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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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2
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Scheppe AD, Pak MV. Perturbing finite temperature multicomponent DFT 1D Kohn-Sham systems: Peierls gap & Kohn anomaly. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2023; 36:075401. [PMID: 37921113 DOI: 10.1088/1361-648x/ad08eb] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/16/2023] [Accepted: 11/01/2023] [Indexed: 11/04/2023]
Abstract
One of the greatest challenges when designing new technologies that make use of non-trivial quantum materials is the difficulty associated with predicting material-specific properties, such as critical temperature, gap parameter, etc. There is naturally a great amount of interest in these types of condensed matter systems because of their application to quantum sensing, quantum electronics, and quantum computation; however, they are exceedingly difficult to address from first principles because of the famous many-body problem. For this reason, a full electron-nuclear quantum calculation will likely remain completely out of reach for the foreseeable future. A practical alternative is provided by finite temperature, multi component density functional theory, which is a formally exact method of computing the equilibrium state energy of a many-body quantum system. In this work, we use this construction alongside a perturbative scheme to demonstrate that the phenomena Peierls effect and Kohn anomaly are both natural features of the Kohn-Sham (KS) equations without additional structure needed. We find the temperature dependent ionic density for a simple 1D lattice which is then used to derive the ionic densities temperature dependent affect on the electronic band structure. This is accomplished by Fourier transforming the ionic density term found within this KS electronic equation. Using the Peierls effect phonon distortion gap openings in relation to the Fermi level, we then perturb the KS ionic equation with a conduction electron density, deriving the Kohn anomaly. This provides a workable predictive strategy for interesting electro-phonon related material properties which could be extended to 2D and 3D real materials while retaining the otherwise complicated temperature dependence.
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Affiliation(s)
- Adrian D Scheppe
- Department of Physics, Air Force Institute of Technology, 2950 Hobson Way, Wright-Patterson AFB, OH 45433, United States of America
| | - Michael V Pak
- Department of Physics, Air Force Institute of Technology, 2950 Hobson Way, Wright-Patterson AFB, OH 45433, United States of America
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Levajac V, Wang JY, Sfiligoj C, Lemang M, Wolff JC, Bordin A, Badawy G, Gazibegovic S, Bakkers EPAM, Kouwenhoven LP. Subgap spectroscopy along hybrid nanowires by nm-thick tunnel barriers. Nat Commun 2023; 14:6647. [PMID: 37863952 PMCID: PMC10589238 DOI: 10.1038/s41467-023-42422-z] [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: 03/15/2023] [Accepted: 10/11/2023] [Indexed: 10/22/2023] Open
Abstract
Tunneling spectroscopy is widely used to examine the subgap spectra in semiconductor-superconductor nanostructures when searching for Majorana zero modes (MZMs). Typically, semiconductor sections controlled by local gates at the ends of hybrids serve as tunnel barriers. Besides detecting states only at the hybrid ends, such gate-defined tunnel probes can cause the formation of non-topological subgap states that mimic MZMs. Here, we develop an alternative type of tunnel probes to overcome these limitations. After the growth of an InSb-Al hybrid nanowire, a precisely controlled in-situ oxidation of the Al shell is performed to yield a nm-thick AlOx layer. In such thin isolating layer, tunnel probes can be arbitrarily defined at any position along the hybrid nanowire by shadow-wall angle-deposition of metallic leads. In this work, we make multiple tunnel probes along single nanowire hybrids and successfully identify Andreev bound states (ABSs) of various spatial extension residing along the hybrids.
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Affiliation(s)
- Vukan Levajac
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology, 2628GA, Delft, The Netherlands
| | - Ji-Yin Wang
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology, 2628GA, Delft, The Netherlands.
