia, Vancouver British Columbia, Canada V6T 1Z4
| | - Leo P Kouwenhoven
- QuTech, Delft University of Technology, 2600 GA Delft, Netherlands
- Kavli Institute of Nanoscience, Delft University of Technology, 2600 GA Delft, Netherlands
- Station Q Delft, Microsoft Research, 2600 GA, Delft, Netherlands
| | - Sergey M Frolov
- Kavli Institute of Nanoscience, Delft University of Technology, 2600 GA Delft, Netherlands
- Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA
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