1
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Reinhardt S, Ascherl T, Costa A, Berger J, Gronin S, Gardner GC, Lindemann T, Manfra MJ, Fabian J, Kochan D, Strunk C, Paradiso N. Link between supercurrent diode and anomalous Josephson effect revealed by gate-controlled interferometry. Nat Commun 2024; 15:4413. [PMID: 38782910 PMCID: PMC11116472 DOI: 10.1038/s41467-024-48741-z] [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: 12/05/2023] [Accepted: 05/07/2024] [Indexed: 05/25/2024] Open
Abstract
In Josephson diodes the asymmetry between positive and negative current branch of the current-phase relation leads to a polarity-dependent critical current and Josephson inductance. The supercurrent nonreciprocity can be described as a consequence of the anomalous Josephson effect -a φ0-shift of the current-phase relation- in multichannel ballistic junctions with strong spin-orbit interaction. In this work, we simultaneously investigate φ0-shift and supercurrent diode efficiency on the same Josephson junction by means of a superconducting quantum interferometer. By electrostatic gating, we reveal a direct link between φ0-shift and diode effect. Our findings show that spin-orbit interaction in combination with a Zeeman field plays an important role in determining the magnetochiral anisotropy and the supercurrent diode effect.
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Affiliation(s)
- S Reinhardt
- Institut für Experimentelle und Angewandte Physik, University of Regensburg, Regensburg, Germany
| | - T Ascherl
- Institut für Experimentelle und Angewandte Physik, University of Regensburg, Regensburg, Germany
| | - A Costa
- Institut für Theoretische Physik, University of Regensburg, Regensburg, Germany
| | - J Berger
- Institut für Experimentelle und Angewandte Physik, University of Regensburg, Regensburg, Germany
| | - S Gronin
- Birck Nanotechnology Center, Purdue University, West Lafayette, IN, USA
| | - G C Gardner
- Birck Nanotechnology Center, Purdue University, West Lafayette, IN, USA
| | - T Lindemann
- Birck Nanotechnology Center, Purdue University, West Lafayette, IN, USA
- Department of Physics and Astronomy, Purdue University, West Lafayette, IN, USA
| | - M J Manfra
- Birck Nanotechnology Center, Purdue University, West Lafayette, IN, USA
- Department of Physics and Astronomy, Purdue University, West Lafayette, IN, USA
- School of Materials Engineering, Purdue University, West Lafayette, IN, USA
- Elmore Family School of Electrical and Computer Engineering, Purdue University, West Lafayette, IN, USA
| | - J Fabian
- Institut für Theoretische Physik, University of Regensburg, Regensburg, Germany
| | - D Kochan
- Institut für Theoretische Physik, University of Regensburg, Regensburg, Germany
- Institute of Physics, Slovak Academy of Sciences, Bratislava, Slovakia
- Center for Quantum Frontiers of Research and Technology (QFort), National Cheng Kung University, Tainan, Taiwan
| | - C Strunk
- Institut für Experimentelle und Angewandte Physik, University of Regensburg, Regensburg, Germany
| | - N Paradiso
- Institut für Experimentelle und Angewandte Physik, University of Regensburg, Regensburg, Germany.
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2
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Coraiola M, Svetogorov AE, Haxell DZ, Sabonis D, Hinderling M, Ten Kate SC, Cheah E, Krizek F, Schott R, Wegscheider W, Cuevas JC, Belzig W, Nichele F. Flux-Tunable Josephson Diode Effect in a Hybrid Four-Terminal Josephson Junction. ACS NANO 2024; 18:9221-9231. [PMID: 38488287 DOI: 10.1021/acsnano.4c01642] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 03/27/2024]
Abstract
We investigate the direction-dependent switching current in a flux-tunable four-terminal Josephson junction defined in an InAs/Al two-dimensional heterostructure. The device exhibits the Josephson diode effect with switching currents that depend on the sign of the bias current. The superconducting diode efficiency, reaching a maximum of |η| ≈ 34%, is widely tunable─both in amplitude and sign─as a function of magnetic fluxes and gate voltages. Our observations are supported by a circuit model of three parallel Josephson junctions with nonsinusoidal current-phase relation. With respect to conventional Josephson interferometers, phase-tunable multiterminal Josephson junctions enable large diode efficiencies in structurally symmetric devices, where local magnetic fluxes generated on the chip break both time-reversal and spatial symmetries. Our work presents an approach for developing Josephson diodes with wide-range tunability that do not rely on exotic materials.