- Beijing Academy of Quantum Information Sciences, 100193, Beijing, China.
| | - Cristina Sfiligoj
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology, 2628GA, Delft, The Netherlands
| | - Mathilde Lemang
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology, 2628GA, Delft, The Netherlands
| | - Jan Cornelis Wolff
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology, 2628GA, Delft, The Netherlands
| | - Alberto Bordin
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology, 2628GA, Delft, The Netherlands
| | - Ghada Badawy
- Department of Applied Physics, Eindhoven University of Technology, 5600MB, Eindhoven, The Netherlands
| | - Sasa Gazibegovic
- Department of Applied Physics, Eindhoven University of Technology, 5600MB, Eindhoven, The Netherlands
| | - Erik P A M Bakkers
- Department of Applied Physics, Eindhoven University of Technology, 5600MB, Eindhoven, The Netherlands
| | - Leo P Kouwenhoven
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology, 2628GA, Delft, The Netherlands
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Yan S, Su H, Pan D, Li W, Lyu Z, Chen M, Wu X, Lu L, Zhao J, Wang JY, Xu H. Supercurrent, Multiple Andreev Reflections and Shapiro Steps in InAs Nanosheet Josephson Junctions. NANO LETTERS 2023. [PMID: 37450769 DOI: 10.1021/acs.nanolett.3c01450] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 07/18/2023]
Abstract
We report an experimental study of proximity induced superconductivity in planar Josephson junction devices made from free-standing InAs nanosheets. The nanosheets are grown by molecular beam epitaxy, and the Josephson junction devices are fabricated by directly contacting the nanosheets with superconductor Al electrodes. The fabricated devices are explored by low-temperature carrier transport measurements. The measurements show that the devices exhibit a gate-tunable supercurrent, multiple Andreev reflections, and a good quality superconductor-semiconductor interface. The superconducting characteristics of the Josephson junctions are investigated at different magnetic fields and temperatures and are analyzed based on the Bardeen-Cooper-Schrieffer (BCS) theory. The measurements of the ac Josephson effect are also conducted under microwave radiations with different radiation powers and frequencies, and integer Shapiro steps are observed. Our work demonstrates that InAs nanosheet based hybrid devices are desired systems for investigating the forefront of physics, such as two-dimensional topological superconductivity.
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Affiliation(s)
- Shili Yan
- Beijing Academy of Quantum Information Sciences, 100193 Beijing, China
| | - Haitian Su
- Beijing Key Laboratory of Quantum Devices, Key Laboratory for the Physics and Chemistry of Nanodevices, and School of Electronics, Peking University, Beijing 100871, China
- Institute of Condensed Matter and Material Physics, School of Physics, Peking University, Beijing 100871, China
| | - Dong Pan
- State Key Laboratory of Superlattices and Microstructures, Institute of Semiconductors, Chinese Academy of Sciences, P.O. Box 912, Beijing 100083, China
| | - Weijie Li
- Beijing Key Laboratory of Quantum Devices, Key Laboratory for the Physics and Chemistry of Nanodevices, and School of Electronics, Peking University, Beijing 100871, China
- Academy for Advanced Interdisciplinary Studies, Peking University, Beijing 100871, China
| | - Zhaozheng Lyu
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences; School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100190, China
| | - Mo Chen
- Beijing Academy of Quantum Information Sciences, 100193 Beijing, China
| | - Xingjun Wu
- Beijing Academy of Quantum Information Sciences, 100193 Beijing, China
| | - Li Lu
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences; School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100190, China
| | - Jianhua Zhao
- State Key Laboratory of Superlattices and Microstructures, Institute of Semiconductors, Chinese Academy of Sciences, P.O. Box 912, Beijing 100083, China
| | - Ji-Yin Wang
- Beijing Academy of Quantum Information Sciences, 100193 Beijing, China
| | - Hongqi Xu
- Beijing Academy of Quantum Information Sciences, 100193 Beijing, China
- Beijing Key Laboratory of Quantum Devices, Key Laboratory for the Physics and Chemistry of Nanodevices, and School of Electronics, Peking University, Beijing 100871, China
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Schrade C, Fu L. Quantum Computing with Majorana Kramers Pairs. PHYSICAL REVIEW LETTERS 2022; 129:227002. [PMID: 36493456 DOI: 10.1103/physrevlett.129.227002] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/17/2018] [Revised: 10/20/2022] [Accepted: 10/28/2022] [Indexed: 06/17/2023]
Abstract
We propose a universal gate set acting on a qubit formed by the degenerate ground states of a Coulomb-blockaded time-reversal invariant topological superconductor island with spatially separated Majorana Kramers pairs: the "Majorana Kramers qubit." All gate operations are implemented by coupling the Majorana Kramers pairs to conventional superconducting leads. Interestingly, in such an all-superconducting device, the energy gap of the leads provides another layer of protection from quasiparticle poisoning independent of the island charging energy. Moreover, the absence of strong magnetic fields-which typically reduce the superconducting gap size of the island-suggests a unique robustness of our qubit to quasiparticle poisoning due to thermal excitations. Consequently, the Majorana Kramers qubit should benefit from prolonged coherence times and may provide an alternative route to a Majorana-based quantum computer.
