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Bento Ribeiro RC, Correa JH, Ricco LS, Shelykh IA, Continentino MA, Seridonio AC, Minissale M, Le Lay G, Figueira MS. Spin-polarized Majorana zero modes in proximitized superconducting penta-silicene nanoribbons. Sci Rep 2023; 13:17965. [PMID: 37863891 PMCID: PMC10589331 DOI: 10.1038/s41598-023-44739-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/06/2023] [Accepted: 10/11/2023] [Indexed: 10/22/2023] Open
Abstract
We theoretically propose penta-silicene nanoribbons (p-SiNRs) with induced p-wave superconductivity as a platform for the emergence of spin-polarized Majorana zero-modes (MZMs). The model explicitly considers the key ingredients of well-known Majorana hybrid nanowire setups: Rashba spin-orbit coupling, magnetic field perpendicular to the nanoribbon plane, and first nearest neighbor hopping with p-wave superconducting pairing. The energy spectrum of the system, as a function of chemical potential, reveals the existence of MZMs with a well-defined spin orientation localized at the opposite ends of both the top and bottom chains of the p-SiNR, associated with well-localized and nonoverlapping wave function profiles. Well-established experimental techniques enable the fabrication of highly ordered p-SiNRs, complemented by a thin lead film on top, responsible for inducing p-wave superconductivity through proximity effect. Moreover, the emergence of MZMs with explicit opposite spin orientations for some set of model parameters opens a new avenue for exploring quantum computing operations, which accounts for both MZMs and spin properties, as well as for new MZMs probe devices based on spin-polarized electronic transport mechanisms.
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Affiliation(s)
- R C Bento Ribeiro
- Centro Brasileiro de Pesquisas Físicas, Rua Dr. Xavier Sigaud, 150, Urca, Rio de Janeiro, RJ, 22290-180, Brazil
| | - J H Correa
- Universidad Tecnológica del Perú, Nathalio Sánchez, 125, 15046, Lima, Peru
- AGH University of Krakow, Academic Centre for Materials and Nanotechnology, al. A. Mickiewicza 30, 30-059, Kraków, Poland
| | - L S Ricco
- Science Institute, University of Iceland, Dunhagi-3, 107, Reykjavik, Iceland
| | - I A Shelykh
- Science Institute, University of Iceland, Dunhagi-3, 107, Reykjavik, Iceland
- Russian Quantum Center, Skolkovo IC, Bolshoy Bulvar 30 bld. 1, Moscow, 121205, Russia
| | - Mucio A Continentino
- Centro Brasileiro de Pesquisas Físicas, Rua Dr. Xavier Sigaud, 150, Urca, Rio de Janeiro, RJ, 22290-180, Brazil
| | - A C Seridonio
- School of Engineering, Department of Physics and Chemistry, São Paulo State University (UNESP), Ilha Solteira, SP, 15385-000, Brazil
| | - M Minissale
- Aix-Marseille Université, CNRS, PIIM UMR 7345, 13397, Marseille Cedex, France
| | - G Le Lay
- Aix-Marseille Université, CNRS, PIIM UMR 7345, 13397, Marseille Cedex, France
| | - M S Figueira
- Instituto de Física, Universidade Federal Fluminense, Av. Litorânea s/N, Niterói, RJ, CEP: 24210-340, Brazil.
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2
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Yang FB. Spin dependent Fano interference in a serial double quantum dot coupled to two topological superconducting quantum wires. PHYSICS LETTERS A 2021; 401:127350. [DOI: 10.1016/j.physleta.2021.127350] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 09/01/2023]
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3
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Qi L, Wang GL, Liu S, Zhang S, Wang HF. Controllable photonic and phononic topological state transfers in a small optomechanical lattice. OPTICS LETTERS 2020; 45:2018-2021. [PMID: 32236057 DOI: 10.1364/ol.388835] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/21/2020] [Accepted: 03/07/2020] [Indexed: 06/11/2023]
Abstract
We propose a scheme to achieve the photonic and the phononic state transfers via the topological protected edge channel based on a one-dimensional small optomechanical lattice. We find that the optomechanical lattice can be mapped into a Su-Schrieffer-Heeger model after eliminating the counter rotating wave terms. By dint of the edge channel of the Su-Schrieffer-Heeger model, we show that the quantum state transfer between the photonic left and the right edge states can be achieved with a high fidelity. Especially, our scheme can also achieve another phononic state transfer based on the same channel via controlling the next-nearest-neighboring interactions between the cavity fields; this is different from the previous investigations achieving only one kind of quantum state transfer. Our scheme provides a novel, to the best of our knowledge, path to switch two different kinds of quantum state transfers in a controllable way.