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Affiliation(s)
- Marco Coraiola
- IBM Research Europe─Zurich, 8803 Rüschlikon, Switzerland
| | | | | | | | | | | | - Erik Cheah
- Laboratory for Solid State Physics, ETH Zürich, 8093 Zürich, Switzerland
| | - Filip Krizek
- IBM Research Europe─Zurich, 8803 Rüschlikon, Switzerland
- Laboratory for Solid State Physics, ETH Zürich, 8093 Zürich, Switzerland
- Institute of Physics, Czech Academy of Sciences, 162 00 Prague, Czech Republic
| | - Rüdiger Schott
- Laboratory for Solid State Physics, ETH Zürich, 8093 Zürich, Switzerland
| | - Werner Wegscheider
- Laboratory for Solid State Physics, ETH Zürich, 8093 Zürich, Switzerland
| | - Juan Carlos Cuevas
- Fachbereich Physik, Universität Konstanz, D-78457 Konstanz, Germany
- Departamento de Física Teórica de la Materia Condensada and Condensed Matter Physics Center (IFIMAC), Universidad Autónoma de Madrid, E-28049 Madrid, Spain
| | - Wolfgang Belzig
- Fachbereich Physik, Universität Konstanz, D-78457 Konstanz, Germany
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3
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Matsuo S, Imoto T, Yokoyama T, Sato Y, Lindemann T, Gronin S, Gardner GC, Manfra MJ, Tarucha S. Phase engineering of anomalous Josephson effect derived from Andreev molecules. SCIENCE ADVANCES 2023; 9:eadj3698. [PMID: 38091387 PMCID: PMC10848717 DOI: 10.1126/sciadv.adj3698] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 06/22/2023] [Accepted: 11/14/2023] [Indexed: 02/12/2024]
Abstract
A Josephson junction (JJ) is a key device for developing superconducting circuits, wherein a supercurrent in the JJ is controlled by the phase difference between the two superconducting electrodes. When two JJs sharing one superconducting electrode are coherently coupled and form the Andreev molecules, a supercurrent of one JJ is expected to be nonlocally controlled by the phase difference of another JJ. Here, we evaluate the supercurrent in one of the coupled two JJs as a function of local and nonlocal phase differences. Consequently, the results exhibit that the nonlocal phase control generates a finite supercurrent even when the local phase difference is zero. In addition, an offset of the local phase difference giving the JJ ground state depends on the nonlocal phase difference. These features demonstrate the anomalous Josephson effect realized by the nonlocal phase control. Our results provide a useful concept for engineering superconducting devices such as phase batteries and dissipationless rectifiers.
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Affiliation(s)
- Sadashige Matsuo
- Center for Emergent Matter Science, RIKEN, Wako, Saitama 351-0198, Japan
| | - Takaya Imoto
- Center for Emergent Matter Science, RIKEN, Wako, Saitama 351-0198, Japan
- Department of Applied Physics, Tokyo University of Science, Shinjuku-ku, Tokyo 162-8601, Japan
| | - Tomohiro Yokoyama
- Department of Materials Engineering Science, Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531, Japan
| | - Yosuke Sato
- Center for Emergent Matter Science, RIKEN, Wako, Saitama 351-0198, Japan
| | - Tyler Lindemann
- Birck Nanotechnology Center, Purdue University,, West Lafayette, IN 47907, USA
- Department of Physics and Astronomy, Purdue University, West Lafayette, IN 47907, USA
| | - Sergei Gronin
- Birck Nanotechnology Center, Purdue University,, West Lafayette, IN 47907, USA
| | - Geoffrey C. Gardner
- Birck Nanotechnology Center, Purdue University,, West Lafayette, IN 47907, USA
| | - Michael J. Manfra
- Birck Nanotechnology Center, Purdue University,, West Lafayette, IN 47907, USA
- Department of Physics and Astronomy, Purdue University, West Lafayette, IN 47907, USA
- School of Materials Engineering, Purdue University, West Lafayette, IN 47907, USA
- Elmore Family School of Electrical and Computer Engineering, Purdue University, West Lafayette, IN 47907, USA
| | - Seigo Tarucha
- Center for Emergent Matter Science, RIKEN, Wako, Saitama 351-0198, Japan
- RIKEN Center for Quantum Computing, RIKEN, Wako, Saitama 351-0198, Japan
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4
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Matsuo S, Imoto T, Yokoyama T, Sato Y, Lindemann T, Gronin S, Gardner GC, Nakosai S, Tanaka Y, Manfra MJ, Tarucha S. Phase-dependent Andreev molecules and superconducting gap closing in coherently-coupled Josephson junctions. Nat Commun 2023; 14:8271. [PMID: 38092786 PMCID: PMC10719386 DOI: 10.1038/s41467-023-44111-3] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/02/2023] [Accepted: 11/30/2023] [Indexed: 12/17/2023] Open
