1
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Ibabe Á, Steffensen GO, Casal I, Gómez M, Kanne T, Nygård J, Levy Yeyati A, Lee EJH. Heat Dissipation Mechanisms in Hybrid Superconductor-Semiconductor Devices Revealed by Joule Spectroscopy. NANO LETTERS 2024; 24:6488-6495. [PMID: 38771151 PMCID: PMC11157656 DOI: 10.1021/acs.nanolett.4c00574] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/02/2024] [Revised: 05/17/2024] [Accepted: 05/17/2024] [Indexed: 05/22/2024]
Abstract
Understanding heating and cooling mechanisms in mesoscopic superconductor-semiconductor devices is crucial for their application in quantum technologies. Owing to their poor thermal conductivity, heating effects can drive superconducting-to-normal transitions even at low bias, observed as sharp conductance dips through the loss of Andreev excess currents. Tracking such dips across magnetic field, cryostat temperature, and applied microwave power allows us to uncover cooling bottlenecks in different parts of a device. By applying this "Joule spectroscopy" technique, we analyze heat dissipation in devices based on InAs-Al nanowires and reveal that cooling of superconducting islands is limited by the rather inefficient electron-phonon coupling, as opposed to grounded superconductors that primarily cool by quasiparticle diffusion. We show that powers as low as 50-150 pW are able to suppress superconductivity on the islands. Applied microwaves lead to similar heating effects but are affected by the interplay of the microwave frequency and the effective electron-phonon relaxation time.
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Affiliation(s)
- Ángel Ibabe
- Departamento
de Física de la Materia Condensada, Universidad Autónoma de Madrid, E-28049 Madrid, Spain
- Condensed
Matter Physics Center (IFIMAC), Universidad
Autónoma de Madrid, E-28049 Madrid, Spain
| | - Gorm O. Steffensen
- Condensed
Matter Physics Center (IFIMAC), Universidad
Autónoma de Madrid, E-28049 Madrid, Spain
- Departamento
de Física Teórica de la Materia Condensada, Universidad Autónoma de Madrid, E-28049 Madrid, Spain
| | - Ignacio Casal
- Departamento
de Física de la Materia Condensada, Universidad Autónoma de Madrid, E-28049 Madrid, Spain
- Condensed
Matter Physics Center (IFIMAC), Universidad
Autónoma de Madrid, E-28049 Madrid, Spain
| | - Mario Gómez
- Departamento
de Física de la Materia Condensada, Universidad Autónoma de Madrid, E-28049 Madrid, Spain
- Condensed
Matter Physics Center (IFIMAC), Universidad
Autónoma de Madrid, E-28049 Madrid, Spain
| | - Thomas Kanne
- Center
for Quantum Devices, Niels Bohr Institute, University of Copenhagen, DK-2100 Copenhagen, Denmark
| | - Jesper Nygård
- Center
for Quantum Devices, Niels Bohr Institute, University of Copenhagen, DK-2100 Copenhagen, Denmark
| | - Alfredo Levy Yeyati
- Condensed
Matter Physics Center (IFIMAC), Universidad
Autónoma de Madrid, E-28049 Madrid, Spain
- Departamento
de Física Teórica de la Materia Condensada, Universidad Autónoma de Madrid, E-28049 Madrid, Spain
- Instituto
Nicolás Cabrera, Universidad Autónoma
de Madrid, E-28049 Madrid, Spain
| | - Eduardo J. H. Lee
- Departamento
de Física de la Materia Condensada, Universidad Autónoma de Madrid, E-28049 Madrid, Spain
- Condensed
Matter Physics Center (IFIMAC), Universidad
Autónoma de Madrid, E-28049 Madrid, Spain
- Instituto
Nicolás Cabrera, Universidad Autónoma
de Madrid, E-28049 Madrid, Spain
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2
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Máthé L, Kovács-Krausz Z, Botiz I, Grosu I, El Anouz K, El Allati A, Zârbo LP. Phonon-Assisted Tunneling through Quantum Dot Systems Connected to Majorana Bound States. NANOMATERIALS (BASEL, SWITZERLAND) 2023; 13:nano13101616. [PMID: 37242032 DOI: 10.3390/nano13101616] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/08/2023] [Revised: 05/05/2023] [Accepted: 05/08/2023] [Indexed: 05/28/2023]
Abstract
We theoretically analyze phonon-assisted tunneling transport in a quantum dot side connected to a Majorana bound state in a topological superconducting nanowire. We investigate the behavior of the current through the dot, for a range of experimentally relevant parameters, in the presence of one long-wave optical phonon mode. We consider the current-gate voltage, the current-bias voltage and the current-dot-Majorana coupling characteristics under the influence of the electron-phonon coupling. In the absence of electron-phonon interaction, the Majorana bound states suppress the current when the gate voltage matches the Fermi level, but the increase in the bias voltage counteracts this effect. In the presence of electron-phonon coupling, the current behaves similarly as a function of the renormalized gate voltage. As an added feature at large bias voltages, it presents a dip or a plateau, depending on the size of the dot-Majorana coupling. Lastly, we show that the currents are most sensitive to, and depend non-trivially on the parameters of the Majorana circuit element, in the regime of low temperatures combined with low voltages. Our results provide insights into the complex physics of quantum dot devices used to probe Majorana bound states.
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Affiliation(s)
- Levente Máthé
- Center of Advanced Research and Technologies for Alternative Energies, National Institute for R & D of Isotopic and Molecular Technologies, 67-103 Donat, 400293 Cluj-Napoca, Romania
- Faculty of Physics, Babeș-Bolyai University, 1 Kogălniceanu, 400084 Cluj-Napoca, Romania
| | - Zoltán Kovács-Krausz
- Department of Physics, Institute of Physics, Budapest University of Technology and Economics, Műegyetem rkp. 3, H-1111 Budapest, Hungary
| | - Ioan Botiz
- Faculty of Physics, Babeș-Bolyai University, 1 Kogălniceanu, 400084 Cluj-Napoca, Romania
- Interdisciplinary Research Institute in Bio-Nano-Sciences, Babeș-Bolyai University, 42 Treboniu Laurian, 400271 Cluj-Napoca, Romania
| | - Ioan Grosu
- Faculty of Physics, Babeș-Bolyai University, 1 Kogălniceanu, 400084 Cluj-Napoca, Romania
| | - Khadija El Anouz
- Laboratory of R & D in Engineering Sciences, Faculty of Sciences and Techniques Al-Hoceima, Abdelmalek Essaadi University, Tetouan 93000, Morocco
| | - Abderrahim El Allati
- Laboratory of R & D in Engineering Sciences, Faculty of Sciences and Techniques Al-Hoceima, Abdelmalek Essaadi University, Tetouan 93000, Morocco
| | - Liviu P Zârbo
- Center of Advanced Research and Technologies for Alternative Energies, National Institute for R & D of Isotopic and Molecular Technologies, 67-103 Donat, 400293 Cluj-Napoca, Romania
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3
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Vekris A, Estrada Saldaña JC, Kanne T, Hvid-Olsen T, Marnauza M, Olsteins D, Wauters MM, Burrello M, Nygård J, Grove-Rasmussen K. Electronic Transport in Double-Nanowire Superconducting Islands with Multiple Terminals. NANO LETTERS 2022; 22:5765-5772. [PMID: 35833741 DOI: 10.1021/acs.nanolett.2c01161] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/15/2023]
Abstract
We characterize in situ grown parallel nanowires bridged by a superconducting island. The magnetic-field and temperature dependence of Coulomb blockade peaks measured across different pairs of nanowire ends suggest the presence of a subgap state extended over the hybrid parallel-nanowire island. Being gate-tunable, accessible by multiple terminals, and free of quasiparticle poisoning, these nanowires show promise for the implementation of several proposals that rely on parallel nanowire platforms.
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Affiliation(s)
- Alexandros Vekris
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark
- Sino-Danish Center for Education and Research (SDC) SDC Building, Yanqihu Campus, University of Chinese Academy of Sciences, 380 Huaibeizhuang, Huairou District, 101408 Beijing, China
| | | | - Thomas Kanne
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark
| | - Thor Hvid-Olsen
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark
| | - Mikelis Marnauza
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark
| | - Dags Olsteins
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark
| | - Matteo M Wauters
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark
- Niels Bohr International Academy, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark
| | - Michele Burrello
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark
- Niels Bohr International Academy, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark
| | - Jesper Nygård
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark
| | - Kasper Grove-Rasmussen
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark
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4
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Subgap dynamics of double quantum dot coupled between superconducting and normal leads. Sci Rep 2021; 11:11138. [PMID: 34045499 PMCID: PMC8160274 DOI: 10.1038/s41598-021-90080-2] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/08/2021] [Accepted: 04/30/2021] [Indexed: 11/17/2022] Open
Abstract
Dynamical processes induced by the external time-dependent fields can provide valuable insight into the characteristic energy scales of a given physical system. We investigate them here in a nanoscopic heterostructure, consisting of the double quantum dot coupled in series to the superconducting and the metallic reservoirs, analyzing its response to (i) abrupt bias voltage applied across the junction, (ii) sudden change of the energy levels, and imposed by (iii) their periodic driving. We explore subgap properties of this setup which are strictly related to the in-gap quasiparticles and discuss their signatures manifested in the time-dependent charge currents. The characteristic multi-mode oscillations, their beating patters and photon-assisted harmonics reveal a rich spectrum of dynamical features that might be important for designing the superconducting qubits.
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5
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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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6
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Grivnin A, Bor E, Heiblum M, Oreg Y, Shtrikman H. Concomitant opening of a bulk-gap with an emerging possible Majorana zero mode. Nat Commun 2019; 10:1940. [PMID: 31036841 PMCID: PMC6488617 DOI: 10.1038/s41467-019-09771-0] [Citation(s) in RCA: 44] [Impact Index Per Article: 8.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/06/2018] [Accepted: 03/20/2019] [Indexed: 11/23/2022] Open
Abstract
Majorana quasiparticles are generally detected in a 1D topological superconductor by tunneling electrons into its edge, with an emergent zero-bias conductance peak (ZBCP). However, such a ZBCP can also result from other mechanisms, hence, additional verifications are required. Since the emergence of a Majorana must be accompanied by an opening of a topological gap in the bulk, two simultaneous measurements are performed: one in the bulk and another at the edge of a 1D InAs nanowire coated with epitaxial aluminum. Only under certain experimental parameters, a closing of the superconducting bulk-gap that is followed by its reopening, appears simultaneously with a ZBCP at the edge. Such events suggest the occurrence of a topologically non-trivial phase. Yet, we also find that ZBCPs are observed under different tuning parameters without simultaneous reopening of a bulk-gap. This demonstrates the importance of simultaneous probing of bulk and edge in the identification of Majorana edge-states.
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Affiliation(s)
- Anna Grivnin
- Braun Center for Submicron Research, Weizmann Institute of Science, Rehovot, 76100, Israel
- Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot, 76100, Israel
| | - Ella Bor
- Braun Center for Submicron Research, Weizmann Institute of Science, Rehovot, 76100, Israel
- Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot, 76100, Israel
| | - Moty Heiblum
- Braun Center for Submicron Research, Weizmann Institute of Science, Rehovot, 76100, Israel.
- Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot, 76100, Israel.
| | - Yuval Oreg
- Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot, 76100, Israel
| | - Hadas Shtrikman
- Braun Center for Submicron Research, Weizmann Institute of Science, Rehovot, 76100, Israel
- Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot, 76100, Israel
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7
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Cao Z, Zhang H, Lü HF, He WX, Lu HZ, Xie XC. Decays of Majorana or Andreev Oscillations Induced by Steplike Spin-Orbit Coupling. PHYSICAL REVIEW LETTERS 2019; 122:147701. [PMID: 31050472 DOI: 10.1103/physrevlett.122.147701] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/07/2018] [Indexed: 06/09/2023]
Abstract
The Majorana zero mode in the semiconductor-superconductor nanowire is one of the promising candidates for topological quantum computing. Recently, in islands of nanowires, subgap-state energies have been experimentally observed to oscillate as a function of the magnetic field, showing a signature of overlapped Majorana bound states. However, the oscillation amplitude either dies away after an overshoot or decays, sharply opposite to the theoretically predicted enhanced oscillations for Majorana bound states. We reveal that a steplike distribution of spin-orbit coupling in realistic devices can induce the decaying Majorana oscillations, resulting from the coupling-induced energy repulsion between the quasiparticle spectra on the two sides of the step. This steplike spin-orbit coupling can also lead to decaying oscillations in the spectrum of the Andreev bound states. For Coulomb-blockade peaks mediated by the Majorana bound states, the peak spacings have been predicted to correlate with peak heights by a π/2 phase shift, which was ambiguous in recent experiments and may be explained by the steplike spin-orbit coupling. Our work will inspire more works to reexamine effects of the nonuniform spin-orbit coupling, which is generally present in experimental devices.
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Affiliation(s)
- Zhan Cao
- Shenzhen Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China
- School of Physics, Southeast University, Nanjing 211189, China
- Peng Cheng Laboratory, Shenzhen 518055, China
- Shenzhen Key Laboratory of Quantum Science and Engineering, Shenzhen 518055, China
| | - Hao Zhang
- State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, China
- Beijing Academy of Quantum Information Sciences, Beijing 100193, China
| | - Hai-Feng Lü
- School of Physics, University of Electronic Science and Technology of China, Chengdu 610054, China
| | - Wan-Xiu He
- Center for Interdisciplinary Studies and Key Laboratory for Magnetism and Magnetic Materials of the Ministry of Education, Lanzhou University, Lanzhou 730000, China
| | - Hai-Zhou Lu
- Shenzhen Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China
- Peng Cheng Laboratory, Shenzhen 518055, China
- Shenzhen Key Laboratory of Quantum Science and Engineering, Shenzhen 518055, China
| | - X C Xie
- Beijing Academy of Quantum Information Sciences, Beijing 100193, China
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
- CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences, Beijing 100190, China
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8
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Size and shape control of metal nanoparticles in millifluidic reactors. PHYSICAL SCIENCES REVIEWS 2018. [DOI: 10.1515/psr-2017-0120] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
Abstract
Abstract
Engineered metal nanoparticles (metal NPs) possess unique size -dependent optical and electronic properties that could enable new applications in biomedicine, energy generation, microelectronics, micro-optics, and catalysis. For metal NPs to make a mark in these fields, however, new synthetic strategies must be developed that permit NP synthesis on the kilogram scale, while maintaining precise control over NP physiochemical properties (size, shape, composition, and surface chemistry). Currently, NP batch syntheses produce product on the milligram scale and rely on synthetic strategies that are not readily amenable to scale-up. Flow reactor systems (including lab-on-a-chip devices) provide a synthesis platform that can circumvent many of the traditional limitations of batch-scale NP syntheses. These reactors provide more uniform reagent mixing, more uniform heat transfer, opportunities to interface in situ monitoring technology, and allow product yield to be scaled up simply by running multiple reactors in parallel. While many NP syntheses have been successfully transferred to microfluidic reactor systems, microfluidic reactor fabrication is time intensive and typically requires sophisticated lithography facilities. Consequently, millifluidic flow reactors (reactors with channel dimensions of 0.5–10.0 mm) are gaining popularity in NP synthesis. These millifluidic reactors provide many of the same synthetic advantages as microfluidic devices, but are simpler to construct, easier to reconfigure, and more straightforward to interface with in situ monitoring techniques. In this chapter, we will discuss the progress that has been made in developing millifluidic reactors for functionalized metal NP synthesis. First, we will review the basic wet-chemical strategies used to control metal NP size and shape in batch reactors. We will then survey some of the basic principles of millifluidic device design, construction, and operation. We will also discuss the potential for incorporating in situ monitoring for quality control during synthesis. We will conclude by highlighting some particularly relevant examples of millifluidic metal NP synthesis that have set new standards for metal NP size, shape, and surface chemistry control.
Graphical Abstract: Credit: Sam Lohse
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9
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Vaitiekėnas S, Whiticar AM, Deng MT, Krizek F, Sestoft JE, Palmstrøm CJ, Marti-Sanchez S, Arbiol J, Krogstrup P, Casparis L, Marcus CM. Selective-Area-Grown Semiconductor-Superconductor Hybrids: A Basis for Topological Networks. PHYSICAL REVIEW LETTERS 2018; 121:147701. [PMID: 30339420 DOI: 10.1103/physrevlett.121.147701] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/18/2018] [Revised: 06/20/2018] [Indexed: 06/08/2023]
Abstract
We introduce selective area grown hybrid InAs/Al nanowires based on molecular beam epitaxy, allowing arbitrary semiconductor-superconductor networks containing loops and branches. Transport reveals a hard induced gap and unpoisoned 2e-periodic Coulomb blockade, with temperature dependent 1e features in agreement with theory. Coulomb peak spacing in parallel magnetic field displays overshoot, indicating an oscillating discrete near-zero subgap state consistent with device length. Finally, we investigate a loop network, finding strong spin-orbit coupling and a coherence length of several microns. These results demonstrate the potential of this platform for scalable topological networks among other applications.
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Affiliation(s)
- S Vaitiekėnas
- Center for Quantum Devices and Station Q Copenhagen, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
| | - A M Whiticar
- Center for Quantum Devices and Station Q Copenhagen, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
| | - M-T Deng
- Center for Quantum Devices and Station Q Copenhagen, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
| | - F Krizek
- Center for Quantum Devices and Station Q Copenhagen, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
| | - J E Sestoft
- Center for Quantum Devices and Station Q Copenhagen, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
| | - C J Palmstrøm
- Materials Department, University of California, Santa Barbara, California 93106, USA
| | - S Marti-Sanchez
- Catalan Institute of Nanoscience and Nanotechnology (ICN2), CSIC and BIST, Campus UAB, 08193 Bellaterra, Barcelona, Spain
| | - J Arbiol
- Catalan Institute of Nanoscience and Nanotechnology (ICN2), CSIC and BIST, Campus UAB, 08193 Bellaterra, Barcelona, Spain
- ICREA, Pg. Lluís Companys 23, 08010 Barcelona, Catalonia, Spain
| | - P Krogstrup
- Center for Quantum Devices and Station Q Copenhagen, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
| | - L Casparis
- Center for Quantum Devices and Station Q Copenhagen, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
| | - C M Marcus
- Center for Quantum Devices and Station Q Copenhagen, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
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10
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Yu-Shiba-Rusinov screening of spins in double quantum dots. Nat Commun 2018; 9:2376. [PMID: 29915280 PMCID: PMC6006160 DOI: 10.1038/s41467-018-04683-x] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/09/2017] [Accepted: 05/17/2018] [Indexed: 11/25/2022] Open
Abstract
A magnetic impurity coupled to a superconductor gives rise to a Yu–Shiba–Rusinov (YSR) state inside the superconducting energy gap. With increasing exchange coupling the excitation energy of this state eventually crosses zero and the system switches to a YSR ground state with bound quasiparticles screening the impurity spin by ħ/2. Here we explore indium arsenide (InAs) nanowire double quantum dots tunnel coupled to a superconductor and demonstrate YSR screening of spin-1/2 and spin-1 states. Gating the double dot through nine different charge states, we show that the honeycomb pattern of zero-bias conductance peaks, archetypal of double dots coupled to normal leads, is replaced by lines of zero-energy YSR states. These enclose regions of YSR-screened dot spins displaying distinctive spectral features, and their characteristic shape and topology change markedly with tunnel coupling strengths. We find excellent agreement with a simple zero-bandwidth approximation, and with numerical renormalization group calculations for the two-orbital Anderson model. Coupling superconductors to mesoscopic systems leads to unusual effects that could be exploited in new devices including topological quantum computers. Here the authors present a double quantum dot with a Yu–Shiba–Rusinov ground state arising from the interplay of Coulomb interactions and superconductivity.