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Abstract
We construct a generalized system by introducing an additional long-range hopping to the well-known Su-Schrieffer-Heeger (SSH) model. This system exhibits richer topological properties including non-trivial topological phases and associated localized edge states. We study the zero-energy edge states in detail and derive the edge-state wave functions using two different methods. Furthermore, we propose a possible setup using octupole moments optically excited on an array of dielectric particles for the realization of the system, and by adjusting the coupling strengths between neighboring particles we can control the hotspots (near-field enhancement) in such structures.
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5
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Zambrano D, Ramos-Andrade JP, Orellana PA. Bound states in the continuum poisoned by Majorana fermions. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2018; 30:375301. [PMID: 30073977 DOI: 10.1088/1361-648x/aad7ca] [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
In this work, we study the bound states in the continuum (BICs) in a system formed by a triple quantum dot array embedded between two one-dimensional topological superconductors (TSCs), both hosting Majorana bound states (MBSs) at their ends. The results show the formation of BICs with topological characteristics due to the presence of MBSs. This is a consequence of the interplay between the BIC arising from quantum dots states by means of energy level symmetry breaking through gate voltages, and MBSs leaked into the quantum dots. The BIC is not observed when both TSCs are in long wire limit, i.e. for vanishing inter MBSs coupling, while it projects into the electronic transmission whenever the inter MBSs couplings are away from zero, regardless if they have different strength and/or the phase difference between both TSCs. We study the behavior of BICs poisoned by MBSs as a function of the parameters that are controlling the system. We believe our findings could be useful to implement a protection tool for BICs using MBSs based on tunable gate voltages.
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Affiliation(s)
- D Zambrano
- Departamento de Física, Universidad Técnica Federico Santa María, Casilla 110 V, Valparaíso, Chile
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6
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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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7
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Ricco LS, Dessotti FA, Shelykh IA, Figueira MS, Seridonio AC. Tuning of heat and charge transport by Majorana fermions. Sci Rep 2018; 8:2790. [PMID: 29434249 PMCID: PMC5809467 DOI: 10.1038/s41598-018-21180-9] [Citation(s) in RCA: 18] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/15/2017] [Accepted: 01/29/2018] [Indexed: 11/08/2022] Open
Abstract
We investigate theoretically thermal and electrical conductances for the system consisting of a quantum dot (QD) connected both to a pair of Majorana fermions residing at the edges of a Kitaev wire and two metallic leads. We demonstrate that both quantities reveal pronounced resonances, whose positions can be controlled by tuning of an asymmetry of the couplings of the QD and a pair of MFs. Similar behavior is revealed for the thermopower, Wiedemann-Franz law and dimensionless thermoelectric figure of merit. The considered geometry can thus be used as a tuner of heat and charge transport assisted by MFs.
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Affiliation(s)
- L S Ricco
- Departamento de Física e Química, Unesp - Univ Estadual Paulista, 15385-000, Ilha Solteira, SP, Brazil
| | - F A Dessotti
- Departamento de Física e Química, Unesp - Univ Estadual Paulista, 15385-000, Ilha Solteira, SP, Brazil
| | - I A Shelykh
- Science Institute, University of Iceland, Dunhagi-3, IS-107, Reykjavik, Iceland
- ITMO University, St. Petersburg, 197101, Russia
| | - M S Figueira
- Instituto de Física, Universidade Federal Fluminense, 24210-340, Niterói, RJ, Brazil
| | - A C Seridonio
- Departamento de Física e Química, Unesp - Univ Estadual Paulista, 15385-000, Ilha Solteira, SP, Brazil.
- IGCE, Departamento de Física, Unesp - Univ Estadual Paulista, 13506-900, Rio Claro, SP, Brazil.