Abstract
The Josephson junction (JJ) is an essential element of superconducting (SC) devices for both fundamental and applied physics. The short-range coherent coupling of two adjacent JJs forms Andreev molecule states (AMSs), which provide a new ingredient to engineer exotic SC phenomena such as topological SC states and Andreev qubits. Here we provide tunneling spectroscopy measurements on a device consisting of two electrically controllable planar JJs sharing a single SC electrode. We discover that Andreev spectra in the coupled JJ are highly modulated from those in the single JJs and possess phase-dependent AMS features reproduced in our numerical calculation. Notably, the SC gap closing due to the AMS formation is experimentally observed. Our results help in understanding SC transport derived from the AMS and promoting the use of AMS physics to engineer topological SC states and quantum information devices.
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Affiliation(s)
- Sadashige Matsuo
- Center for Emergent Matter Science, RIKEN, Saitama, 351-0198, Japan.
| | - Takaya Imoto
- Center for Emergent Matter Science, RIKEN, Saitama, 351-0198, Japan
- Department of Applied Physics, Tokyo University of Science, Tokyo, 162-8601, Japan
| | - Tomohiro Yokoyama
- Department of Materials Engineering Science, Osaka University, Osaka, 560-8531, Japan.
| | - Yosuke Sato
- Center for Emergent Matter Science, RIKEN, Saitama, 351-0198, Japan
| | - Tyler Lindemann
- Department of Physics and Astronomy, Purdue University, West Lafayette, Indiana, IN, 47907, USA
- Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana, IN, 47907, USA
| | - Sergei Gronin
- Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana, IN, 47907, USA
| | - Geoffrey C Gardner
- Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana, IN, 47907, USA
| | - Sho Nakosai
- Department of Applied Physics, Nagoya University, Nagoya, 464-8603, Japan
| | - Yukio Tanaka
- Department of Applied Physics, Nagoya University, Nagoya, 464-8603, Japan
| | - Michael J Manfra
- Department of Physics and Astronomy, Purdue University, West Lafayette, Indiana, IN, 47907, USA
- Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana, IN, 47907, USA
- School of Materials Engineering, Purdue University, West Lafayette, Indiana, IN, 47907, USA
- Elmore Family School of Electrical and Computer Engineering, Purdue University, West Lafayette, Indiana, IN, 47907, USA
| | - Seigo Tarucha
- Center for Emergent Matter Science, RIKEN, Saitama, 351-0198, Japan.
- RIKEN Center for Quantum Computing, RIKEN, Saitama, 351-0198, Japan.
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5
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Banerjee A, Geier M, Rahman MA, Thomas C, Wang T, Manfra MJ, Flensberg K, Marcus CM. Phase Asymmetry of Andreev Spectra from Cooper-Pair Momentum. PHYSICAL REVIEW LETTERS 2023; 131:196301. [PMID: 38000437 DOI: 10.1103/physrevlett.131.196301] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/04/2023] [Revised: 08/10/2023] [Accepted: 10/16/2023] [Indexed: 11/26/2023]
Abstract
In analogy to conventional semiconductor diodes, the Josephson diode exhibits superconducting properties that are asymmetric in applied bias. The effect has been investigated in a number of systems recently, and requires a combination of broken time-reversal and inversion symmetries. We demonstrate a dual of the usual Josephson diode effect, a nonreciprocal response of Andreev bound states to a superconducting phase difference across the normal region of a superconductor-normal-superconductor Josephson junction, fabricated using an epitaxial InAs/Al heterostructure. Phase asymmetry of the subgap Andreev spectrum is absent in the absence of in-plane magnetic field and reaches a maximum at 0.15 T applied in the plane of the junction transverse to the current direction. We interpret the phase diode effect in this system as resulting from finite-momentum Cooper pairing due to orbital coupling to the in-plane magnetic field. At higher magnetic fields, we observe a sign reversal of the diode effect that appears together with a reopening of the spectral gap. Within our model, the sign reversal of the diode effect at higher fields is correlated with a topological phase transition that requires Zeeman and spin-orbit interactions in addition to orbital coupling.