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Affiliation(s)
- Constantin Schrade
- Department of Physics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, USA
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark
| | - Liang Fu
- Department of Physics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, USA
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Wang JY, Schrade C, Levajac V, van Driel D, Li K, Gazibegovic S, Badawy G, Op het Veld RLM, Lee JS, Pendharkar M, Dempsey CP, Palmstrøm CJ, Bakkers EPAM, Fu L, Kouwenhoven LP, Shen J. Supercurrent parity meter in a nanowire Cooper pair transistor. SCIENCE ADVANCES 2022; 8:eabm9896. [PMID: 35452283 PMCID: PMC9032955 DOI: 10.1126/sciadv.abm9896] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 10/30/2021] [Accepted: 03/07/2022] [Indexed: 06/14/2023]
Abstract
We study a Cooper pair transistor realized by two Josephson weak links that enclose a superconducting island in an InSb-Al hybrid nanowire. When the nanowire is subject to a magnetic field, isolated subgap levels arise in the superconducting island and, because of the Coulomb blockade, mediate a supercurrent by coherent cotunneling of Cooper pairs. We show that the supercurrent resulting from such cotunneling events exhibits, for low to moderate magnetic fields, a phase offset that discriminates even and odd charge ground states on the superconducting island. Notably, this phase offset persists when a subgap state approaches zero energy and, based on theoretical considerations, permits parity measurements of subgap states by supercurrent interferometry. Such supercurrent parity measurements could, in a series of experiments, provide an alternative approach for manipulating and protecting quantum information stored in the isolated subgap levels of superconducting islands.
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Affiliation(s)
- Ji-Yin Wang
- QuTech and Kavli Institute of NanoScience, Delft University of Technology, 2600 GA Delft, Netherlands
| | - Constantin Schrade
- Department of Physics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA
| | - Vukan Levajac
- QuTech and Kavli Institute of NanoScience, Delft University of Technology, 2600 GA Delft, Netherlands
| | - David van Driel
- QuTech and Kavli Institute of NanoScience, Delft University of Technology, 2600 GA Delft, Netherlands
| | - Kongyi Li
- QuTech and Kavli Institute of NanoScience, Delft University of Technology, 2600 GA Delft, Netherlands
| | - Sasa Gazibegovic
- Department of Applied Physics, Eindhoven University of Technology, 5600 MB Eindhoven, Netherlands
| | - Ghada Badawy
- Department of Applied Physics, Eindhoven University of Technology, 5600 MB Eindhoven, Netherlands
| | - Roy L. M. Op het Veld
- Department of Applied Physics, Eindhoven University of Technology, 5600 MB Eindhoven, Netherlands
| | - Joon Sue Lee
- California NanoSystems Institute, University of California, Santa Barbara, Santa Barbara, CA 93106, USA
| | - Mihir Pendharkar
- Electrical and Computer Engineering, University of California, Santa Barbara, Santa Barbara, CA 93106, USA
| | - Connor P. Dempsey
- Electrical and Computer Engineering, University of California, Santa Barbara, Santa Barbara, CA 93106, USA
| | - Chris J. Palmstrøm
- California NanoSystems Institute, University of California, Santa Barbara, Santa Barbara, CA 93106, USA
- Electrical and Computer Engineering, University of California, Santa Barbara, Santa Barbara, CA 93106, USA
- Materials Department, University of California, Santa Barbara, Santa Barbara, CA 93106, USA
| | - Erik P. A. M. Bakkers
- Department of Applied Physics, Eindhoven University of Technology, 5600 MB Eindhoven, Netherlands
| | - Liang Fu
- Department of Physics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA
| | - Leo P. Kouwenhoven
- QuTech and Kavli Institute of NanoScience, Delft University of Technology, 2600 GA Delft, Netherlands
- Microsoft Quantum Lab Delft, 2600 GA Delft, Netherlands
| | - Jie Shen
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
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Ottar Klausen K, Sitek A, Erlingsson SI, Manolescu A. Majorana zero modes in nanowires with combined triangular and hexagonal geometry. NANOTECHNOLOGY 2020; 31:354001. [PMID: 32408282 DOI: 10.1088/1361-6528/ab932e] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
The effects of geometry on the hosting of Majorana zero modes are explored in core-shell nanowires with a hexagonal core and a triangular shell, and vice versa. The energy interval separating electronic states localized in the corners from states localized on the sides of the shell is shown to be larger for a triangular nanowire with a hexagonal core, than a triangular one. We build the topological phase diagram for both cases and compare them to earlier work on prismatic nanowires with matching core and shell geometry. We suggest that a dual core nanowire is needed to allow for braiding operations of Majorana zero modes at the nanowire end plane.
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Affiliation(s)
- Kristjan Ottar Klausen
- Department of Engineering, Reykjavik University, Menntavegur 1, IS-101 Reykjavik, Iceland
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8
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Manna S, Wei P, Xie Y, Law KT, Lee PA, Moodera JS. Signature of a pair of Majorana zero modes in superconducting gold surface states. Proc Natl Acad Sci U S A 2020; 117:8775-8782. [PMID: 32253317 PMCID: PMC7183215 DOI: 10.1073/pnas.1919753117] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
Under certain conditions, a fermion in a superconductor can separate in space into two parts known as Majorana zero modes, which are immune to decoherence from local noise sources and are attractive building blocks for quantum computers. Promising experimental progress has been made to demonstrate Majorana zero modes in materials with strong spin-orbit coupling proximity coupled to superconductors. Here we report signatures of Majorana zero modes in a material platform utilizing the surface states of gold. Using scanning tunneling microscope to probe EuS islands grown on top of gold nanowires, we observe two well-separated zero-bias tunneling conductance peaks aligned along the direction of the applied magnetic field, as expected for a pair of Majorana zero modes. This platform has the advantage of having a robust energy scale and the possibility of realizing complex designs using lithographic methods.
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Affiliation(s)
- Sujit Manna
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139
- Department of Physics, Indian Institute of Technology Delhi, 110 016 New Delhi, India
| | - Peng Wei
- Department of Physics and Astronomy, University of California, Riverside, CA 92521;
| | - Yingming Xie
- Department of Physics, Hong Kong University of Science and Technology, Hong Kong
| | - Kam Tuen Law
- Department of Physics, Hong Kong University of Science and Technology, Hong Kong
| | - Patrick A Lee
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139;
| | - Jagadeesh S Moodera
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139;
- Francis Bitter Magnet Laboratory, Massachusetts Institute of Technology, Cambridge, MA 02139
- Plasma Science and Fusion Center, Massachusetts Institute of Technology, Cambridge, MA 02139
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Awoga OA, Cayao J, Black-Schaffer AM. Supercurrent Detection of Topologically Trivial Zero-Energy States in Nanowire Junctions. PHYSICAL REVIEW LETTERS 2019; 123:117001. [PMID: 31573272 DOI: 10.1103/physrevlett.123.117001] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/08/2019] [Indexed: 06/10/2023]
Abstract
We report the emergence of zero-energy states in the trivial phase of a short nanowire junction with a strong spin-orbit coupling and magnetic field, formed by strong coupling between the nanowire and two superconductors. The zero-energy states appear in the junction when the superconductors induce a large energy shift in the nanowire, such that the junction naturally forms a quantum dot, a process that is highly tunable by the superconductor width. Most importantly, we demonstrate that the zero-energy states produce a π shift in the phase-biased supercurrent, which can be used as a simple tool for their unambiguous detection, ruling out any Majorana-like interpretation.
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Affiliation(s)
- Oladunjoye A Awoga
- Department of Physics and Astronomy, Uppsala University, Box 516, S-751 20 Uppsala, Sweden
| | - Jorge Cayao
- Department of Physics and Astronomy, Uppsala University, Box 516, S-751 20 Uppsala, Sweden
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