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11
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Ren JT, Lü HF, Ke SS, Guo Y, Zhang HW. Disorder-induced suppression of the zero-bias conductance peak splitting in topological superconducting nanowires. BEILSTEIN JOURNAL OF NANOTECHNOLOGY 2018; 9:1358-1369. [PMID: 29977670 PMCID: PMC6009613 DOI: 10.3762/bjnano.9.128] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 11/16/2017] [Accepted: 03/27/2018] [Indexed: 06/08/2023]
Abstract
We investigate the effect of three types of intrinsic disorder, including that in pairing energy, chemical potential, and hopping amplitude, on the transport properties through the superconducting nanowires with Majorana bound states (MBSs). The conductance and the noise Fano factor are calculated based on a tight-binding model by adopting a non-equilibrium Green's function method. It is found that the disorder can effectively lead to a reduction in the conductance peak spacings and significantly suppress the peak height. Remarkably, for a longer nanowire, the zero-bias peak could be reproduced by weak disorder for a finite Majorana energy splitting. It is interesting that the shot noise provides a signature to discriminate whether the zero-bias peak is induced by Majorana zero mode or disorder. For Majorana zero mode, the noise Fano factor approaches zero in the low bias voltage limit due to the resonant Andreev tunneling. However, the Fano factor is finite in the case of a disorder-induced zero-bias peak.
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Affiliation(s)
- Jun-Tong Ren
- State Key Laboratory of Electronic Thin Films and Integrated Devices and School of Physical Electronics, University of Electronic Science and Technology of China, Chengdu 610054, China
| | - Hai-Feng Lü
- State Key Laboratory of Electronic Thin Films and Integrated Devices and School of Physical Electronics, University of Electronic Science and Technology of China, Chengdu 610054, China
- Department of Physics and State Key Laboratory of Low-Dimensional Quantum Physics, Tsinghua University, Beijing 100084, China
| | - Sha-Sha Ke
- State Key Laboratory of Electronic Thin Films and Integrated Devices and School of Physical Electronics, University of Electronic Science and Technology of China, Chengdu 610054, China
| | - Yong Guo
- Department of Physics and State Key Laboratory of Low-Dimensional Quantum Physics, Tsinghua University, Beijing 100084, China
| | - Huai-Wu Zhang
- State Key Laboratory of Electronic Thin Films and Integrated Devices and School of Physical Electronics, University of Electronic Science and Technology of China, Chengdu 610054, China
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12
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Su Z, Tacla AB, Hocevar M, Car D, Plissard SR, Bakkers EPAM, Daley AJ, Pekker D, Frolov SM. Andreev molecules in semiconductor nanowire double quantum dots. Nat Commun 2017; 8:585. [PMID: 28928420 PMCID: PMC5605684 DOI: 10.1038/s41467-017-00665-7] [Citation(s) in RCA: 21] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/11/2016] [Accepted: 07/19/2017] [Indexed: 11/13/2022] Open
Abstract
Chains of quantum dots coupled to superconductors are promising for the realization of the Kitaev model of a topological superconductor. While individual superconducting quantum dots have been explored, control of longer chains requires understanding of interdot coupling. Here, double quantum dots are defined by gate voltages in indium antimonide nanowires. High transparency superconducting niobium titanium nitride contacts are made to each of the dots in order to induce superconductivity, as well as probe electron transport. Andreev bound states induced on each of dots hybridize to define Andreev molecular states. The evolution of these states is studied as a function of charge parity on the dots, and in magnetic field. The experiments are found in agreement with a numerical model. Quantum dots in a nanowire are one possible approach to creating a solid-state quantum simulator. Here, the authors demonstrate the coupling of electronic states in a double quantum dot to form Andreev molecule states; a potential building block for longer chains suitable for quantum simulation.
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Affiliation(s)
- Zhaoen Su
- Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, PA, 15260, USA
| | - Alexandre B Tacla
- Department of Physics and SUPA, University of Strathclyde, Glasgow, G4 0NG, UK
| | - Moïra Hocevar
- Universite Grenoble Alpes, F-38000, Grenoble, France.,CNRS, Institut Neel, F-38000, Grenoble, France
| | - Diana Car
- 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.,QuTech and Kavli Institute of Nanoscience, Delft University of Technology, 2628 CJ, Delft, The Netherlands
| | - Andrew J Daley
- Department of Physics and SUPA, University of Strathclyde, Glasgow, G4 0NG, UK
| | - David Pekker
- Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, PA, 15260, USA
| | - Sergey M Frolov
- Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, PA, 15260, USA.
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13
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Pustilnik M, van Heck B, Lutchyn RM, Glazman LI. Quantum Criticality in Resonant Andreev Conduction. PHYSICAL REVIEW LETTERS 2017; 119:116802. [PMID: 28949231 DOI: 10.1103/physrevlett.119.116802] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/14/2017] [Indexed: 06/07/2023]
Abstract
Motivated by recent experiments with proximitized nanowires, we study a mesoscopic s-wave superconductor connected via point contacts to normal-state leads. We demonstrate that at energies below the charging energy the system is described by the two-channel Kondo model, which can be brought to the quantum critical regime by varying the gate potential and conductances of the contacts.
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Affiliation(s)
- M Pustilnik
- School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332, USA
| | - B van Heck
- Department of Physics, Yale University, New Haven, Connecticut 06520, USA
| | - R M Lutchyn
- Station Q, Microsoft Research, Santa Barbara, California 93106-6105, USA
| | - L I Glazman
- Department of Physics, Yale University, New Haven, Connecticut 06520, USA
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14
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Albrecht SM, Hansen EB, Higginbotham AP, Kuemmeth F, Jespersen TS, Nygård J, Krogstrup P, Danon J, Flensberg K, Marcus CM. Transport Signatures of Quasiparticle Poisoning in a Majorana Island. PHYSICAL REVIEW LETTERS 2017; 118:137701. [PMID: 28409973 DOI: 10.1103/physrevlett.118.137701] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/17/2016] [Indexed: 06/07/2023]
Abstract
We investigate effects of quasiparticle poisoning in a Majorana island with strong tunnel coupling to normal-metal leads. In addition to the main Coulomb blockade diamonds, "shadow" diamonds appear, shifted by 1e in gate voltage, consistent with transport through an excited (poisoned) state of the island. Comparison to a simple model yields an estimate of parity lifetime for the strongly coupled island (∼1 μs) and sets a bound for a weakly coupled island (>10 μs). Fluctuations in the gate-voltage spacing of Coulomb peaks at high field, reflecting Majorana hybridization, are enhanced by the reduced lever arm at strong coupling. When converted from gate voltage to energy units, fluctuations are consistent with previous measurements.
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Affiliation(s)
- S M Albrecht
- Center for Quantum Devices and Station Q Copenhagen, Niels Bohr Institute, University of Copenhagen, Copenhagen 2100, Denmark
| | - E B Hansen
- Center for Quantum Devices and Station Q Copenhagen, Niels Bohr Institute, University of Copenhagen, Copenhagen 2100, Denmark
| | - A P Higginbotham
- Center for Quantum Devices and Station Q Copenhagen, Niels Bohr Institute, University of Copenhagen, Copenhagen 2100, Denmark
- JILA, University of Colorado and NIST, Boulder, Colorado 80309, USA
| | - F Kuemmeth
- Center for Quantum Devices and Station Q Copenhagen, Niels Bohr Institute, University of Copenhagen, Copenhagen 2100, Denmark
| | - T S Jespersen
- Center for Quantum Devices and Station Q Copenhagen, Niels Bohr Institute, University of Copenhagen, Copenhagen 2100, Denmark
| | - J Nygård
- Center for Quantum Devices and Station Q Copenhagen, Niels Bohr Institute, University of Copenhagen, Copenhagen 2100, Denmark
| | - P Krogstrup
- Center for Quantum Devices and Station Q Copenhagen, Niels Bohr Institute, University of Copenhagen, Copenhagen 2100, Denmark
| | - J Danon
- Center for Quantum Devices and Station Q Copenhagen, Niels Bohr Institute, University of Copenhagen, Copenhagen 2100, Denmark
- Department of Physics, NTNU, Norwegian University of Science and Technology, 7491 Trondheim, Norway
| | - K Flensberg
- Center for Quantum Devices and Station Q Copenhagen, Niels Bohr Institute, University of Copenhagen, Copenhagen 2100, Denmark
| | - C M Marcus
- Center for Quantum Devices and Station Q Copenhagen, Niels Bohr Institute, University of Copenhagen, Copenhagen 2100, Denmark
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