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8
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Ramos-Andrade JP, Orellana PA, Ulloa SE. Detecting coupling of Majorana bound states with an Aharonov-Bohm interferometer. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2018; 30:045301. [PMID: 29239309 DOI: 10.1088/1361-648x/aaa1b2] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
We study the transport properties of an interferometer composed by a quantum dot (QD) coupled with two normal leads and two one-dimensional topological superconductor nanowires (TNWs) hosting Majorana bound states (MBS) at their ends. The geometry considered is such that one TNW has both ends connected with the QD, forming an Aharonov-Bohm (AB) interferometer threaded by an external magnetic flux, while the other TNW is placed near the interferometer TNW. This geometry can alternatively be seen as a long wire contacted across a local defect, with possible coupling between independent-MBS. We use the Green's function formalism to calculate the conductance across normal current leads on the QD. We find that the conductance exhibits a half-quantum value regardless of the AB phase and location of the dot energy level, whenever the interferometer configuration interacts with the neighboring TNW. These findings suggest that such a geometry could be used for a sensitive detection of MBS interactions across TNWs, exploiting the high sensitivity of conductance to the AB phase in the interferometer.
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Affiliation(s)
- J P Ramos-Andrade
- Departamento de Física, Universidad Técnica Federico Santa María, Casilla 110 V, Valparaíso, Chile. Department of Physics and Astronomy, and Nanoscale and Quantum Phenomena Institute, Ohio University, Athens, OH 45701-2979, United States of America
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9
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Romito A, Gefen Y. Ubiquitous Nonlocal Entanglement with Majorana Zero Modes. PHYSICAL REVIEW LETTERS 2017; 119:157702. [PMID: 29077455 DOI: 10.1103/physrevlett.119.157702] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/29/2017] [Indexed: 06/07/2023]
Abstract
Entanglement in quantum mechanics contradicts local realism and is a manifestation of quantum nonlocality. Its presence can be detected through the violation of Bell, or Clauser-Horne-Shimony-Holt (CHSH) inequalities. Paradigmatic quantum systems provide examples of both, nonentangled and entangled states. Here, we consider a minimal complexity setup consisting of six Majorana zero modes. We find that any allowed state in the degenerate Majorana space is nonlocally entangled. We show how to measure (with available techniques) the CHSH-violating correlations using either intermediate strength or weak measurement protocols.
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Affiliation(s)
- Alessandro Romito
- Department of Condensed Matter Physics, The Weizmann Institute of Science, Rehovot 76100, Israel
| | - Yuval Gefen
- Department of Physics, Lancaster University, Lancaster LA1 4YB, United Kingdom
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10
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Jeon S, Xie Y, Li J, Wang Z, Bernevig BA, Yazdani A. Distinguishing a Majorana zero mode using spin-resolved measurements. Science 2017; 358:772-776. [DOI: 10.1126/science.aan3670] [Citation(s) in RCA: 153] [Impact Index Per Article: 21.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/03/2017] [Accepted: 09/29/2017] [Indexed: 12/13/2022]
Abstract
One-dimensional topological superconductors host Majorana zero modes (MZMs), the nonlocal property of which could be exploited for quantum computing applications. We use spin-polarized scanning tunneling microscopy to show that MZMs realized in self-assembled Fe chains on the surface of Pb have a spin polarization that exceeds that stemming from the magnetism of these chains. This feature, captured by our model calculations, is a direct consequence of the nonlocality of the Hilbert space of MZMs emerging from a topological band structure. Our study establishes spin-polarization measurements as a diagnostic tool to distinguish topological MZMs from trivial in-gap states of a superconductor.
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Affiliation(s)
- Sangjun Jeon
- Joseph Henry Laboratories and Department of Physics, Princeton University, Princeton, NJ 08544, USA
| | - Yonglong Xie
- Joseph Henry Laboratories and Department of Physics, Princeton University, Princeton, NJ 08544, USA
| | - Jian Li
- Joseph Henry Laboratories and Department of Physics, Princeton University, Princeton, NJ 08544, USA
- Institute for Natural Sciences, Westlake Institute for Advanced Study, Hangzhou, Zhejiang, China
- Westlake University, Hangzhou, Zhejiang, China
| | - Zhijun Wang
- Joseph Henry Laboratories and Department of Physics, Princeton University, Princeton, NJ 08544, USA
| | - B. Andrei Bernevig
- Joseph Henry Laboratories and Department of Physics, Princeton University, Princeton, NJ 08544, USA
| | - Ali Yazdani
- Joseph Henry Laboratories and Department of Physics, Princeton University, Princeton, NJ 08544, USA
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11
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Drachmann ACC, Suominen HJ, Kjaergaard M, Shojaei B, Palmstrøm CJ, Marcus CM, Nichele F. Proximity Effect Transfer from NbTi into a Semiconductor Heterostructure via Epitaxial Aluminum. NANO LETTERS 2017; 17:1200-1203. [PMID: 28072541 DOI: 10.1021/acs.nanolett.6b04964] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
We demonstrate the transfer of the superconducting properties of NbTi, a large-gap high-critical-field superconductor, into an InAs heterostructure via a thin intermediate layer of epitaxial Al. Two device geometries, a Josephson junction and a gate-defined quantum point contact, are used to characterize interface transparency and the two-step proximity effect. In the Josephson junction, multiple Andreev reflections reveal near-unity transparency with an induced gap Δ* = 0.50 meV and a critical temperature of 7.8 K. Tunneling spectroscopy yields a hard induced gap in the InAs adjacent to the superconductor of Δ* = 0.43 meV with substructure characteristic of both Al and NbTi.
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Affiliation(s)
- A C C Drachmann
- Center for Quantum Devices and Station Q Copenhagen, Niels Bohr Institute University of Copenhagen , Universitetsparken 5, 2100 Copenhagen, Denmark
| | - H J Suominen
- Center for Quantum Devices and Station Q Copenhagen, Niels Bohr Institute University of Copenhagen , Universitetsparken 5, 2100 Copenhagen, Denmark
| | - M Kjaergaard
- 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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12
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Li Y. Noise Threshold and Resource Cost of Fault-Tolerant Quantum Computing with Majorana Fermions in Hybrid Systems. PHYSICAL REVIEW LETTERS 2016; 117:120403. [PMID: 27689257 DOI: 10.1103/physrevlett.117.120403] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/11/2016] [Indexed: 06/06/2023]
Abstract
Fault-tolerant quantum computing in systems composed of both Majorana fermions and topologically unprotected quantum systems, e.g., superconducting circuits or quantum dots, is studied in this Letter. Errors caused by topologically unprotected quantum systems need to be corrected with error-correction schemes, for instance, the surface code. We find that the error-correction performance of such a hybrid topological quantum computer is not superior to a normal quantum computer unless the topological charge of Majorana fermions is insusceptible to noise. If errors changing the topological charge are rare, the fault-tolerance threshold is much higher than the threshold of a normal quantum computer and a surface-code logical qubit could be encoded in only tens of topological qubits instead of about 1,000 normal qubits.
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Affiliation(s)
- Ying Li
- Department of Materials, University of Oxford, Parks Road, Oxford OX1 3PH, United Kingdom
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13
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Shi ZC, Wang W, Yi XX. Quantum gates by periodic driving. Sci Rep 2016; 6:22077. [PMID: 26911900 PMCID: PMC4766515 DOI: 10.1038/srep22077] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/06/2015] [Accepted: 02/05/2016] [Indexed: 12/04/2022] Open
Abstract
Topological quantum computation has been extensively studied in the past decades due to its robustness against decoherence. One way to realize the topological quantum computation is by adiabatic evolutions—it requires relatively long time to complete a gate, so the speed of quantum computation slows down. In this work, we present a method to realize single qubit quantum gates by periodic driving. Compared to adiabatic evolution, the single qubit gates can be realized at a fixed time much shorter than that by adiabatic evolution. The driving fields can be sinusoidal or square-well field. With the sinusoidal driving field, we derive an expression for the total operation time in the high-frequency limit, and an exact analytical expression for the evolution operator without any approximations is given for the square well driving. This study suggests that the period driving could provide us with a new direction in regulations of the operation time in topological quantum computation.
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Affiliation(s)
- Z C Shi
- Center for Quantum Sciences and School of Physics, Northeast Normal University, Changchun 130024, China.,School of Physics and Optoelectronic Technology Dalian University of Technology, Dalian 116024, China
| | - W Wang
- Center for Quantum Sciences and School of Physics, Northeast Normal University, Changchun 130024, China
| | - X X Yi
- Center for Quantum Sciences and School of Physics, Northeast Normal University, Changchun 130024, China
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14
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Abstract
Hybrid architectures, consisting of conventional and topological qubits, have recently attracted much attention due to their capability in consolidating robustness of topological qubits and universality of conventional qubits. However, these two kinds of qubits are normally constructed in significantly different energy scales, and thus the energy mismatch is a major obstacle for their coupling, which can support the exchange of quantum information between them. Here we propose a microwave photonic quantum bus for a strong direct coupling between the topological and conventional qubits, where the energy mismatch is compensated by an external driving field. In the framework of tight-binding simulation and perturbation approach, we show that the energy splitting of Majorana fermions in a finite length nanowire, which we use to define topological qubits, is still robust against local perturbations due to the topology of the system. Therefore, the present scheme realizes a rather robust interface between the flying and topological qubits. Finally, we demonstrate that this quantum bus can also be used to generate multipartitie entangled states with the topological qubits.
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Affiliation(s)
- Zheng-Yuan Xue
- 1] Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, and School of Physics and Telecommunication Engineering, South China Normal University, Guangzhou 510006, China [2] Department of Physics and Center of Theoretical and Computational Physics, The University of Hong Kong, Pokfulam Road, Hong Kong, China
| | - Ming Gong
- Department of Physics and Center for Quantum Coherence, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong, China
| | - Jia Liu
- Department of Physics and Center for Quantum Coherence, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong, China
| | - Yong Hu
- 1] Department of Physics and Center of Theoretical and Computational Physics, The University of Hong Kong, Pokfulam Road, Hong Kong, China [2] School of Physics, Huazhong University of Science and Technology, Wuhan 430074, China
| | - Shi-Liang Zhu
- 1] National Laboratory of Solid State Microstructure and School of Physics, Nanjing University, Nanjing 210093, China [2] Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
| | - Z D Wang
- Department of Physics and Center of Theoretical and Computational Physics, The University of Hong Kong, Pokfulam Road, Hong Kong, China
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15
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Haim A, Berg E, von Oppen F, Oreg Y. Signatures of majorana zero modes in spin-resolved current correlations. PHYSICAL REVIEW LETTERS 2015; 114:166406. [PMID: 25955064 DOI: 10.1103/physrevlett.114.166406] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/11/2014] [Indexed: 06/04/2023]
Abstract
We consider a normal lead coupled to a Majorana bound state. We show that the spin-resolved current correlations exhibit unique features which distinguish Majorana bound states from other low-energy resonances. In particular, the spin-up and spin-down currents from a Majorana bound state are anticorrelated at low bias voltages, and become uncorrelated at higher voltages. This behavior is independent of the exact form of coupling to the lead, and of the direction of the spin polarization. In contrast, an ordinary low-energy Andreev bound state gives rise to a positive correlation between the spin-up and spin-down currents, and this spin-resolved current-current correlation approaches a nonzero constant at high bias voltages. We discuss experimental setups in which this effect can be measured.
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Affiliation(s)
- Arbel Haim
- Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 76100, Israel
| | - Erez Berg
- Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 76100, Israel
| | - Felix von Oppen
- Dahlem Center for Complex Quantum Systems and Fachbereich Physik, Freie Universität Berlin, 14195 Berlin, Germany
| | - Yuval Oreg
- Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 76100, Israel
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16
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He JJ, Ng TK, Lee PA, Law KT. Selective equal-spin Andreev reflections induced by Majorana fermions. PHYSICAL REVIEW LETTERS 2014; 112:037001. [PMID: 24484161 DOI: 10.1103/physrevlett.112.037001] [Citation(s) in RCA: 31] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/10/2013] [Indexed: 06/03/2023]
Abstract
In this work, we find that Majorana fermions induce selective equal spin Andreev reflections (SESARs), in which incoming electrons with certain spin polarization in the lead are reflected as counterpropagating holes with the same spin. The spin polarization direction of the electrons of this Andreev reflected channel is selected by the Majorana fermions. Moreover, electrons with opposite spin polarization are always reflected as electrons with unchanged spin. As a result, the charge current in the lead is spin polarized. Therefore, a topological superconductor which supports Majorana fermions can be used as a novel device to create fully spin-polarized currents in paramagnetic leads. We point out that SESARs can also be used to detect Majorana fermions in topological superconductors.
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Affiliation(s)
- James J He
- Department of Physics, Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong, China
| | - T K Ng
- Department of Physics, Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong, China
| | - Patrick A Lee
- Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - K T Law
- Department of Physics, Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong, China
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17
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Reynoso AA, Frustaglia D. Complex band structure eigenvalue method adapted to Floquet systems: topological superconducting wires as a case study. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2014; 26:035301. [PMID: 24353216 DOI: 10.1088/0953-8984/26/3/035301] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
For systems that can be modeled as a single-particle lattice extended along a privileged direction, such as, for example, quantum wires, the so-called eigenvalue method provides full information about the propagating and evanescent modes as a function of energy. This complex band structure method can be applied either to lattices consisting of an infinite succession of interconnected layers described by the same local Hamiltonian or to superlattices: systems in which the spatial periodicity involves more than one layer. Here, for time-dependent systems subject to a periodic driving, we present an adapted version of the superlattice scheme capable of obtaining the Floquet states and the Floquet quasienergy spectrum. Within this scheme the time periodicity is treated as existing along a spatial dimension added to the original system. The solutions at a single energy for the enlarged artificial system provide the solutions of the original Floquet problem. The method is suited for arbitrary periodic excitations, including strong and anharmonic drivings. We illustrate the capabilities of the methods for both time-independent and time-dependent systems by discussing: (a) topological superconductors in multimode quantum wires with spin-orbit interaction and (b) microwave driven quantum dots in contact with a topological superconductor.
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Affiliation(s)
- Andres A Reynoso
- ARC Centre for Engineered Quantum Systems, School of Physics, The University of Sydney, NSW 2006, Australia
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18
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Deng MT, Yu CL, Huang GY, Larsson M, Caroff P, Xu HQ. Anomalous zero-bias conductance peak in a Nb-InSb nanowire-Nb hybrid device. NANO LETTERS 2012; 12:6414-6419. [PMID: 23181691 DOI: 10.1021/nl303758w] [Citation(s) in RCA: 346] [Impact Index Per Article: 28.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
Abstract
Semiconductor InSb nanowires are expected to provide an excellent material platform for the study of Majorana fermions in solid state systems. Here, we report on the realization of a Nb-InSb nanowire-Nb hybrid quantum device and the observation of a zero-bias conductance peak structure in the device. An InSb nanowire quantum dot is formed in the device between the two Nb contacts. Due to the proximity effect, the InSb nanowire segments covered by the superconductor Nb contacts turn to superconductors with a superconducting energy gap Δ(InSb) ∼ 0.25 meV. A tunable critical supercurrent is observed in the device in high back gate voltage regions in which the Fermi level in the InSb nanowire is located above the tunneling barriers of the quantum dot and the device is open to conduction. When a perpendicular magnetic field is applied to the devices, the critical supercurrent is seen to decrease as the magnetic field increases. However, at sufficiently low back gate voltages, the device shows the quasi-particle Coulomb blockade characteristics and the supercurrent is strongly suppressed even at zero magnetic field. This transport characteristic changes when a perpendicular magnetic field stronger than a critical value, at which the Zeeman energy in the InSb nanowire is E(z) ∼ Δ(InSb), is applied to the device. In this case, the transport measurements show a conductance peak at the zero bias voltage and the entire InSb nanowire in the device behaves as in a topological superconductor phase. We also show that this zero-bias conductance peak structure can persist over a large range of applied magnetic fields and could be interpreted as a transport signature of Majorana fermions in the InSb nanowire.
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Affiliation(s)
- M T Deng
- Division of Solid State Physics, Lund University, Box 118, S-221 00 Lund, Sweden
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