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Affiliation(s)
- Abhishek Banerjee
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
| | - Max Geier
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
| | - Md Ahnaf Rahman
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
| | - Candice Thomas
- Department of Physics and Astronomy, and Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907, USA
| | - Tian Wang
- Department of Physics and Astronomy, and Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907, USA
| | - Michael J Manfra
- Department of Physics and Astronomy, and Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907, USA
- School of Materials Engineering, and School of Electrical and Computer Engineering, Purdue University, West Lafayette, Indiana 47907, USA
| | - Karsten Flensberg
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
| | - Charles M Marcus
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
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6
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Haxell DZ, Coraiola M, Sabonis D, Hinderling M, Ten Kate SC, Cheah E, Krizek F, Schott R, Wegscheider W, Belzig W, Cuevas JC, Nichele F. Microwave-induced conductance replicas in hybrid Josephson junctions without Floquet-Andreev states. Nat Commun 2023; 14:6798. [PMID: 37884490 PMCID: PMC10603169 DOI: 10.1038/s41467-023-42357-5] [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: 06/12/2023] [Accepted: 10/09/2023] [Indexed: 10/28/2023] Open
Abstract
Light-matter coupling allows control and engineering of complex quantum states. Here we investigate a hybrid superconducting-semiconducting Josephson junction subject to microwave irradiation by means of tunnelling spectroscopy of the Andreev bound state spectrum and measurements of the current-phase relation. For increasing microwave power, discrete levels in the tunnelling conductance develop into a series of equally spaced replicas, while the current-phase relation changes amplitude and skewness, and develops dips. Quantitative analysis of our results indicates that conductance replicas originate from photon assisted tunnelling of quasiparticles into Andreev bound states through the tunnelling barrier. Despite strong qualitative similarities with proposed signatures of Floquet-Andreev states, our study rules out this scenario. The distortion of the current-phase relation is explained by the interaction of Andreev bound states with microwave photons, including a non-equilibrium Andreev bound state occupation. The techniques outlined here establish a baseline to study light-matter coupling in hybrid nanostructures and distinguish photon assisted tunnelling from Floquet-Andreev states in mesoscopic devices.
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Affiliation(s)
| | - Marco Coraiola
- IBM Research Europe-Zurich, 8803, Rüschlikon, Switzerland
| | | | | | | | - Erik Cheah
- Laboratory for Solid State Physics, ETH Zürich, 8093, Zürich, Switzerland
| | - Filip Krizek
- IBM Research Europe-Zurich, 8803, Rüschlikon, Switzerland
- Laboratory for Solid State Physics, ETH Zürich, 8093, Zürich, Switzerland
| | - Rüdiger Schott
- Laboratory for Solid State Physics, ETH Zürich, 8093, Zürich, Switzerland
| | - Werner Wegscheider
- Laboratory for Solid State Physics, ETH Zürich, 8093, Zürich, Switzerland
| | - Wolfgang Belzig
- Fachbereich Physik, Universität Konstanz, D-78457, Konstanz, Germany
| | - Juan Carlos Cuevas
- Fachbereich Physik, Universität Konstanz, D-78457, Konstanz, Germany
- Departamento de Física Teórica de la Materia Condensada and Condensed Matter Physics Center (IFIMAC), Universidad Autónoma de Madrid, E-28049, Madrid, Spain
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7
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Coraiola M, Haxell DZ, Sabonis D, Weisbrich H, Svetogorov AE, Hinderling M, Ten Kate SC, Cheah E, Krizek F, Schott R, Wegscheider W, Cuevas JC, Belzig W, Nichele F. Phase-engineering the Andreev band structure of a three-terminal Josephson junction. Nat Commun 2023; 14:6784. [PMID: 37880228 PMCID: PMC10600130 DOI: 10.1038/s41467-023-42356-6] [Citation(s) in RCA: 5] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/02/2023] [Accepted: 10/09/2023] [Indexed: 10/27/2023] Open
Abstract
In hybrid Josephson junctions with three or more superconducting terminals coupled to a semiconducting region, Andreev bound states may form unconventional energy band structures, or Andreev matter, which are engineered by controlling superconducting phase differences. Here we report tunnelling spectroscopy measurements of three-terminal Josephson junctions realised in an InAs/Al heterostructure. The three terminals are connected to form two loops, enabling independent control over two phase differences and access to a synthetic Andreev band structure in the two-dimensional phase space. Our results demonstrate a phase-controlled Andreev molecule, originating from two discrete Andreev levels that spatially overlap and hybridise. Signatures of hybridisation are observed in the form of avoided crossings in the spectrum and band structure anisotropies in the phase space, all explained by a numerical model. Future extensions of this work could focus on addressing spin-resolved energy levels, ground state fermion parity transitions and Weyl bands in multiterminal geometries.
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Affiliation(s)
- Marco Coraiola
- IBM Research Europe-Zurich, 8803, Rüschlikon, Switzerland
| | | | | | - Hannes Weisbrich
- Fachbereich Physik, Universität Konstanz, D-78457, Konstanz, Germany
| | | | | | | | - Erik Cheah
- Laboratory for Solid State Physics, ETH Zürich, 8093, Zürich, Switzerland
| | - Filip Krizek
- IBM Research Europe-Zurich, 8803, Rüschlikon, Switzerland
- Laboratory for Solid State Physics, ETH Zürich, 8093, Zürich, Switzerland
- Institute of Physics, Czech Academy of Sciences, 162 00, Prague, Czech Republic
| | - Rüdiger Schott
- Laboratory for Solid State Physics, ETH Zürich, 8093, Zürich, Switzerland
| | - Werner Wegscheider
- Laboratory for Solid State Physics, ETH Zürich, 8093, Zürich, Switzerland
| | - Juan Carlos Cuevas
- Departamento de Física Teórica de la Materia Condensada and Condensed Matter Physics Center (IFIMAC), Universidad Autónoma de Madrid, E-28049, Madrid, Spain
| | - Wolfgang Belzig
- Fachbereich Physik, Universität Konstanz, D-78457, Konstanz, Germany
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8
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Haxell D, Coraiola M, Sabonis D, Hinderling M, ten Kate SC, Cheah E, Krizek F, Schott R, Wegscheider W, Nichele F. Zeeman- and Orbital-Driven Phase Shifts in Planar Josephson Junctions. ACS NANO 2023; 17:18139-18147. [PMID: 37694539 PMCID: PMC10540266 DOI: 10.1021/acsnano.3c04957] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/02/2023] [Accepted: 08/25/2023] [Indexed: 09/12/2023]
Abstract
We perform supercurrent and tunneling spectroscopy measurements on gate-tunable InAs/Al Josephson junctions (JJs) in an in-plane magnetic field and report on phase shifts in the current-phase relation measured with respect to an absolute phase reference. The impact of orbital effects is investigated by studying multiple devices with different superconducting lead sizes. At low fields, we observe gate-dependent phase shifts of up to φ0 = 0.5π, which are consistent with a Zeeman field coupling to highly transmissive Andreev bound states via Rashba spin-orbit interaction. A distinct phase shift emerges at larger fields, concomitant with a switching current minimum and the closing and reopening of the superconducting gap. These signatures of an induced phase transition, which might resemble a topological transition, scale with the superconducting lead size, demonstrating the crucial role of orbital effects. Our results elucidate the interplay of Zeeman, spin-orbit, and orbital effects in InAs/Al JJs, giving improved understanding of phase transitions in hybrid JJs and their applications in quantum computing and superconducting electronics.
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Affiliation(s)
| | - Marco Coraiola
- IBM
Research Europe−Zurich, 8803 Rüschlikon, Switzerland
| | | | | | | | - Erik Cheah
- Laboratory
for Solid State Physics, ETH Zürich, 8093 Zürich, Switzerland
| | - Filip Krizek
- IBM
Research Europe−Zurich, 8803 Rüschlikon, Switzerland
- Laboratory
for Solid State Physics, ETH Zürich, 8093 Zürich, Switzerland
- Institute
of Physics, Czech Academy of Sciences, 162 00 Prague, Czech Republic
| | - Rüdiger Schott
- Laboratory
for Solid State Physics, ETH Zürich, 8093 Zürich, