1
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Ten Haaf SLD, Wang Q, Bozkurt AM, Liu CX, Kulesh I, Kim P, Xiao D, Thomas C, Manfra MJ, Dvir T, Wimmer M, Goswami S. A two-site Kitaev chain in a two-dimensional electron gas. Nature 2024; 630:329-334. [PMID: 38867129 DOI: 10.1038/s41586-024-07434-9] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/18/2023] [Accepted: 04/17/2024] [Indexed: 06/14/2024]
Abstract
Artificial Kitaev chains can be used to engineer Majorana bound states (MBSs) in superconductor-semiconductor hybrids1-4. In this work, we realize a two-site Kitaev chain in a two-dimensional electron gas by coupling two quantum dots through a region proximitized by a superconductor. We demonstrate systematic control over inter-dot couplings through in-plane rotations of the magnetic field and via electrostatic gating of the proximitized region. This allows us to tune the system to sweet spots in parameter space, where robust correlated zero-bias conductance peaks are observed in tunnelling spectroscopy. To study the extent of hybridization between localized MBSs, we probe the evolution of the energy spectrum with magnetic field and estimate the Majorana polarization, an important metric for Majorana-based qubits5,6. The implementation of a Kitaev chain on a scalable and flexible two-dimensional platform provides a realistic path towards more advanced experiments that require manipulation and readout of multiple MBSs.
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Affiliation(s)
- Sebastiaan L D Ten Haaf
- QuTech and Kavli Institute of NanoScience, Delft University of Technology, Delft, The Netherlands
| | - Qingzhen Wang
- QuTech and Kavli Institute of NanoScience, Delft University of Technology, Delft, The Netherlands
| | - A Mert Bozkurt
- QuTech and Kavli Institute of NanoScience, Delft University of Technology, Delft, The Netherlands
| | - Chun-Xiao Liu
- QuTech and Kavli Institute of NanoScience, Delft University of Technology, Delft, The Netherlands
| | - Ivan Kulesh
- QuTech and Kavli Institute of NanoScience, Delft University of Technology, Delft, The Netherlands
| | - Philip Kim
- QuTech and Kavli Institute of NanoScience, Delft University of Technology, Delft, The Netherlands
| | - Di Xiao
- Department of Physics and Astronomy, Purdue University, West Lafayette, IN, USA
| | - Candice Thomas
- Department of Physics and Astronomy, Purdue University, West Lafayette, IN, USA
| | - Michael J Manfra
- Department of Physics and Astronomy, Purdue University, West Lafayette, IN, USA
- Elmore School of Electrical and Computer Engineering, Purdue University, West Lafayette, IN, USA
- School of Materials Engineering, Purdue University, West Lafayette, IN, USA
| | - Tom Dvir
- QuTech and Kavli Institute of NanoScience, Delft University of Technology, Delft, The Netherlands
| | - Michael Wimmer
- QuTech and Kavli Institute of NanoScience, Delft University of Technology, Delft, The Netherlands
| | - Srijit Goswami
- QuTech and Kavli Institute of NanoScience, Delft University of Technology, Delft, The Netherlands.
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2
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Wang SZ, Yu XQ, Wei LX, Wang L, Cheng QJ, Peng K, Cheng FJ, Liu Y, Li FS, Ma XC, Xue QK, Song CL. Quantum spin driven Yu-Shiba-Rusinov multiplets and fermion-parity-preserving phase transition in K 3C 60. Sci Bull (Beijing) 2024; 69:1392-1399. [PMID: 38594099 DOI: 10.1016/j.scib.2024.03.052] [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: 12/12/2023] [Revised: 02/07/2024] [Accepted: 03/22/2024] [Indexed: 04/11/2024]
Abstract
Magnetic impurities in superconductors are of increasing interest due to emergent Yu-Shiba-Rusinov (YSR) states and Majorana zero modes for fault-tolerant quantum computation. However, a direct relationship between the YSR multiple states and magnetic anisotropy splitting of quantum impurity spins remains poorly characterized. By using scanning tunneling microscopy, we systematically resolve individual transition-metal (Fe, Cr, and Ni) impurities induced YSR multiplets as well as their Zeeman effects in the K3C60 superconductor. The YSR multiplets show identical d orbital-like wave functions that are symmetry-mismatched to the threefold K3C60(1 1 1) host surface, breaking point-group symmetries of the spatial distribution of YSR bound states in real space. Remarkably, we identify an unprecedented fermion-parity-preserving quantum phase transition between ground states with opposite signs of the uniaxial magnetic anisotropy that can be manipulated by an external magnetic field. These findings can be readily understood in terms of anisotropy splitting of quantum impurity spins, and thus elucidate the intricate interplay between the magnetic anisotropy and YSR multiplets.
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Affiliation(s)
- Shu-Ze Wang
- State Key Laboratory of Low-Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, China
| | - Xue-Qing Yu
- State Key Laboratory of Low-Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, China
| | - Li-Xuan Wei
- State Key Laboratory of Low-Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, China
| | - Li Wang
- Vacuum Interconnected Nanotech Workstation, Suzhou Institute of Nano-Tech and Nano-Bionics, Chinese Academy of Sciences, Suzhou 215123, China
| | - Qiang-Jun Cheng
- State Key Laboratory of Low-Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, China
| | - Kun Peng
- Vacuum Interconnected Nanotech Workstation, Suzhou Institute of Nano-Tech and Nano-Bionics, Chinese Academy of Sciences, Suzhou 215123, China
| | - Fang-Jun Cheng
- State Key Laboratory of Low-Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, China
| | - Yu Liu
- State Key Laboratory of Low-Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, China
| | - Fang-Sen Li
- Vacuum Interconnected Nanotech Workstation, Suzhou Institute of Nano-Tech and Nano-Bionics, Chinese Academy of Sciences, Suzhou 215123, China.
| | - Xu-Cun Ma
- State Key Laboratory of Low-Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, China; Frontier Science Center for Quantum Information, Beijing 100084, China
| | - Qi-Kun Xue
- State Key Laboratory of Low-Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, China; Frontier Science Center for Quantum Information, Beijing 100084, China; Beijing Academy of Quantum Information Sciences, Beijing 100193, China; Southern University of Science and Technology, Shenzhen 518055, China.
| | - Can-Li Song
- State Key Laboratory of Low-Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, China; Frontier Science Center for Quantum Information, Beijing 100084, China.
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3
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Mao Y, Yan Q, Zhuang YC, Sun QF. Universal Spin Superconducting Diode Effect from Spin-Orbit Coupling. PHYSICAL REVIEW LETTERS 2024; 132:216001. [PMID: 38856265 DOI: 10.1103/physrevlett.132.216001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/27/2023] [Revised: 04/11/2024] [Accepted: 04/24/2024] [Indexed: 06/11/2024]
Abstract
We propose a universal spin superconducting diode effect (SDE) induced by spin-orbit coupling (SOC) in systems with spin-triplet correlations, where the critical spin supercurrents in opposite directions are unequal. By analysis from both the Ginzburg-Landau theory and energy band analysis, we show that the spin-↑↑ and spin-↓↓ Cooper pairs possess opposite phase gradients and opposite momenta from the SOC, which leads to the spin SDE. Two superconductors with SOC, a p-wave superconductor as a toy model and a practical superconducting nanowire, are numerically studied and they both exhibit spin SDE. In addition, our theory also provides a unified picture for both spin and charge SDEs.
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Affiliation(s)
- Yue Mao
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
| | - Qing Yan
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
| | - Yu-Chen Zhuang
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
| | - Qing-Feng Sun
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
- Hefei National Laboratory, Hefei 230088, China
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4
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Levajac V, Barakov H, Mazur GP, van Loo N, Kouwenhoven LP, Nazarov YV, Wang JY. Supercurrent in the Presence of Direct Transmission and a Resonant Localized State. PHYSICAL REVIEW LETTERS 2024; 132:176304. [PMID: 38728734 DOI: 10.1103/physrevlett.132.176304] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/08/2023] [Revised: 01/25/2024] [Accepted: 04/02/2024] [Indexed: 05/12/2024]
Abstract
We study the current-phase relation (CPR) of an InSb-Al nanowire Josephson junction in parallel magnetic fields up to 700 mT. At high magnetic fields and in narrow voltage intervals of a gate under the junction, the CPR exhibits π shifts. The supercurrent declines within these gate intervals and shows asymmetric gate voltage dependence above and below them. We detect these features sometimes also at zero magnetic field. The observed CPR properties are reproduced by a theoretical model of supercurrent transport via interference between direct transmission and a resonant localized state.
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Affiliation(s)
- Vukan Levajac
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology, 2600 GA Delft, The Netherlands
| | - Hristo Barakov
- Kavli Institute of Nanoscience, Delft University of Technology, 2628 CJ Delft, The Netherlands
| | - Grzegorz P Mazur
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology, 2600 GA Delft, The Netherlands
| | - Nick van Loo
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology, 2600 GA Delft, The Netherlands
| | - Leo P Kouwenhoven
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology, 2600 GA Delft, The Netherlands
| | - Yuli V Nazarov
- Kavli Institute of Nanoscience, Delft University of Technology, 2628 CJ Delft, The Netherlands
| | - Ji-Yin Wang
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology, 2600 GA Delft, The Netherlands
- Beijing Academy of Quantum Information Sciences, 100193 Beijing, China
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5
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Estrada Saldaña JC, Vekris A, Pavešič L, Žitko R, Grove-Rasmussen K, Nygård J. Correlation between two distant quasiparticles in separate superconducting islands mediated by a single spin. Nat Commun 2024; 15:3465. [PMID: 38658553 PMCID: PMC11043349 DOI: 10.1038/s41467-024-47694-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/20/2023] [Accepted: 04/05/2024] [Indexed: 04/26/2024] Open
Abstract
Controlled coupling between distant particles is a key requirement for the implementation of quantum information technologies. A promising platform are hybrid systems of semiconducting quantum dots coupled to superconducting islands, where the tunability of the dots is combined with the macroscopic coherence of the islands to produce states with non-local correlations, e.g. in Cooper pair splitters. Electrons in hybrid quantum dots are typically not amenable to long-distance spin alignment as they tend to be screened into a localized singlet state by bound superconducting quasiparticles. However, two quasiparticles coming from different superconductors can overscreen the quantum dot into a doublet state, leading to ferromagnetic correlations between the superconducting islands. We present experimental evidence of a stabilized overscreened state, implying correlated quasiparticles over a micrometer distance. We propose alternating chains of quantum dots and superconducting islands as a novel platform for controllable large-scale spin coupling.
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Affiliation(s)
| | - Alexandros Vekris
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, 2100, Copenhagen, Denmark
- Sino-Danish College (SDC), University of Chinese Academy of Sciences, Beijing, China
| | - Luka Pavešič
- Jožef Stefan Institute, Jamova 39, SI-1000, Ljubljana, Slovenia
- Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, SI-1000, Ljubljana, Slovenia
| | - Rok Žitko
- Jožef Stefan Institute, Jamova 39, SI-1000, Ljubljana, Slovenia.
- Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, SI-1000, Ljubljana, Slovenia.
| | - Kasper Grove-Rasmussen
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, 2100, Copenhagen, Denmark
| | - Jesper Nygård
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, 2100, Copenhagen, Denmark.
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6
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Bordin A, Li X, van Driel D, Wolff JC, Wang Q, Ten Haaf SLD, Wang G, van Loo N, Kouwenhoven LP, Dvir T. Crossed Andreev Reflection and Elastic Cotunneling in Three Quantum Dots Coupled by Superconductors. PHYSICAL REVIEW LETTERS 2024; 132:056602. [PMID: 38364137 DOI: 10.1103/physrevlett.132.056602] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/14/2023] [Revised: 12/03/2023] [Accepted: 01/05/2024] [Indexed: 02/18/2024]
Abstract
The formation of a topological superconducting phase in a quantum-dot-based Kitaev chain requires nearest neighbor crossed Andreev reflection and elastic cotunneling. Here, we report on a hybrid InSb nanowire in a three-site Kitaev chain geometry-the smallest system with well-defined bulk and edge-where two superconductor-semiconductor hybrids separate three quantum dots. We demonstrate pairwise crossed Andreev reflection and elastic cotunneling between both pairs of neighboring dots and show sequential tunneling processes involving all three quantum dots. These results are the next step toward the realization of topological superconductivity in long Kitaev chain devices with many coupled quantum dots.
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Affiliation(s)
- Alberto Bordin
- QuTech and Kavli Institute of NanoScience, Delft University of Technology, 2600 GA Delft, The Netherlands
| | - Xiang Li
- QuTech and Kavli Institute of NanoScience, Delft University of Technology, 2600 GA Delft, The Netherlands
| | - David van Driel
- QuTech and Kavli Institute of NanoScience, Delft University of Technology, 2600 GA Delft, The Netherlands
| | - Jan Cornelis Wolff
- QuTech and Kavli Institute of NanoScience, Delft University of Technology, 2600 GA Delft, The Netherlands
| | - Qingzhen Wang
- QuTech and Kavli Institute of NanoScience, Delft University of Technology, 2600 GA Delft, The Netherlands
| | - Sebastiaan L D Ten Haaf
- QuTech and Kavli Institute of NanoScience, Delft University of Technology, 2600 GA Delft, The Netherlands
| | - Guanzhong Wang
- QuTech and Kavli Institute of NanoScience, Delft University of Technology, 2600 GA Delft, The Netherlands
| | - Nick van Loo
- QuTech and Kavli Institute of NanoScience, Delft University of Technology, 2600 GA Delft, The Netherlands
| | - Leo P Kouwenhoven
- QuTech and Kavli Institute of NanoScience, Delft University of Technology, 2600 GA Delft, The Netherlands
| | - Tom Dvir
- QuTech and Kavli Institute of NanoScience, Delft University of Technology, 2600 GA Delft, The Netherlands
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7
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Karan S, Huang H, Ivanovic A, Padurariu C, Kubala B, Kern K, Ankerhold J, Ast CR. Tracking a spin-polarized superconducting bound state across a quantum phase transition. Nat Commun 2024; 15:459. [PMID: 38212303 PMCID: PMC10784290 DOI: 10.1038/s41467-024-44708-2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/17/2023] [Accepted: 01/02/2024] [Indexed: 01/13/2024] Open
Abstract
The magnetic exchange coupling between magnetic impurities and a superconductor induce so-called Yu-Shiba-Rusinov (YSR) states which undergo a quantum phase transition (QPT) upon increasing the exchange interaction beyond a critical value. While the evolution through the QPT is readily observable, in particular if the YSR state features an electron-hole asymmetry, the concomitant change in the ground state is more difficult to identify. We use ultralow temperature scanning tunneling microscopy to demonstrate how the change in the YSR ground state across the QPT can be directly observed for a spin-1/2 impurity in a magnetic field. The excitation spectrum changes from featuring two peaks in the doublet (free spin) state to four peaks in the singlet (screened spin) ground state. We also identify a transition regime, where the YSR excitation energy is smaller than the Zeeman energy. We thus demonstrate a straightforward way for unambiguously identifying the ground state of a spin-1/2 YSR state.
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Affiliation(s)
- Sujoy Karan
- Max Planck Institute for Solid State Research, Heisenbergstraße 1, 70569, Stuttgart, Germany.
| | - Haonan Huang
- Max Planck Institute for Solid State Research, Heisenbergstraße 1, 70569, Stuttgart, Germany
| | - Alexander Ivanovic
- Institute for Complex Quantum Systems and IQST, Universität Ulm, Albert-Einstein-Allee 11, 89069, Ulm, Germany
| | - Ciprian Padurariu
- Institute for Complex Quantum Systems and IQST, Universität Ulm, Albert-Einstein-Allee 11, 89069, Ulm, Germany
| | - Björn Kubala
- Institute for Complex Quantum Systems and IQST, Universität Ulm, Albert-Einstein-Allee 11, 89069, Ulm, Germany
- Institute for Quantum Technologies, German Aerospace Center (DLR), Wilhelm-Runge-Straße 10, 89081, Ulm, Germany
| | - Klaus Kern
- Max Planck Institute for Solid State Research, Heisenbergstraße 1, 70569, Stuttgart, Germany
- Institut de Physique, Ecole Polytechnique Fédérale de Lausanne, 1015, Lausanne, Switzerland
| | - Joachim Ankerhold
- Institute for Complex Quantum Systems and IQST, Universität Ulm, Albert-Einstein-Allee 11, 89069, Ulm, Germany
| | - Christian R Ast
- Max Planck Institute for Solid State Research, Heisenbergstraße 1, 70569, Stuttgart, Germany.
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8
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Debbarma R, Tsintzis A, Aspegren M, Souto RS, Lehmann S, Dick K, Leijnse M, Thelander C. Josephson Junction π-0 Transition Induced by Orbital Hybridization in a Double Quantum Dot. PHYSICAL REVIEW LETTERS 2023; 131:256001. [PMID: 38181374 DOI: 10.1103/physrevlett.131.256001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/06/2023] [Accepted: 11/20/2023] [Indexed: 01/07/2024]
Abstract
In this Letter, we manipulate the phase shift of a Josephson junction using a parallel double quantum dot (QD). By employing a superconducting quantum interference device, we determine how orbital hybridization and detuning affect the current-phase relation in the Coulomb blockade regime. For weak hybridization between the QDs, we find π junction characteristics if at least one QD has an unpaired electron. Notably the critical current is higher when both QDs have an odd electron occupation. By increasing the inter-QD hybridization the critical current is reduced, until eventually a π-0 transition occurs. A similar transition appears when detuning the QD levels at finite hybridization. Based on a zero-bandwidth model, we argue that both cases of phase-shift transitions can be understood considering an increased weight of states with a double occupancy in the ground state and with the Cooper pair transport dominated by local Andreev reflection.
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Affiliation(s)
- Rousan Debbarma
- Division of Solid State Physics and NanoLund, Lund University, S-221 00 Lund, Sweden
| | - Athanasios Tsintzis
- Division of Solid State Physics and NanoLund, Lund University, S-221 00 Lund, Sweden
| | - Markus Aspegren
- Division of Solid State Physics and NanoLund, Lund University, S-221 00 Lund, Sweden
| | - Rubén Seoane Souto
- Departamento de Física Teórica de la Materia Condensada, Condensed Matter Physics Center (IFIMAC) and Instituto Nicolás Cabrera, Universidad Autónoma de Madrid, 28049 Madrid, Spain
- Instituto de Ciencia de Materiales de Madrid (ICMM), Consejo Superior de Investigaciones Científicas (CSIC), Sor Juana Inés de la Cruz 3, 28049 Madrid, Spain
| | - Sebastian Lehmann
- Division of Solid State Physics and NanoLund, Lund University, S-221 00 Lund, Sweden
| | - Kimberly Dick
- Division of Solid State Physics and NanoLund, Lund University, S-221 00 Lund, Sweden
- Center for Analysis and Synthesis, Lund University, S-221 00 Lund, Sweden
| | - Martin Leijnse
- Division of Solid State Physics and NanoLund, Lund University, S-221 00 Lund, Sweden
| | - Claes Thelander
- Division of Solid State Physics and NanoLund, Lund University, S-221 00 Lund, Sweden
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9
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van Driel D, Wang G, Bordin A, van Loo N, Zatelli F, Mazur GP, Xu D, Gazibegovic S, Badawy G, Bakkers EPAM, Kouwenhoven LP, Dvir T. Spin-filtered measurements of Andreev bound states in semiconductor-superconductor nanowire devices. Nat Commun 2023; 14:6880. [PMID: 37898657 PMCID: PMC10613242 DOI: 10.1038/s41467-023-42026-7] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/11/2023] [Accepted: 09/27/2023] [Indexed: 10/30/2023] Open
Abstract
Semiconductor nanowires coupled to superconductors can host Andreev bound states with distinct spin and parity, including a spin-zero state with an even number of electrons and a spin-1/2 state with odd-parity. Considering the difference in spin of the even and odd states, spin-filtered measurements can reveal the underlying ground state. To directly measure the spin of single-electron excitations, we probe an Andreev bound state using a spin-polarized quantum dot that acts as a bipolar spin filter, in combination with a non-polarized tunnel junction in a three-terminal circuit. We observe a spin-polarized excitation spectrum of the Andreev bound state, which can be fully spin-polarized, despite strong spin-orbit interaction in the InSb nanowires. Decoupling the hybrid from the normal lead causes a current blockade, by trapping the Andreev bound state in an excited state. Spin-polarized spectroscopy of hybrid nanowire devices, as demonstrated here, is proposed as an experimental tool to support the observation of topological superconductivity.
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Affiliation(s)
- David van Driel
- QuTech and Kavli Institute of NanoScience, Delft University of Technology, 2600, GA, Delft, The Netherlands
| | - Guanzhong Wang
- QuTech and Kavli Institute of NanoScience, Delft University of Technology, 2600, GA, Delft, The Netherlands
| | - Alberto Bordin
- QuTech and Kavli Institute of NanoScience, Delft University of Technology, 2600, GA, Delft, The Netherlands
| | - Nick van Loo
- QuTech and Kavli Institute of NanoScience, Delft University of Technology, 2600, GA, Delft, The Netherlands
| | - Francesco Zatelli
- QuTech and Kavli Institute of NanoScience, Delft University of Technology, 2600, GA, Delft, The Netherlands
| | - Grzegorz P Mazur
- QuTech and Kavli Institute of NanoScience, Delft University of Technology, 2600, GA, Delft, The Netherlands
| | - Di Xu
- QuTech and Kavli Institute of NanoScience, Delft University of Technology, 2600, GA, Delft, The Netherlands
| | - Sasa Gazibegovic
- Department of Applied Physics, Eindhoven University of Technology, 5600, MB, Eindhoven, The Netherlands
| | - Ghada Badawy
- Department of Applied Physics, Eindhoven University of Technology, 5600, MB, Eindhoven, The Netherlands
| | - Erik P A M Bakkers
- Department of Applied Physics, Eindhoven University of Technology, 5600, MB, Eindhoven, The Netherlands
| | - Leo P Kouwenhoven
- QuTech and Kavli Institute of NanoScience, Delft University of Technology, 2600, GA, Delft, The Netherlands
| | - Tom Dvir
- QuTech and Kavli Institute of NanoScience, Delft University of Technology, 2600, GA, Delft, The Netherlands.
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10
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Pal S, Benjamin C. Honing in on a topological zero-bias conductance peak. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2023; 36:035601. [PMID: 37813102 DOI: 10.1088/1361-648x/ad0192] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/04/2023] [Accepted: 10/09/2023] [Indexed: 10/11/2023]
Abstract
A popular signature of Majorana bound states in topological superconductors is the quantized zero-energy conductance peak. However, a similar zero energy conductance peak can also arise due to non-topological reasons. Here we show that these trivial and topological zero energy conductance peaks can be distinguished via the zero energy local density of states (LDOSs) and local magnetization density of states (LMDOSs). We find that the zero-energy LDOSs and the LMDOSs exhibit periodic oscillations for a trivial zero-bias conductance peak (ZBCP). In contrast, these oscillations disappear for the topological ZBCP because of perfect Andreev reflection at zero energy in topological superconductor junctions. Our results suggest that the zero-energy LDOSs and the LMDOSs can be used as an experimental probe to distinguish a trivial zero-energy conductance peak from a topological zero-energy conductance peak.
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Affiliation(s)
- Subhajit Pal
- School of Physical Sciences, National Institute of Science Education & Research, Jatni 752050, India
- Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai 400094, India
| | - Colin Benjamin
- School of Physical Sciences, National Institute of Science Education & Research, Jatni 752050, India
- Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai 400094, India
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11
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Yazdani A, von Oppen F, Halperin BI, Yacoby A. Hunting for Majoranas. Science 2023; 380:eade0850. [PMID: 37347870 DOI: 10.1126/science.ade0850] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/25/2022] [Accepted: 05/22/2023] [Indexed: 06/24/2023]
Abstract
Over the past decade, there have been considerable efforts to observe non-abelian quasiparticles in novel quantum materials and devices. These efforts are motivated by the goals of demonstrating quantum statistics of quasiparticles beyond those of fermions and bosons and of establishing the underlying science for the creation of topologically protected quantum bits. In this Review, we focus on efforts to create topological superconducting phases that host Majorana zero modes. We consider the lessons learned from existing experimental efforts, which are motivating both improvements to present platforms and the exploration of new approaches. Although the experimental detection of non-abelian quasiparticles remains challenging, the knowledge gained thus far and the opportunities ahead offer high potential for discovery and advances in this exciting area of quantum physics.
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Affiliation(s)
- Ali Yazdani
- Joseph Henry Laboratories and Department of Physics, Princeton University, Princeton, NJ 08540, USA
| | - Felix von Oppen
- Dahlem Center for Complex Quantum Systems and Fachbereich Physik, Freie Universität Berlin, 14195 Berlin, Germany
| | | | - Amir Yacoby
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
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12
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van Loo N, Mazur GP, Dvir T, Wang G, Dekker RC, Wang JY, Lemang M, Sfiligoj C, Bordin A, van Driel D, Badawy G, Gazibegovic S, Bakkers EPAM, Kouwenhoven LP. Electrostatic control of the proximity effect in the bulk of semiconductor-superconductor hybrids. Nat Commun 2023; 14:3325. [PMID: 37286544 DOI: 10.1038/s41467-023-39044-w] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/23/2022] [Accepted: 05/17/2023] [Indexed: 06/09/2023] Open
Abstract
The proximity effect in semiconductor-superconductor nanowires is expected to generate an induced gap in the semiconductor. The magnitude of this induced gap, together with the semiconductor properties like spin-orbit coupling and g-factor, depends on the coupling between the materials. It is predicted that this coupling can be adjusted through the use of electric fields. We study this phenomenon in InSb/Al/Pt hybrids using nonlocal spectroscopy. We show that these hybrids can be tuned such that the semiconductor and superconductor are strongly coupled. In this case, the induced gap is similar to the superconducting gap in the Al/Pt shell and closes only at high magnetic fields. In contrast, the coupling can be suppressed which leads to a strong reduction of the induced gap and critical magnetic field. At the crossover between the strong-coupling and weak-coupling regimes, we observe the closing and reopening of the induced gap in the bulk of a nanowire. Contrary to expectations, it is not accompanied by the formation of zero-bias peaks in the local conductance spectra. As a result, this cannot be attributed conclusively to the anticipated topological phase transition and we discuss possible alternative explanations.
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Affiliation(s)
- Nick van Loo
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology, 2628 CJ, Delft, The Netherlands
| | - Grzegorz P Mazur
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology, 2628 CJ, Delft, The Netherlands.
| | - Tom Dvir
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology, 2628 CJ, Delft, The Netherlands
| | - Guanzhong Wang
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology, 2628 CJ, Delft, The Netherlands
| | - Robin C Dekker
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology, 2628 CJ, Delft, The Netherlands
| | - Ji-Yin Wang
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology, 2628 CJ, Delft, The Netherlands
| | - Mathilde Lemang
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology, 2628 CJ, Delft, The Netherlands
| | - Cristina Sfiligoj
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology, 2628 CJ, Delft, The Netherlands
| | - Alberto Bordin
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology, 2628 CJ, Delft, The Netherlands
| | - David van Driel
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology, 2628 CJ, Delft, The Netherlands
| | - Ghada Badawy
- Department of Applied Physics, Eindhoven University of Technology, 5600 MB, Eindhoven, The Netherlands
| | - Sasa Gazibegovic
- Department of Applied Physics, Eindhoven University of Technology, 5600 MB, Eindhoven, The Netherlands
| | - Erik P A M Bakkers
- Department of Applied Physics, Eindhoven University of Technology, 5600 MB, Eindhoven, The Netherlands
| | - Leo P Kouwenhoven
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology, 2628 CJ, Delft, The Netherlands.
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13
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Zhang T, Hu Y, Su W, Chen C, Wang X, Li D, Lu Z, Yang W, Zhang Q, Dong X, Wang R, Wang X, Feng D, Zhang T. Phase Shift and Magnetic Anisotropy Induced Field Splitting of Impurity States in (Li_{1-x}Fe_{x})OHFeSe Superconductor. PHYSICAL REVIEW LETTERS 2023; 130:206001. [PMID: 37267540 DOI: 10.1103/physrevlett.130.206001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/14/2022] [Revised: 03/21/2023] [Accepted: 04/10/2023] [Indexed: 06/04/2023]
Abstract
Revealing the energy and spatial characteristics of impurity-induced states in superconductors is essential for understanding their mechanism and fabricating a new quantum state by manipulating impurities. Here, by using high-resolution scanning tunneling microscopy and spectroscopy, we investigate the spatial distribution and magnetic field response of the impurity states in (Li_{1-x}Fe_{x})OHFeSe. We detect two pairs of strong in-gap states on the "dumbbell-shaped" defects. They display damped oscillations with different phase shifts and a direct phase-energy correlation. These features have long been predicted for the classical Yu-Shiba-Rusinov (YSR) state and are demonstrated here with unprecedented resolution for the first time. Moreover, upon applying magnetic field, all in-gap state peaks remarkably split into two rather than shift, and the splitting strength is field orientation dependent. Via detailed numerical model calculations, we find such an anisotropic splitting behavior can be naturally induced by a high-spin impurity coupled to an anisotropic environment, highlighting how magnetic anisotropy affects the behavior of YSR states.
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Affiliation(s)
- Tianzhen Zhang
- Department of Physics, State Key Laboratory of Surface Physics and Advanced Material Laboratory, Fudan University, Shanghai 200438, China
| | - Yining Hu
- Department of Physics, State Key Laboratory of Surface Physics and Advanced Material Laboratory, Fudan University, Shanghai 200438, China
| | - Wei Su
- Beijing Computational Science Research Center, Beijing 100084, China
- College of Physics and Electronic Engineering, Center for Computational Sciences, Sichuan Normal University, Chengdu 610068, China
| | - Chen Chen
- Department of Physics, State Key Laboratory of Surface Physics and Advanced Material Laboratory, Fudan University, Shanghai 200438, China
| | - Xu Wang
- Department of Physics, State Key Laboratory of Surface Physics and Advanced Material Laboratory, Fudan University, Shanghai 200438, China
| | - Dong Li
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Zouyouwei Lu
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
| | - Wentao Yang
- Department of Physics, State Key Laboratory of Surface Physics and Advanced Material Laboratory, Fudan University, Shanghai 200438, China
| | - Qingle Zhang
- Department of Physics, State Key Laboratory of Surface Physics and Advanced Material Laboratory, Fudan University, Shanghai 200438, China
| | - Xiaoli Dong
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
- Songshan Lake Materials Laboratory, Dongguan, Guangdong 523808, China
| | - Rui Wang
- National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University, Nanjing 210093, China
- Collaborative Innovation Center for Advanced Microstructures, Nanjing 210093, China
| | - Xiaoqun Wang
- School of Physics, Zhejiang University, Hangzhou 310058 Zhejiang, China
| | - Donglai Feng
- Department of Physics, State Key Laboratory of Surface Physics and Advanced Material Laboratory, Fudan University, Shanghai 200438, China
- National Synchrotron Radiation Laboratory and Department of Physics, University of Science and Technology of China, Hefei 230026, China
- Collaborative Innovation Center for Advanced Microstructures, Nanjing 210093, China
- Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
| | - Tong Zhang
- Department of Physics, State Key Laboratory of Surface Physics and Advanced Material Laboratory, Fudan University, Shanghai 200438, China
- Collaborative Innovation Center for Advanced Microstructures, Nanjing 210093, China
- Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
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14
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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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15
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Barański J, Barańska M, Zienkiewicz T, Kapcia KJ. Quench dynamics of Fano-like resonances in the presence of the on-dot superconducting pairing. Sci Rep 2023; 13:7639. [PMID: 37169768 PMCID: PMC10175302 DOI: 10.1038/s41598-023-34376-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/02/2022] [Accepted: 04/28/2023] [Indexed: 05/13/2023] Open
Abstract
We explore the electron dynamics of a system composed of double quantum dot embedded between metallic and superconducting leads in a "T-shape" geometry. In nanoscopic systems, where electron transfer between electrodes can be realized via different paths, interference effects play an important role. For double quantum dot system in the chosen geometry, interference of electrons transferred between electrodes via the interfacial quantum dot and electrons scattered on the side dot gives rise to Fano-like interference. If such a system is additionally coupled to a superconducting electrode, together with the well-understood Fano resonance an additional resonance appears on the opposite side of the Fermi level. In the recent work (Barański et al. in Sci Rep 10:2881, 2020), we showed that this resonance occurs solely as a result of the local pairing of non-scattered electrons with scattered ones. In this work, considering the quench dynamics, we explore how much time is required for formation of each of these resonances. In particular, (i) we analyze the charge oscillations between subsystems; (ii) we estimate the time required for each resonance to achieve stable equilibrium upon an abrupt change of interdot connection; (iii) we discuss a typical energy and time scales for experiments on similar architectures.
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Affiliation(s)
- Jan Barański
- Department of General Education, Polish Air Force University, ul. Dywizjonu 303 nr 35, 08521, Deblin, Poland.
| | - Magdalena Barańska
- Department of General Education, Polish Air Force University, ul. Dywizjonu 303 nr 35, 08521, Deblin, Poland
| | - Tomasz Zienkiewicz
- Department of General Education, Polish Air Force University, ul. Dywizjonu 303 nr 35, 08521, Deblin, Poland
| | - Konrad Jerzy Kapcia
- Institute of Spintronics and Quantum Information, Faculty of Physics, Adam Mickiewicz University in Poznań, ul. Uniwersytetu Poznańskiego 2, 61614, Poznań, Poland.
- Center for Free-Electron Laser Science CFEL, Deutsches Elektronen-Synchrotron DESY, Notkestr. 85, 22607, Hamburg, Germany.
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16
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Harle N, Shtanko O, Movassagh R. Observing and braiding topological Majorana modes on programmable quantum simulators. Nat Commun 2023; 14:2286. [PMID: 37085488 PMCID: PMC10121601 DOI: 10.1038/s41467-023-37725-0] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/25/2022] [Accepted: 03/24/2023] [Indexed: 04/23/2023] Open
Abstract
Electrons are indivisible elementary particles, yet paradoxically a collection of them can act as a fraction of a single electron, exhibiting exotic and useful properties. One such collective excitation, known as a topological Majorana mode, is naturally stable against perturbations, such as unwanted local noise, and can thereby robustly store quantum information. As such, Majorana modes serve as the basic primitive of topological quantum computing, providing resilience to errors. However, their demonstration on quantum hardware has remained elusive. Here, we demonstrate a verifiable identification and braiding of topological Majorana modes using a superconducting quantum processor as a quantum simulator. By simulating fermions on a one-dimensional lattice subject to a periodic drive, we confirm the existence of Majorana modes localized at the edges, and distinguish them from other trivial modes. To simulate a basic logical operation of topological quantum computing known as braiding, we propose a non-adiabatic technique, whose implementation reveals correct braiding statistics in our experiments. This work could further be used to study topological models of matter using circuit-based simulations, and shows that long-sought quantum phenomena can be realized by anyone in cloud-run quantum simulations, whereby accelerating fundamental discoveries in quantum science and technology.
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Affiliation(s)
- Nikhil Harle
- Department of Physics, Yale University, New Haven, CT, 06520, USA
- IBM Quantum, MIT-IBM Watson AI lab, Cambridge, MA, 02142, USA
| | - Oles Shtanko
- IBM Quantum, IBM Research - Almaden, San Jose, CA, 95120, USA
| | - Ramis Movassagh
- IBM Quantum, MIT-IBM Watson AI lab, Cambridge, MA, 02142, USA.
- Google Quantum AI, Venice Beach, CA, 90291, USA.
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17
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Karnatak P, Mingazheva Z, Watanabe K, Taniguchi T, Berger H, Forró L, Schönenberger C. Origin of Subgap States in Normal-Insulator-Superconductor van der Waals Heterostructures. NANO LETTERS 2023; 23:2454-2459. [PMID: 36926934 PMCID: PMC10103330 DOI: 10.1021/acs.nanolett.2c02777] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 07/13/2022] [Revised: 02/21/2023] [Indexed: 06/18/2023]
Abstract
Superconductivity in van der Waals materials, such as NbSe2 and TaS2, is fundamentally novel due to the effects of dimensionality, crystal symmetries, and strong spin-orbit coupling. In this work, we perform tunnel spectroscopy on NbSe2 by utilizing MoS2 or hexagonal boron nitride (hBN) as a tunnel barrier. We observe subgap excitations and probe their origin by studying various heterostructure designs. We show that the edge of NbSe2 hosts many defect states, which strongly couple to the superconductor and form Andreev bound states. Furthermore, by isolating the NbSe2 edge we show that the subgap states are ubiquitous in MoS2 tunnel barriers but absent in hBN tunnel barriers, suggesting defects in MoS2 as their origin. Their magnetic nature reveals a singlet- or a doublet-type ground state, and based on nearly vanishing g factors or avoided crossings of subgap excitations, we highlight the role of strong spin-orbit coupling.
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Affiliation(s)
- Paritosh Karnatak
- Department
of Physics and Swiss
Nanoscience Institute, University
of Basel, CH-4056 Basel, Switzerland
| | - Zarina Mingazheva
- Department
of Physics and Swiss
Nanoscience Institute, University
of Basel, CH-4056 Basel, Switzerland
| | - Kenji Watanabe
- Research
Center for Functional Materials, National
Institute for Material Science, 1-1 Namiki, Tsukuba 305-0044, Japan
| | - Takashi Taniguchi
- International
Center for Materials Nanoarchitectonics, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan
| | - Helmuth Berger
- Institute
of Condensed Matter Physics, Ecole Polytechnique
Fédérale de Lausanne, CH-1015 Lausanne, Switzerland
| | - László Forró
- Institute
of Condensed Matter Physics, Ecole Polytechnique
Fédérale de Lausanne, CH-1015 Lausanne, Switzerland
- Stavropoulos
Center for Complex Quantum Matter, Department of Physics, University of Notre Dame, Notre Dame, Indiana 46556, United States
| | - Christian Schönenberger
- Department
of Physics and Swiss
Nanoscience Institute, University
of Basel, CH-4056 Basel, Switzerland
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18
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Potts H, Aspegren M, Debbarma R, Lehmann S, Thelander C. Large-bias spectroscopy of Yu-Shiba-Rusinov states in a double quantum dot. NANOTECHNOLOGY 2023; 34:135002. [PMID: 36595334 DOI: 10.1088/1361-6528/aca90e] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/09/2022] [Accepted: 12/05/2022] [Indexed: 06/17/2023]
Abstract
We have performed tunnel transport spectroscopy on a quantum dot (QD) molecule proximitized by a superconducting contact. In such a system, the scattering between QD spins and Bogoliubov quasiparticles leads to the formation of Yu-Shiba-Rusinov (YSR) states within the superconducting gap. In this work, we investigate interactions appearing when one- and two-electron spin states in a double-QD energetically align with the superconducting gap edge. We find that the inter-dot spin-triplet state interacts considerably stronger with the superconductor than the corresponding singlet, pointing to stronger screening. By forming a ring molecule with a significant orbital contribution to the effectiveg-factor, we observe interactions of all four spin-orbital one-electron states with the superconductor under a weak magnetic field.
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Affiliation(s)
- Heidi Potts
- Division of Solid State Physics and NanoLund, Lund University, SE-221 00 Lund, Sweden
| | - Markus Aspegren
- Division of Solid State Physics and NanoLund, Lund University, SE-221 00 Lund, Sweden
| | - Rousan Debbarma
- Division of Solid State Physics and NanoLund, Lund University, SE-221 00 Lund, Sweden
| | - Sebastian Lehmann
- Division of Solid State Physics and NanoLund, Lund University, SE-221 00 Lund, Sweden
| | - Claes Thelander
- Division of Solid State Physics and NanoLund, Lund University, SE-221 00 Lund, Sweden
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19
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Hu LH, Wu X, Liu CX, Zhang RX. Competing Vortex Topologies in Iron-Based Superconductors. PHYSICAL REVIEW LETTERS 2022; 129:277001. [PMID: 36638298 DOI: 10.1103/physrevlett.129.277001] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/03/2021] [Accepted: 12/07/2022] [Indexed: 06/17/2023]
Abstract
In this Letter, we establish a new theoretical paradigm for vortex Majorana physics in the recently discovered topological iron-based superconductors (TFeSCs). While TFeSCs are widely accepted as an exemplar of topological insulators (TIs) with intrinsic s-wave superconductivity, our theory implies that such a common belief could be oversimplified. Our main finding is that the normal-state bulk Dirac nodes, usually ignored in TI-based vortex Majorana theories for TFeSCs, will play a key role of determining the vortex state topology. In particular, the interplay between TI and Dirac nodal bands will lead to multiple competing topological phases for a superconducting vortex line in TFeSCs, including an unprecedented hybrid topological vortex state that carries both Majorana bound states and a gapless dispersion. Remarkably, this exotic hybrid vortex phase generally exists in the vortex phase diagram for our minimal model for TFeSCs and is directly relevant to TFeSC candidates such as LiFeAs. When the fourfold rotation symmetry is broken by vortex-line tilting or curving, the hybrid vortex gets topologically trivialized and becomes Majorana free, which could explain the puzzle of ubiquitous trivial vortices observed in LiFeAs. The origin of the Majorana signal in other TFeSC candidates such as FeTe_{x}Se_{1-x} and CaKFe_{4}As_{4} is also interpreted within our theory framework. Our theory sheds new light on theoretically understanding and experimentally engineering Majorana physics in high-temperature iron-based systems.
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Affiliation(s)
- Lun-Hui Hu
- Department of Physics and Astronomy, The University of Tennessee, Knoxville, Tennessee 37996, USA
- Institute for Advanced Materials and Manufacturing, The University of Tennessee, Knoxville, Tennessee 37920, USA
- Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802, USA
| | - Xianxin Wu
- CAS Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China
- Max-Planck-Institut für Festkörperforschung, Heisenbergstrasse 1, D-70569 Stuttgart, Germany
| | - Chao-Xing Liu
- Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802, USA
| | - Rui-Xing Zhang
- Department of Physics and Astronomy, The University of Tennessee, Knoxville, Tennessee 37996, USA
- Institute for Advanced Materials and Manufacturing, The University of Tennessee, Knoxville, Tennessee 37920, USA
- Department of Materials Science and Engineering, The University of Tennessee, Knoxville, Tennessee 37996, USA
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20
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Valentini M, Borovkov M, Prada E, Martí-Sánchez S, Botifoll M, Hofmann A, Arbiol J, Aguado R, San-Jose P, Katsaros G. Majorana-like Coulomb spectroscopy in the absence of zero-bias peaks. Nature 2022; 612:442-447. [PMID: 36517713 DOI: 10.1038/s41586-022-05382-w] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/24/2022] [Accepted: 09/22/2022] [Indexed: 12/15/2022]
Abstract
Hybrid semiconductor-superconductor devices hold great promise for realizing topological quantum computing with Majorana zero modes1-5. However, multiple claims of Majorana detection, based on either tunnelling6-10 or Coulomb blockade (CB) spectroscopy11,12, remain disputed. Here we devise an experimental protocol that allows us to perform both types of measurement on the same hybrid island by adjusting its charging energy via tunable junctions to the normal leads. This method reduces ambiguities of Majorana detections by checking the consistency between CB spectroscopy and zero-bias peaks in non-blockaded transport. Specifically, we observe junction-dependent, even-odd modulated, single-electron CB peaks in InAs/Al hybrid nanowires without concomitant low-bias peaks in tunnelling spectroscopy. We provide a theoretical interpretation of the experimental observations in terms of low-energy, longitudinally confined island states rather than overlapping Majorana modes. Our results highlight the importance of combined measurements on the same device for the identification of topological Majorana zero modes.
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Affiliation(s)
- Marco Valentini
- Institute of Science and Technology Austria, Klosterneuburg, Austria.
| | - Maksim Borovkov
- Institute of Science and Technology Austria, Klosterneuburg, Austria.,Department of Physics, Princeton University, Princeton, NJ, USA
| | - Elsa Prada
- Instituto de Ciencia de Materiales de Madrid (ICMM), Consejo Superior de Investigaciones Científicas (CSIC), Madrid, Spain
| | - Sara Martí-Sánchez
- Catalan Institute of Nanoscience and Nanotechnology (ICN2), CSIC and BIST, Barcelona, Spain
| | - Marc Botifoll
- Catalan Institute of Nanoscience and Nanotechnology (ICN2), CSIC and BIST, Barcelona, Spain
| | - Andrea Hofmann
- Institute of Science and Technology Austria, Klosterneuburg, Austria.,Universität Basel, Basel, Switzerland
| | - Jordi Arbiol
- Catalan Institute of Nanoscience and Nanotechnology (ICN2), CSIC and BIST, Barcelona, Spain.,ICREA, Passeig de Lluís, Barcelona, Spain
| | - Ramón Aguado
- Instituto de Ciencia de Materiales de Madrid (ICMM), Consejo Superior de Investigaciones Científicas (CSIC), Madrid, Spain
| | - Pablo San-Jose
- Instituto de Ciencia de Materiales de Madrid (ICMM), Consejo Superior de Investigaciones Científicas (CSIC), Madrid, Spain.
| | - Georgios Katsaros
- Institute of Science and Technology Austria, Klosterneuburg, Austria.
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21
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Fatemi V, Kurilovich PD, Hays M, Bouman D, Connolly T, Diamond S, Frattini NE, Kurilovich VD, Krogstrup P, Nygård J, Geresdi A, Glazman LI, Devoret MH. Microwave Susceptibility Observation of Interacting Many-Body Andreev States. PHYSICAL REVIEW LETTERS 2022; 129:227701. [PMID: 36493424 DOI: 10.1103/physrevlett.129.227701] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/17/2021] [Accepted: 09/13/2022] [Indexed: 06/17/2023]
Abstract
Electrostatic charging affects the many-body spectrum of Andreev states, yet its influence on their microwave properties has not been elucidated. We developed a circuit quantum electrodynamics probe that, in addition to transition spectroscopy, measures the microwave susceptibility of different states of a semiconductor nanowire weak link with a single dominant (spin-degenerate) Andreev level. We found that the microwave susceptibility does not exhibit a particle-hole symmetry, which we qualitatively explain as an influence of Coulomb interaction. Moreover, our state-selective measurement reveals a large, π-phase shifted contribution to the response common to all many-body states which can be interpreted as arising from a phase-dependent continuum in the superconducting density of states.
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Affiliation(s)
- V Fatemi
- Departments of Physics and Applied Physics, Yale University, New Haven, Connecticut 06520, USA
| | - P D Kurilovich
- Departments of Physics and Applied Physics, Yale University, New Haven, Connecticut 06520, USA
| | - M Hays
- Departments of Physics and Applied Physics, Yale University, New Haven, Connecticut 06520, USA
| | - D Bouman
- QuTech and Delft University of Technology, 2600 GA Delft, Netherlands
- Kavli Institute of Nanoscience, Delft University of Technology, 2600 GA Delft, Netherlands
| | - T Connolly
- Departments of Physics and Applied Physics, Yale University, New Haven, Connecticut 06520, USA
| | - S Diamond
- Departments of Physics and Applied Physics, Yale University, New Haven, Connecticut 06520, USA
| | - N E Frattini
- Departments of Physics and Applied Physics, Yale University, New Haven, Connecticut 06520, USA
| | - V D Kurilovich
- Departments of Physics and Applied Physics, Yale University, New Haven, Connecticut 06520, USA
| | - P Krogstrup
- Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
| | - J Nygård
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
| | - A Geresdi
- QuTech and Delft University of Technology, 2600 GA Delft, Netherlands
- Kavli Institute of Nanoscience, Delft University of Technology, 2600 GA Delft, Netherlands
- Quantum Device Physics Laboratory, Department of Microtechnology and Nanoscience, Chalmers University of Technology, SE 41296 Gothenburg, Sweden
| | - L I Glazman
- Departments of Physics and Applied Physics, Yale University, New Haven, Connecticut 06520, USA
| | - M H Devoret
- Departments of Physics and Applied Physics, Yale University, New Haven, Connecticut 06520, USA
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22
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Exactly solving the Kitaev chain and generating Majorana-zero-modes out of noisy qubits. Sci Rep 2022; 12:19882. [DOI: 10.1038/s41598-022-24341-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/20/2022] [Accepted: 11/14/2022] [Indexed: 11/19/2022] Open
Abstract
AbstractMajorana-zero-modes (MZMs) were predicted to exist as edge states of a physical system called the Kitaev chain. MZMs should host particles that are their own antiparticles and could be used as a basis for a qubit which is robust-to-noise. However, all attempts to prove their existence gave inconclusive results. Here, the Kitaev chain is exactly solved with a quantum computing methodology and properties of MZMs are probed by generating eigenstates of the Kitev Hamiltonian on 3 noisy qubits of a publicly available quantum computer. After an ontological elaboration I show that two eigenstates of the Kitaev Hamiltonian exhibit eight signatures attributed to MZMs. The results presented here are a most comprehensive set of validations of MZMs ever conducted in an actual physical system. Furthermore, the findings of this manuscript are easily reproducible for any user of publicly available quantum computers, solving another important problem of research with MZMs—the result reproducibility crisis.
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23
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Mazur GP, van Loo N, Wang JY, Dvir T, Wang G, Khindanov A, Korneychuk S, Borsoi F, Dekker RC, Badawy G, Vinke P, Gazibegovic S, Bakkers EPAM, Pérez MQ, Heedt S, Kouwenhoven LP. Spin-Mixing Enhanced Proximity Effect in Aluminum-Based Superconductor-Semiconductor Hybrids. ADVANCED MATERIALS (DEERFIELD BEACH, FLA.) 2022; 34:e2202034. [PMID: 35680622 DOI: 10.1002/adma.202202034] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/03/2022] [Revised: 04/25/2022] [Indexed: 06/15/2023]
Abstract
In superconducting quantum circuits, aluminum is one of the most widely used materials. It is currently also the superconductor of choice for the development of topological qubits. However, aluminum-based devices suffer from poor magnetic field compatibility. Herein, this limitation is resolved by showing that adatoms of heavy elements (e.g., platinum) increase the critical field of thin aluminum films by more than a factor of two. Using tunnel junctions, it is shown that the increased field resilience originates from spin-orbit scattering introduced by Pt. This property is exploited in the context of the superconducting proximity effect in semiconductor-superconductor hybrids, where it is shown that InSb nanowires strongly coupled to Al/Pt films can maintain superconductivity up to 7 T. The two-electron charging effect is shown to be robust against the presence of heavy adatoms. Additionally, non-local spectroscopy is used in a three-terminal geometry to probe the bulk of hybrid devices, showing that it remains free of sub-gap states. Finally, it is demonstrated that proximitized semiconductor states maintain their ability to Zeeman-split in an applied magnetic field. Combined with the chemical stability and well-known fabrication routes of aluminum, Al/Pt emerges as the natural successor to Al-based systems and is a compelling alternative to other superconductors, whenever high-field resilience is required.
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Affiliation(s)
- Grzegorz P Mazur
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology, Delft, 2600 GA, The Netherlands
| | - Nick van Loo
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology, Delft, 2600 GA, The Netherlands
| | - Ji-Yin Wang
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology, Delft, 2600 GA, The Netherlands
| | - Tom Dvir
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology, Delft, 2600 GA, The Netherlands
| | - Guanzhong Wang
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology, Delft, 2600 GA, The Netherlands
| | - Aleksei Khindanov
- Department of Physics, University of California, Santa Barbara, CA, 93106, USA
| | - Svetlana Korneychuk
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology, Delft, 2600 GA, The Netherlands
| | - Francesco Borsoi
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology, Delft, 2600 GA, The Netherlands
| | - Robin C Dekker
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology, Delft, 2600 GA, The Netherlands
| | - Ghada Badawy
- Department of Applied Physics, Eindhoven University of Technology, Eindhoven, 5600 MB, The Netherlands
| | - Peter Vinke
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology, Delft, 2600 GA, The Netherlands
| | - Sasa Gazibegovic
- Department of Applied Physics, Eindhoven University of Technology, Eindhoven, 5600 MB, The Netherlands
| | - Erik P A M Bakkers
- Department of Applied Physics, Eindhoven University of Technology, Eindhoven, 5600 MB, The Netherlands
| | - Marina Quintero- Pérez
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology, Delft, 2600 GA, The Netherlands
- Netherlands Organisation for Applied Scientific Research (TNO), Delft, 2600 AD, The Netherlands
| | - Sebastian Heedt
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology, Delft, 2600 GA, The Netherlands
| | - Leo P Kouwenhoven
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology, Delft, 2600 GA, The Netherlands
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24
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Matute-Cañadas FJ, Metzger C, Park S, Tosi L, Krogstrup P, Nygård J, Goffman MF, Urbina C, Pothier H, Yeyati AL. Signatures of Interactions in the Andreev Spectrum of Nanowire Josephson Junctions. PHYSICAL REVIEW LETTERS 2022; 128:197702. [PMID: 35622049 DOI: 10.1103/physrevlett.128.197702] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/17/2021] [Accepted: 04/01/2022] [Indexed: 06/15/2023]
Abstract
We performed microwave spectroscopy of an InAs nanowire between superconducting contacts implementing a finite-length, multichannel Josephson weak link. Certain features in the spectra, such as the splitting by spin-orbit interactions of the transition lines among Andreev states, have been already understood in terms of noninteracting models. However, we identify here additional transitions, which evidence the presence of Coulomb interactions. By combining experimental measurements and model calculations, we reach a qualitative understanding of these very rich Andreev spectra.
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Affiliation(s)
- F J Matute-Cañadas
- Departamento de Física Teórica de la Materia Condensada, Condensed Matter Physics Center (IFIMAC) and Instituto Nicolás Cabrera, Universidad Autónoma de Madrid, 28049 Madrid, Spain
| | - C Metzger
- Quantronics group, Service de Physique de l'État Condensé (CNRS, UMR 3680), IRAMIS, CEA-Saclay, Université Paris-Saclay, 91191 Gif-sur-Yvette, France
| | - Sunghun Park
- Departamento de Física Teórica de la Materia Condensada, Condensed Matter Physics Center (IFIMAC) and Instituto Nicolás Cabrera, Universidad Autónoma de Madrid, 28049 Madrid, Spain
| | - L Tosi
- Centro Atómico Bariloche and Instituto Balseiro, CNEA, CONICET, 8400 San Carlos de Bariloche, Río Negro, Argentina
| | - P Krogstrup
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
| | - J Nygård
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
| | - M F Goffman
- Quantronics group, Service de Physique de l'État Condensé (CNRS, UMR 3680), IRAMIS, CEA-Saclay, Université Paris-Saclay, 91191 Gif-sur-Yvette, France
| | - C Urbina
- Quantronics group, Service de Physique de l'État Condensé (CNRS, UMR 3680), IRAMIS, CEA-Saclay, Université Paris-Saclay, 91191 Gif-sur-Yvette, France
| | - H Pothier
- Quantronics group, Service de Physique de l'État Condensé (CNRS, UMR 3680), IRAMIS, CEA-Saclay, Université Paris-Saclay, 91191 Gif-sur-Yvette, France
| | - A Levy Yeyati
- Departamento de Física Teórica de la Materia Condensada, Condensed Matter Physics Center (IFIMAC) and Instituto Nicolás Cabrera, Universidad Autónoma de Madrid, 28049 Madrid, Spain
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25
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Schneider L, Beck P, Neuhaus-Steinmetz J, Rózsa L, Posske T, Wiebe J, Wiesendanger R. Precursors of Majorana modes and their length-dependent energy oscillations probed at both ends of atomic Shiba chains. NATURE NANOTECHNOLOGY 2022; 17:384-389. [PMID: 35256768 PMCID: PMC9018407 DOI: 10.1038/s41565-022-01078-4] [Citation(s) in RCA: 12] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/12/2021] [Accepted: 01/12/2022] [Indexed: 05/27/2023]
Abstract
Isolated Majorana modes (MMs) are highly non-local quantum states with non-Abelian exchange statistics, which localize at the two ends of finite-size 1D topological superconductors of sufficient length. Experimental evidence for MMs is so far based on the detection of several key signatures: for example, a conductance peak pinned to the Fermi energy or an oscillatory peak splitting in short 1D systems when the MMs overlap. However, most of these key signatures were probed only on one of the ends of the 1D system, and firm evidence for an MM requires the simultaneous detection of all the key signatures on both ends. Here we construct short atomic spin chains on a superconductor-also known as Shiba chains-up to a chain length of 45 atoms using tip-assisted atom manipulation in scanning tunnelling microscopy experiments. We observe zero-energy conductance peaks localized at both ends of the chain that simultaneously split off from the Fermi energy in an oscillatory fashion after altering the chain length. By fitting the parameters of a low-energy model to the data, we find that the peaks are consistent with precursors of MMs that evolve into isolated MMs protected by an estimated topological gap of 50 μeV in chains of at least 35 nm length, corresponding to 70 atoms.
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Affiliation(s)
- Lucas Schneider
- Department of Physics, Universität Hamburg, Hamburg, Germany
| | - Philip Beck
- Department of Physics, Universität Hamburg, Hamburg, Germany
| | | | - Levente Rózsa
- Department of Physics, University of Konstanz, Konstanz, Germany
| | - Thore Posske
- I. Institute for Theoretical Physics, Universität Hamburg, Hamburg, Germany
- The Hamburg Centre for Ultrafast Imaging, Luruper Chaussee, Hamburg, Germany
| | - Jens Wiebe
- Department of Physics, Universität Hamburg, Hamburg, Germany.
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26
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Phan D, Senior J, Ghazaryan A, Hatefipour M, Strickland WM, Shabani J, Serbyn M, Higginbotham AP. Detecting Induced p±ip Pairing at the Al-InAs Interface with a Quantum Microwave Circuit. PHYSICAL REVIEW LETTERS 2022; 128:107701. [PMID: 35333085 DOI: 10.1103/physrevlett.128.107701] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/14/2021] [Revised: 12/15/2021] [Accepted: 01/31/2022] [Indexed: 06/14/2023]
Abstract
Superconductor-semiconductor hybrid devices are at the heart of several proposed approaches to quantum information processing, but their basic properties remain to be understood. We embed a two-dimensional Al-InAs hybrid system in a resonant microwave circuit, probing the breakdown of superconductivity due to an applied magnetic field. We find a fingerprint from the two-component nature of the hybrid system, and quantitatively compare with a theory that includes the contribution of intraband p±ip pairing in the InAs, as well as the emergence of Bogoliubov-Fermi surfaces due to magnetic field. Separately resolving the Al and InAs contributions allows us to determine the carrier density and mobility in the InAs.
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Affiliation(s)
- D Phan
- IST Austria, Am Campus 1, 3400 Klosterneuburg, Austria
| | - J Senior
- IST Austria, Am Campus 1, 3400 Klosterneuburg, Austria
| | - A Ghazaryan
- IST Austria, Am Campus 1, 3400 Klosterneuburg, Austria
| | - M Hatefipour
- Department of Physics, New York University, New York, New York 10003, USA
| | - W M Strickland
- Department of Physics, New York University, New York, New York 10003, USA
| | - J Shabani
- Department of Physics, New York University, New York, New York 10003, USA
| | - M Serbyn
- IST Austria, Am Campus 1, 3400 Klosterneuburg, Austria
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27
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Zhang S, Wang Z, Pan D, Li H, Lu S, Li Z, Zhang G, Liu D, Cao Z, Liu L, Wen L, Liao D, Zhuo R, Shang R, Liu DE, Zhao J, Zhang H. Suppressing Andreev Bound State Zero Bias Peaks Using a Strongly Dissipative Lead. PHYSICAL REVIEW LETTERS 2022; 128:076803. [PMID: 35244449 DOI: 10.1103/physrevlett.128.076803] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/02/2021] [Accepted: 01/25/2022] [Indexed: 06/14/2023]
Abstract
Hybrid semiconductor-superconductor nanowires are predicted to host Majorana zero modes that induce zero-bias peaks (ZBPs) in tunneling conductance. ZBPs alone, however, are not sufficient evidence due to the ubiquitous presence of Andreev bound states. Here, we implement a strongly resistive normal lead in InAs-Al nanowire devices and show that most of the expected Andreev bound state-induced ZBPs can be suppressed, a phenomenon known as environmental Coulomb blockade. Our result is the first experimental demonstration of this dissipative interaction effect on Andreev bound states and can serve as a possible filter to narrow down the ZBP phase diagram in future Majorana searches.
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Affiliation(s)
- Shan Zhang
- State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, China
| | - Zhichuan Wang
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Dong Pan
- State Key Laboratory of Superlattices and Microstructures, Institute of Semiconductors, Chinese Academy of Sciences, P.O. Box 912, Beijing 100083, China
| | - Hangzhe Li
- State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, China
| | - Shuai Lu
- State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, China
| | - Zonglin Li
- State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, China
| | - Gu Zhang
- Beijing Academy of Quantum Information Sciences, 100193 Beijing, China
| | - Donghao Liu
- State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, China
| | - Zhan Cao
- Beijing Academy of Quantum Information Sciences, 100193 Beijing, China
| | - Lei Liu
- State Key Laboratory of Superlattices and Microstructures, Institute of Semiconductors, Chinese Academy of Sciences, P.O. Box 912, Beijing 100083, China
| | - Lianjun Wen
- State Key Laboratory of Superlattices and Microstructures, Institute of Semiconductors, Chinese Academy of Sciences, P.O. Box 912, Beijing 100083, China
| | - Dunyuan Liao
- State Key Laboratory of Superlattices and Microstructures, Institute of Semiconductors, Chinese Academy of Sciences, P.O. Box 912, Beijing 100083, China
| | - Ran Zhuo
- State Key Laboratory of Superlattices and Microstructures, Institute of Semiconductors, Chinese Academy of Sciences, P.O. Box 912, Beijing 100083, China
| | - Runan Shang
- Beijing Academy of Quantum Information Sciences, 100193 Beijing, 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, 100193 Beijing, China
- Frontier Science Center for Quantum Information, 100084 Beijing, China
| | - Jianhua Zhao
- State Key Laboratory of Superlattices and Microstructures, Institute of Semiconductors, Chinese Academy of Sciences, P.O. Box 912, Beijing 100083, 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, 100193 Beijing, China
- Frontier Science Center for Quantum Information, 100084 Beijing, China
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28
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Zhang P, Wu H, Chen J, Khan SA, Krogstrup P, Pekker D, Frolov SM. Signatures of Andreev Blockade in a Double Quantum Dot Coupled to a Superconductor. PHYSICAL REVIEW LETTERS 2022; 128:046801. [PMID: 35148137 DOI: 10.1103/physrevlett.128.046801] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/03/2021] [Revised: 10/01/2021] [Accepted: 01/07/2022] [Indexed: 06/14/2023]
Abstract
We investigate an electron transport blockade regime in which a spin triplet localized in the path of current is forbidden from entering a spin-singlet superconductor. To stabilize the triplet, a double quantum dot is created electrostatically near a superconducting Al lead in an InAs nanowire. The quantum dot closest to the normal lead exhibits Coulomb diamonds, and the dot closest to the superconducting lead exhibits Andreev bound states and an induced gap. The experimental observations compare favorably to a theoretical model of Andreev blockade, named so because the triplet double dot configuration suppresses Andreev reflections. Observed leakage currents can be accounted for by finite temperature. We observe the predicted quadruple level degeneracy points of high current and a periodic conductance pattern controlled by the occupation of the normal dot. Even-odd transport asymmetry is lifted with increased temperature and magnetic field. This blockade phenomenon can be used to study spin structure of superconductors. It may also find utility in quantum computing devices that use Andreev or Majorana states.
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Affiliation(s)
- Po Zhang
- Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA
| | - Hao Wu
- Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA
| | - Jun Chen
- Department of Electrical and Computer Engineering, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA
| | - Sabbir A Khan
- Microsoft Quantum Materials Lab Copenhagen, 2800 Lyngby, Denmark
- 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
| | - David Pekker
- Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA
| | - Sergey M Frolov
- Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA
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29
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Steiner JF, Mora C, Franke KJ, von Oppen F. Quantum Magnetism and Topological Superconductivity in Yu-Shiba-Rusinov Chains. PHYSICAL REVIEW LETTERS 2022; 128:036801. [PMID: 35119905 DOI: 10.1103/physrevlett.128.036801] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/04/2021] [Revised: 11/02/2021] [Accepted: 01/07/2022] [Indexed: 06/14/2023]
Abstract
Chains of magnetic adatoms on superconductors have been discussed as promising systems for realizing Majorana end states. Here, we show that dilute Yu-Shiba-Rusinov (YSR) chains are also a versatile platform for quantum magnetism and correlated electron dynamics, with widely adjustable spin values and couplings. Focusing on subgap excitations, we derive an extended t-J model for dilute quantum YSR chains and use it to study the phase diagram as well as tunneling spectra. We explore the implications of quantum magnetism for the formation of a topological superconducting phase, contrasting it to existing models assuming classical spin textures.
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Affiliation(s)
- Jacob F Steiner
- Dahlem Center for Complex Quantum Systems and Fachbereich Physik, Freie Universität Berlin, 14195 Berlin, Germany
| | - Christophe Mora
- Dahlem Center for Complex Quantum Systems and Fachbereich Physik, Freie Universität Berlin, 14195 Berlin, Germany
- Laboratoire Matériaux et Phénomènes Quantiques, CNRS, Université de Paris, 75013 Paris, France
| | | | - Felix von Oppen
- Dahlem Center for Complex Quantum Systems and Fachbereich Physik, Freie Universität Berlin, 14195 Berlin, Germany
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30
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Ritter M, Schmid H, Sousa M, Staudinger P, Haxell DZ, Mueed MA, Madon B, Pushp A, Riel H, Nichele F. Semiconductor Epitaxy in Superconducting Templates. NANO LETTERS 2021; 21:9922-9929. [PMID: 34788993 PMCID: PMC8662718 DOI: 10.1021/acs.nanolett.1c03133] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 08/13/2021] [Revised: 11/10/2021] [Indexed: 06/13/2023]
Abstract
Integration of high-quality semiconductor-superconductor devices into scalable and complementary metal-oxide-semiconductor compatible architectures remains an outstanding challenge, currently hindering their practical implementation. Here, we demonstrate growth of InAs nanowires monolithically integrated on Si inside lateral cavities containing superconducting TiN elements. This technique allows growth of hybrid devices characterized by sharp semiconductor-superconductor interfaces and with alignment along arbitrary crystallographic directions. Electrical characterization at low temperature reveals proximity induced superconductivity in InAs via a transparent interface.
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Affiliation(s)
- Markus
F. Ritter
- IBM
Research Europe, Säumerstrasse
4, 8803 Rüschlikon, Switzerland
| | - Heinz Schmid
- IBM
Research Europe, Säumerstrasse
4, 8803 Rüschlikon, Switzerland
| | - Marilyne Sousa
- IBM
Research Europe, Säumerstrasse
4, 8803 Rüschlikon, Switzerland
| | | | - Daniel Z. Haxell
- IBM
Research Europe, Säumerstrasse
4, 8803 Rüschlikon, Switzerland
| | - M. A. Mueed
- IBM
Almaden Research Center, San Jose, California 95120, United States
| | - Benjamin Madon
- IBM
Almaden Research Center, San Jose, California 95120, United States
| | - Aakash Pushp
- IBM
Almaden Research Center, San Jose, California 95120, United States
| | - Heike Riel
- IBM
Research Europe, Säumerstrasse
4, 8803 Rüschlikon, Switzerland
| | - Fabrizio Nichele
- IBM
Research Europe, Säumerstrasse
4, 8803 Rüschlikon, Switzerland
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31
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Bjergfelt MS, Carrad DJ, Kanne T, Johnson E, Fiordaliso EM, Jespersen TS, Nygård J. Superconductivity and Parity Preservation in As-Grown In Islands on InAs Nanowires. NANO LETTERS 2021; 21:9875-9881. [PMID: 34807620 DOI: 10.1021/acs.nanolett.1c02487] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
We report in situ synthesis of crystalline indium islands on InAs nanowires grown by molecular beam epitaxy. Structural analysis by transmission electron microscopy showed that In crystals grew in a tetragonal body-centered crystal structure within two families of orientations relative to wurtzite InAs. The crystalline islands had lengths < 500 nm and low-energy surfaces, suggesting that growth was driven mainly by surface energy minimization. Electrical transport through In/InAs devices exhibited Cooper pair charging, evidencing charge parity preservation and a pristine In/InAs interface, with an induced superconducting gap ∼ 0.45 meV. Cooper pair charging persisted to temperatures > 1.2 K and magnetic fields ∼ 0.7 T, demonstrating that In/InAs hybrids belong to an expanding class of semiconductor/superconductor hybrids operating over a wider parameter space than state-of-the-art Al-based hybrids. Engineering crystal morphology while isolating single islands using shadow epitaxy provides an interesting alternative to previous semiconductor/superconductor hybrid morphologies and device geometries.
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Affiliation(s)
- Martin Saurbrey Bjergfelt
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark
| | - Damon J Carrad
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark
- Department of Energy Conversion and Storage, Technical University of Denmark, 2800 Kongens Lyngby Denmark
| | - Thomas Kanne
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark
| | - Erik Johnson
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark
- DTU Mechanical Engineering, Technical University of Denmark, 2800 Kongens Lyngby Denmark
| | | | - Thomas Sand Jespersen
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark
- Department of Energy Conversion and Storage, Technical University of Denmark, 2800 Kongens Lyngby Denmark
| | - Jesper Nygård
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark
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32
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Kürtössy O, Scherübl Z, Fülöp G, Lukács IE, Kanne T, Nygård J, Makk P, Csonka S. Andreev Molecule in Parallel InAs Nanowires. NANO LETTERS 2021; 21:7929-7937. [PMID: 34538054 PMCID: PMC8517978 DOI: 10.1021/acs.nanolett.1c01956] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 05/19/2021] [Indexed: 06/13/2023]
Abstract
Coupling individual atoms fundamentally changes the state of matter: electrons bound to atomic cores become delocalized turning an insulating state to a metallic one. A chain of atoms could lead to more exotic states if the tunneling takes place via the superconducting vacuum and can induce topologically protected excitations like Majorana or parafermions. Although coupling a single atom to a superconductor is well studied, the hybridization of two sites with individual tunability was not reported yet. The peculiar vacuum of the Bardeen-Cooper-Schrieffer (BCS) condensate opens the way to annihilate or generate two electrons from the bulk resulting in a so-called Andreev molecular state. By employing parallel nanowires with an Al shell, two artificial atoms were created at a minimal distance with an epitaxial superconducting link between. Hybridization via the BCS vacuum was observed and the spectrum of an Andreev molecule as a function of level positions was explored for the first time.
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Affiliation(s)
- Olivér Kürtössy
- Department
of Physics and Nanoelectronics “Momentum” Research Group
of the Hungarian Academy of Sciences, Budapest
University of Technology and Economics, Budafoki út 8, 1111 Budapest, Hungary
| | - Zoltán Scherübl
- Department
of Physics and Nanoelectronics “Momentum” Research Group
of the Hungarian Academy of Sciences, Budapest
University of Technology and Economics, Budafoki út 8, 1111 Budapest, Hungary
- University
of Grenoble Alpes, CEA, Grenoble INP, IRIG, PHELIQS, 38000 Grenoble, France
| | - Gergö Fülöp
- Department
of Physics and Nanoelectronics “Momentum” Research Group
of the Hungarian Academy of Sciences, Budapest
University of Technology and Economics, Budafoki út 8, 1111 Budapest, Hungary
| | - István Endre Lukács
- Center
for Energy Research, Institute of Technical
Physics and Material Science, Konkoly-Thege Miklós út 29-33, H-1121, Budapest, Hungary
| | - Thomas Kanne
- Center
for Quantum Devices, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark
| | - Jesper Nygård
- Center
for Quantum Devices, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark
| | - Péter Makk
- Department
of Physics and Nanoelectronics “Momentum” Research Group
of the Hungarian Academy of Sciences, Budapest
University of Technology and Economics, Budafoki út 8, 1111 Budapest, Hungary
| | - Szabolcs Csonka
- Department
of Physics and Nanoelectronics “Momentum” Research Group
of the Hungarian Academy of Sciences, Budapest
University of Technology and Economics, Budafoki út 8, 1111 Budapest, Hungary
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33
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Ricco LS, Sanches JE, Marques Y, de Souza M, Figueira MS, Shelykh IA, Seridonio AC. Topological isoconductance signatures in Majorana nanowires. Sci Rep 2021; 11:17310. [PMID: 34453069 PMCID: PMC8397770 DOI: 10.1038/s41598-021-96415-3] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/07/2021] [Accepted: 08/04/2021] [Indexed: 11/23/2022] Open
Abstract
We consider transport properties of a hybrid device composed by a quantum dot placed between normal and superconducting reservoirs, and coupled to a Majorana nanowire: a topological superconducting segment hosting Majorana bound states (MBSs) at the opposite ends. It is demonstrated that if highly nonlocal and nonoverlapping MBSs are formed in the system, the zero-bias Andreev conductance through the dot exhibits characteristic isoconductance profiles with the shape depending on the spin asymmetry of the coupling between the dot and the topological superconductor. Otherwise, for overlapping MBSs with less degree of nonlocality, the conductance is insensitive to the spin polarization and the isoconductance signatures disappear. This allows to propose an alternative experimental protocol for probing the nonlocality of the MBSs in Majorana nanowires.
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Affiliation(s)
- L S Ricco
- Science Institute, University of Iceland, Dunhagi-3, 107, Reykjavik, Iceland.
| | - J E Sanches
- School of Engineering, Department of Physics and Chemistry, São Paulo State University (Unesp), 15385-000, Ilha Solteira, SP, Brazil
| | - Y Marques
- Department of Physics, ITMO University, 197101, St. Petersburg, Russia
| | - M de Souza
- Department of Physics, São Paulo State University (Unesp), IGCE, 13506-970, Rio Claro, SP, Brazil
| | - M S Figueira
- Instituto de Física, Universidade Federal Fluminense, 24210-340, Niterói, Rio de Janeiro, Brazil
| | - I A Shelykh
- Science Institute, University of Iceland, Dunhagi-3, 107, Reykjavik, Iceland
- Department of Physics, ITMO University, 197101, St. Petersburg, Russia
| | - A C Seridonio
- School of Engineering, Department of Physics and Chemistry, São Paulo State University (Unesp), 15385-000, Ilha Solteira, SP, Brazil
- Department of Physics, São Paulo State University (Unesp), IGCE, 13506-970, Rio Claro, SP, Brazil
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Devidas TR, Keren I, Steinberg H. Spectroscopy of NbSe 2 Using Energy-Tunable Defect-Embedded Quantum Dots. NANO LETTERS 2021; 21:6931-6937. [PMID: 34351777 DOI: 10.1021/acs.nanolett.1c02177] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
Quantum dots have sharply defined energy levels, which can be used for high resolution energy spectroscopy when integrated in tunneling circuitry. Here we report dot-assisted spectroscopy measurements of the superconductor NbSe2, using a van der Waals device consisting of a vertical stack of graphene-MoS2-NbSe2. The MoS2 tunnel barriers host naturally occurring defects which function as quantum dots, allowing transport via resonant tunneling. The dot energies are tuned by an electric field exerted by a back-gate, which penetrates the graphene source electrode. Scanning the dot potential across the superconductor Fermi energy, we reproduce the NbSe2 density of states which exhibits a well-resolved two-gap spectrum. Surprisingly, we find that the dot-assisted current is dominated by the lower energy feature of the two NbSe2 gaps, possibly due to a selection rule which favors coupling between the dots and the orbitals which exhibit this gap.
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Affiliation(s)
- T R Devidas
- The Racah Institute of Physics, The Center for Nanoscience and Nanotechnology, The Hebrew University, Jerusalem 91904, Israel
| | - Itai Keren
- The Racah Institute of Physics, The Center for Nanoscience and Nanotechnology, The Hebrew University, Jerusalem 91904, Israel
| | - Hadar Steinberg
- The Racah Institute of Physics, The Center for Nanoscience and Nanotechnology, The Hebrew University, Jerusalem 91904, Israel
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35
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Valentini M, Peñaranda F, Hofmann A, Brauns M, Hauschild R, Krogstrup P, San-Jose P, Prada E, Aguado R, Katsaros G. Nontopological zero-bias peaks in full-shell nanowires induced by flux-tunable Andreev states. Science 2021; 373:82-88. [PMID: 34210881 DOI: 10.1126/science.abf1513] [Citation(s) in RCA: 33] [Impact Index Per Article: 11.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/07/2020] [Accepted: 05/21/2021] [Indexed: 11/02/2022]
Abstract
A semiconducting nanowire fully wrapped by a superconducting shell has been proposed as a platform for obtaining Majorana modes at small magnetic fields. In this study, we demonstrate that the appearance of subgap states in such structures is actually governed by the junction region in tunneling spectroscopy measurements and not the full-shell nanowire itself. Short tunneling regions never show subgap states, whereas longer junctions always do. This can be understood in terms of quantum dots forming in the junction and hosting Andreev levels in the Yu-Shiba-Rusinov regime. The intricate magnetic field dependence of the Andreev levels, through both the Zeeman and Little-Parks effects, may result in robust zero-bias peaks-features that could be easily misinterpreted as originating from Majorana zero modes but are unrelated to topological superconductivity.
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Affiliation(s)
- Marco Valentini
- Institute of Science and Technology Austria, Am Campus 1, 3400 Klosterneuburg, Austria.
| | - Fernando Peñaranda
- Instituto de Ciencia de Materiales de Madrid (ICMM), Consejo Superior de Investigaciones Científicas (CSIC), Sor Juana Inés de la Cruz 3, 28049 Madrid, Spain
| | - Andrea Hofmann
- Institute of Science and Technology Austria, Am Campus 1, 3400 Klosterneuburg, Austria
| | - Matthias Brauns
- Institute of Science and Technology Austria, Am Campus 1, 3400 Klosterneuburg, Austria
| | - Robert Hauschild
- Institute of Science and Technology Austria, Am Campus 1, 3400 Klosterneuburg, Austria
| | - Peter Krogstrup
- Microsoft Quantum Materials Lab and Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, Kanalvej 7, 2800 Kongens Lyngby, Denmark
| | - Pablo San-Jose
- Instituto de Ciencia de Materiales de Madrid (ICMM), Consejo Superior de Investigaciones Científicas (CSIC), Sor Juana Inés de la Cruz 3, 28049 Madrid, Spain
| | - Elsa Prada
- Instituto de Ciencia de Materiales de Madrid (ICMM), Consejo Superior de Investigaciones Científicas (CSIC), Sor Juana Inés de la Cruz 3, 28049 Madrid, Spain.,Departamento de Física de la Materia Condensada, Condensed Matter Physics Center (IFIMAC) and Instituto Nicolás Cabrera, Universidad Autónoma de Madrid, E-28049 Madrid, Spain
| | - Ramón Aguado
- Instituto de Ciencia de Materiales de Madrid (ICMM), Consejo Superior de Investigaciones Científicas (CSIC), Sor Juana Inés de la Cruz 3, 28049 Madrid, Spain.
| | - Georgios Katsaros
- Institute of Science and Technology Austria, Am Campus 1, 3400 Klosterneuburg, Austria.
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36
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37
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38
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Measuring the Electron–Phonon Interaction in Two-Dimensional Superconductors with He-Atom Scattering. CONDENSED MATTER 2020. [DOI: 10.3390/condmat5040079] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
Helium-atom scattering (HAS) spectroscopy from conducting surfaces has been shown to provide direct information on the electron–phonon interaction, more specifically the mass-enhancement factor λ from the temperature dependence of the Debye–Waller exponent, and the mode-selected electron–phonon coupling constants λQν from the inelastic HAS intensities from individual surface phonons. The recent applications of the method to superconducting ultra-thin films, quasi-1D high-index surfaces, and layered transition-metal and topological pnictogen chalcogenides are briefly reviewed.
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39
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Chandramouli RS, Srivastav RK, Kumar S. Electronic transport in chaotic mesoscopic cavities: A Kwant and random matrix theory based exploration. CHAOS (WOODBURY, N.Y.) 2020; 30:123120. [PMID: 33380063 DOI: 10.1063/5.0026039] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/21/2020] [Accepted: 11/20/2020] [Indexed: 06/12/2023]
Abstract
We investigate the spectral fluctuations and electronic transport properties of chaotic mesoscopic cavities using Kwant, an open source Python programming language based package. Discretized chaotic billiard systems are used to model these mesoscopic cavities. For the spectral fluctuations, we study the ratio of consecutive eigenvalue spacings, and for the transport properties, we focus on Landauer conductance and shot noise power. We generate an ensemble of scattering matrices in Kwant, with desired number of open channels in the leads attached to the cavity. The results obtained from Kwant simulations, performed without or with magnetic field, are compared with the corresponding random matrix theory predictions for orthogonally and unitarily invariant ensembles. These two cases apply to the scenarios of preserved and broken time-reversal symmetry, respectively. In addition, we explore the orthogonal to unitary crossover statistics by varying the magnetic field and examine its relationship with the random matrix transition parameter.
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Affiliation(s)
| | - Rohit Kumar Srivastav
- Department of Physics, Shiv Nadar University, Gautam Buddha Nagar, Uttar Pradesh 201314, India
| | - Santosh Kumar
- Department of Physics, Shiv Nadar University, Gautam Buddha Nagar, Uttar Pradesh 201314, India
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40
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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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41
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Verma S, Singh A. Influence of superconductivity on the magnetic moment of quantum impurity embedded in BCS superconductor. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2020; 33:085603. [PMID: 33212435 DOI: 10.1088/1361-648x/abcc0e] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
We study the influence of superconductivity on the formation of the localized magnetic moment for a single-level quantum impurity embedded in an s-wave Bardeen-Cooper-Schrieffer (BCS) superconducting medium, modeled by single-impurity Anderson Hamiltonian. We have combined Bogoliubov transformation with Green's function method within self-consistent Hartree-Fock Mean Field approximation to analyze the conditions necessary in metal (in the superconducting) for the formation of the magnetic moment at the impurity site for the low-frequency limit $|\omega|<<\Delta_{sc}$ as well as for the finite superconducting gap $\Delta_{sc}$. We have compared these results with other theoretical results and with the single-level quantum impurity embedded in the normal metallic host. Further we analyze the electronic spectral density of the quantum impurity embedded in superconducting host with the finite superconducting gap to study the sub-gap states as a function of impurity parameters.
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Affiliation(s)
- Sachin Verma
- Physics, Indian Institute of Technology Roorkee, Cautey Bhawan, I.I.T Roorkee, Haridwar, Roorkee, UTTARAKHAND, 247667, INDIA
| | - Ajay Singh
- Physics, Indian Institute of Technology Roorkee, Department of Physics, I.I.T Roorkee, Haridwar, Roorkee, UTTARAKHAND, 247667, INDIA
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42
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Park S, Sim HS, Recher P. Electron-Tunneling-Assisted Non-Abelian Braiding of Rotating Majorana Bound States. PHYSICAL REVIEW LETTERS 2020; 125:187702. [PMID: 33196222 DOI: 10.1103/physrevlett.125.187702] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/22/2018] [Revised: 02/03/2020] [Accepted: 09/29/2020] [Indexed: 06/11/2023]
Abstract
It has been argued that fluctuations of fermion parity are harmful for the demonstration of non-Abelian anyonic statistics. Here, we demonstrate a striking exception in which such fluctuations are actively used. We present a theory of coherent electron transport from a tunneling tip into a Corbino geometry Josephson junction where four Majorana bound states (MBSs) rotate. While the MBSs rotate, electron tunneling happens from the tip to one of the MBSs thereby changing the fermion parity of the MBSs. The tunneling events in combination with the rotation allow us to identify a novel braiding operator that does not commute with the braiding cycles in the absence of tunneling, revealing the non-Abelian nature of MBSs. The time-averaged tunneling current exhibits resonances as a function of the tip voltage with a period that is a direct consequence of the interference between the noncommuting braiding operations. Our work opens up a possibility for utilizing parity nonconserving processes to control non-Abelian states.
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Affiliation(s)
- Sunghun Park
- Departamento de Física Teórica de la Materia Condensada, Condensed Matter Physics Center (IFIMAC) and Instituto Nicolás Cabrera, Universidad Autónoma de Madrid, 28049 Madrid, Spain
| | - H-S Sim
- Department of Physics, Korea Advanced Institute of Science and Technology, Daejeon 34141, Korea
| | - Patrik Recher
- Institute for Mathematical Physics, TU Braunschweig, D-38106 Braunschweig, Germany
- Laboratory for Emerging Nanometrology Braunschweig, D-38106 Braunschweig, Germany
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43
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Górski G, Kucab K, Domański T. Magnetic field effect on trivial and topological bound states of superconducting quantum dot. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2020; 32:445803. [PMID: 32634785 DOI: 10.1088/1361-648x/aba38a] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/12/2020] [Accepted: 07/07/2020] [Indexed: 06/11/2023]
Abstract
We investigate the properties of a quantum dot embedded between the normal and superconducting leads which is additionally side-attached to the topological superconducting nanowire, hosting the Majorana modes. This setup enables formation of the trivial (finite-energy) bound states induced in the quantum dot through the superconducting proximity effect, coexisting/competing with the topological (zero-energy) mode transmitted from the topological superconductor. We analyze their interplay, focusing on a role played by the external magnetic field. To distinguish between these bound states we analyze the qualitative and quantitative features manifested in the subgap charge tunneling originating under nonequilibrium conditions from the Andreev (particle to hole) scattering processes.
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Affiliation(s)
- G Górski
- Institute of Physics, College of Natural Sciences, University of Rzeszów, ul. Pigonia 1, PL-35-310 Rzeszów, Poland
| | - K Kucab
- Institute of Physics, College of Natural Sciences, University of Rzeszów, ul. Pigonia 1, PL-35-310 Rzeszów, Poland
| | - T Domański
- Institute of Physics, M. Curie-Skłodowska University, ul. Radziszewskiego 10, PL-20-031 Lublin, Poland
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44
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Jünger C, Delagrange R, Chevallier D, Lehmann S, Dick KA, Thelander C, Klinovaja J, Loss D, Baumgartner A, Schönenberger C. Magnetic-Field-Independent Subgap States in Hybrid Rashba Nanowires. PHYSICAL REVIEW LETTERS 2020; 125:017701. [PMID: 32678659 DOI: 10.1103/physrevlett.125.017701] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/21/2020] [Accepted: 06/04/2020] [Indexed: 06/11/2023]
Abstract
Subgap states in semiconducting-superconducting nanowire hybrid devices are controversially discussed as potential topologically nontrivial quantum states. One source of ambiguity is the lack of an energetically and spatially well defined tunnel spectrometer. Here, we use quantum dots directly integrated into the nanowire during the growth process to perform tunnel spectroscopy of discrete subgap states in a long nanowire segment. In addition to subgap states with a standard magnetic field dependence, we find topologically trivial subgap states that are independent of the external magnetic field, i.e., that are pinned to a constant energy as a function of field. We explain this effect qualitatively and quantitatively by taking into account the strong spin-orbit interaction in the nanowire, which can lead to a decoupling of Andreev bound states from the field due to a spatial spin texture of the confined eigenstates. This result constitutes an important step forward in the research on superconducting subgap states in nanowires, such as Majorana bound states.
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Affiliation(s)
- Christian Jünger
- Department of Physics, University of Basel, Klingelbergstrasse 82, CH-4056 Basel, Switzerland
| | - Raphaëlle Delagrange
- Department of Physics, University of Basel, Klingelbergstrasse 82, CH-4056 Basel, Switzerland
| | - Denis Chevallier
- Department of Physics, University of Basel, Klingelbergstrasse 82, CH-4056 Basel, Switzerland
| | - Sebastian Lehmann
- Division of Solid State Physics and NanoLund, Lund University, S-221 00 Lund, Sweden
| | - Kimberly A Dick
- Division of Solid State Physics and NanoLund, Lund University, S-221 00 Lund, Sweden
- Center for Analysis and Synthesis Lund University, S-221 00 Lund, Sweden
| | - Claes Thelander
- Division of Solid State Physics and NanoLund, Lund University, S-221 00 Lund, Sweden
| | - Jelena Klinovaja
- Department of Physics, University of Basel, Klingelbergstrasse 82, CH-4056 Basel, Switzerland
| | - Daniel Loss
- Department of Physics, University of Basel, Klingelbergstrasse 82, CH-4056 Basel, Switzerland
| | - Andreas Baumgartner
- Department of Physics, University of Basel, Klingelbergstrasse 82, CH-4056 Basel, Switzerland
- Swiss Nanoscience Institute, University of Basel, Klingelbergstrasse 82, CH-4056 Basel, Switzerland
| | - Christian Schönenberger
- Department of Physics, University of Basel, Klingelbergstrasse 82, CH-4056 Basel, Switzerland
- Swiss Nanoscience Institute, University of Basel, Klingelbergstrasse 82, CH-4056 Basel, Switzerland
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45
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Yang FB. Kondo-assistant Aharonov-Bohm transport in a quantum dot-Majorana wire system. PHYSICS LETTERS A 2020; 384:126424. [DOI: 10.1016/j.physleta.2020.126424] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 09/01/2023]
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46
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Carrad DJ, Bjergfelt M, Kanne T, Aagesen M, Krizek F, Fiordaliso EM, Johnson E, Nygård J, Jespersen TS. Shadow Epitaxy for In Situ Growth of Generic Semiconductor/Superconductor Hybrids. ADVANCED MATERIALS (DEERFIELD BEACH, FLA.) 2020; 32:e1908411. [PMID: 32337791 DOI: 10.1002/adma.201908411] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/23/2019] [Revised: 02/27/2020] [Accepted: 03/23/2020] [Indexed: 06/11/2023]
Abstract
Uniform, defect-free crystal interfaces and surfaces are crucial ingredients for realizing high-performance nanoscale devices. A pertinent example is that advances in gate-tunable and topological superconductivity using semiconductor/superconductor electronic devices are currently built on the hard proximity-induced superconducting gap obtained from epitaxial indium arsenide/aluminum heterostructures. Fabrication of devices requires selective etch processes; these exist only for InAs/Al hybrids, precluding the use of other, potentially superior material combinations. This work introduces a crystal growth platform-based on 3D structuring of growth substrates-which enables synthesis of semiconductor nanowire hybrids with in situ patterned superconductor shells. The platform eliminates the need for etching, thereby enabling full freedom in the choice of hybrid constituents. All of the most frequently used superconducting hybrid device architectures are realized and characterized. These devices exhibit increased yield and electrostatic stability compared to etched devices, and evidence of ballistic superconductivity is observed. In addition to aluminum, hybrid structures based on tantalum, niobium, and vanadium are presented.
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Affiliation(s)
- Damon J Carrad
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, Copenhagen, 2100, Denmark
| | - Martin Bjergfelt
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, Copenhagen, 2100, Denmark
| | - Thomas Kanne
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, Copenhagen, 2100, Denmark
| | - Martin Aagesen
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, Copenhagen, 2100, Denmark
- Danish Defence Research Center, Ballerup, 2750, Denmark
| | - Filip Krizek
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, Copenhagen, 2100, Denmark
- Department of Spintronics, Institute of Physics, Czech Academy of Sciences, Praha 6, Prague, 162 00, Czech Republic
| | | | - Erik Johnson
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, Copenhagen, 2100, Denmark
- Department of Mechanical Engineering, Technical University of Denmark, Kgs. Lyngby, 2800, Denmark
| | - Jesper Nygård
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, Copenhagen, 2100, Denmark
| | - Thomas Sand Jespersen
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, Copenhagen, 2100, Denmark
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47
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Large spatial extension of the zero-energy Yu-Shiba-Rusinov state in a magnetic field. Nat Commun 2020; 11:1834. [PMID: 32286260 PMCID: PMC7156378 DOI: 10.1038/s41467-020-15322-9] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/19/2019] [Accepted: 03/03/2020] [Indexed: 11/30/2022] Open
Abstract
Various promising qubit concepts have been put forward recently based on engineered superconductor subgap states like Andreev bound states, Majorana zero modes or the Yu-Shiba-Rusinov (Shiba) states. The coupling of these subgap states via a superconductor strongly depends on their spatial extension and is an essential next step for future quantum technologies. Here we investigate the spatial extension of a Shiba state in a semiconductor quantum dot coupled to a superconductor. With detailed transport measurements and numerical renormalization group calculations we find a remarkable more than 50 nm extension of the zero energy Shiba state, much larger than the one observed in very recent scanning tunneling microscopy measurements. Moreover, we demonstrate that its spatial extension increases substantially in a magnetic field. Local magnetic moments coupled to superconductors can form subgap Yu-Shiba-Rusinov states. Here the authors show that Shiba states made with an InAs nanowire quantum dot have large spatial extent, which is beneficial for making Shiba chains that are predicted to host Majorana zero modes.
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48
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Gao F, Wang JH, Watzinger H, Hu H, Rančić MJ, Zhang JY, Wang T, Yao Y, Wang GL, Kukučka J, Vukušić L, Kloeffel C, Loss D, Liu F, Katsaros G, Zhang JJ. Site-Controlled Uniform Ge/Si Hut Wires with Electrically Tunable Spin-Orbit Coupling. ADVANCED MATERIALS (DEERFIELD BEACH, FLA.) 2020; 32:e1906523. [PMID: 32105375 DOI: 10.1002/adma.201906523] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/05/2019] [Revised: 12/30/2019] [Indexed: 06/10/2023]
Abstract
Semiconductor nanowires have been playing a crucial role in the development of nanoscale devices for the realization of spin qubits, Majorana fermions, single photon emitters, nanoprocessors, etc. The monolithic growth of site-controlled nanowires is a prerequisite toward the next generation of devices that will require addressability and scalability. Here, combining top-down nanofabrication and bottom-up self-assembly, the growth of Ge wires on prepatterned Si (001) substrates with controllable position, distance, length, and structure is reported. This is achieved by a novel growth process that uses a SiGe strain-relaxation template and can be potentially generalized to other material combinations. Transport measurements show an electrically tunable spin-orbit coupling, with a spin-orbit length similar to that of III-V materials. Also, charge sensing between quantum dots in closely spaced wires is observed, which underlines their potential for the realization of advanced quantum devices. The reported results open a path toward scalable qubit devices using nanowires on silicon.
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Affiliation(s)
- Fei Gao
- National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing, 100190, China
- CAS Center for Excellence in Topological Quantum Computation and School of Physics, University of Chinese Academy of Sciences, Beijing, 100049, China
| | - Jian-Huan Wang
- National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing, 100190, China
- CAS Center for Excellence in Topological Quantum Computation and School of Physics, University of Chinese Academy of Sciences, Beijing, 100049, China
| | - Hannes Watzinger
- Institute of Science and Technology Austria, Am Campus 1, Klosterneuburg, 3400, Austria
| | - Hao Hu
- Frontier Institute of Science and Technology, Xi'an Jiaotong University, Xi'an, 710054, China
| | - Marko J Rančić
- Department of Physics, University of Basel, Klingelbergstrasse 82, Basel, CH-4056, Switzerland
| | - Jie-Yin Zhang
- National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing, 100190, China
- CAS Center for Excellence in Topological Quantum Computation and School of Physics, University of Chinese Academy of Sciences, Beijing, 100049, China
| | - Ting Wang
- National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing, 100190, China
- CAS Center for Excellence in Topological Quantum Computation and School of Physics, University of Chinese Academy of Sciences, Beijing, 100049, China
- Songshan Lake Materials Laboratory, Dongguan, Guangdong, 523808, China
| | - Yuan Yao
- National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing, 100190, China
| | - Gui-Lei Wang
- Institute of Microelectronics, Chinese Academy of Sciences, Beijing, 100029, China
| | - Josip Kukučka
- Institute of Science and Technology Austria, Am Campus 1, Klosterneuburg, 3400, Austria
| | - Lada Vukušić
- Institute of Science and Technology Austria, Am Campus 1, Klosterneuburg, 3400, Austria
| | - Christoph Kloeffel
- Department of Physics, University of Basel, Klingelbergstrasse 82, Basel, CH-4056, Switzerland
| | - Daniel Loss
- Department of Physics, University of Basel, Klingelbergstrasse 82, Basel, CH-4056, Switzerland
| | - Feng Liu
- Department of Materials Science and Engineering, University of Utah, Salt Lake City, UT, 84112, USA
| | - Georgios Katsaros
- Institute of Science and Technology Austria, Am Campus 1, Klosterneuburg, 3400, Austria
| | - Jian-Jun Zhang
- National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing, 100190, China
- CAS Center for Excellence in Topological Quantum Computation and School of Physics, University of Chinese Academy of Sciences, Beijing, 100049, China
- Songshan Lake Materials Laboratory, Dongguan, Guangdong, 523808, China
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Anomalous Fano Resonance in Double Quantum Dot System Coupled to Superconductor. Sci Rep 2020; 10:2881. [PMID: 32076018 PMCID: PMC7031304 DOI: 10.1038/s41598-020-59498-y] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/14/2019] [Accepted: 01/22/2020] [Indexed: 11/24/2022] Open
Abstract
We analyze the influence of a local pairing on the quantum interference in nanoscopic systems. As a model system we choose the double quantum dot coupled to one metallic and one superconducting electrode in the T-shape geometry. The analysis is particularly valuable for systems containing coupled objects with considerably different broadening of energy levels. In such systems, the scattering of itinerant electrons on a discrete (or narrow) energy level gives rise to the Fano-type interference. Systems with induced superconducting order, along well understood Fano resonances, exhibit also another features on the opposite side of the Fermi level. The lineshape of these resonances differs significantly from their reflection on the opposite side of the Fermi level, and their origin was not fully understood. Here, considering the spin-polarized tunneling model, we explain a microscopic mechanism of a formation of these resonances and discuss the nature of their uncommon lineshapes. We show that the anomalous Fano profiles originate solely from the pairing of nonscattered electrons with scattered ones. We investigate also the interplay of each type of resonances with the Kondo physics and discuss the resonant features in differential conductivity.
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Wang H, Liang X, Wang J, Jiao S, Xue D. Multifunctional inorganic nanomaterials for energy applications. NANOSCALE 2020; 12:14-42. [PMID: 31808494 DOI: 10.1039/c9nr07008g] [Citation(s) in RCA: 29] [Impact Index Per Article: 7.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
Our society has been facing more and more serious challenges towards achieving highly efficient utilization of energy. In the field of energy applications, multifunctional nanomaterials have been attracting increasing attention. Various energy applications, such as energy generation, conversion, storage, saving and transmission, are strongly dependent upon the electrical, thermal, mechanical, optical and catalytic functions of materials. In the nanoscale range, thermoelectric, piezoelectric, triboelectric, photovoltaic, catalytic and electrochromic materials have made major contributions to various energy applications. Inorganic nanomaterials' unique properties, such as excellent electrical and thermal conductivity, large surface area and chemical stability, make them highly competitive in energy applications. In this review, the latest research and development of multifunctional inorganic nanomaterials in energy applications were summarized from the perspective of different energy applications. Furthermore, we also illustrated the unique functions of inorganic nanomaterials to improve their performances and the combination of the functions of nanomaterials into a device. However, challenges may be traced back to the limitations set by scaling the relations between multifunctional inorganic nanomaterials and energy devices.
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Affiliation(s)
- Huilin Wang
- State Key Laboratory of Rare Earth Resource Utilization, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, China. and University of Science and Technology of China, Hefei 230026, China
| | - Xitong Liang
- State Key Laboratory of Rare Earth Resource Utilization, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, China. and University of Science and Technology of China, Hefei 230026, China
| | - Jiutian Wang
- State Key Laboratory of Rare Earth Resource Utilization, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, China. and University of Science and Technology of China, Hefei 230026, China
| | - Shengjian Jiao
- State Key Laboratory of Rare Earth Resource Utilization, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, China. and University of Science and Technology of China, Hefei 230026, China
| | - Dongfeng Xue
- State Key Laboratory of Rare Earth Resource Utilization, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, China. and University of Science and Technology of China, Hefei 230026, China
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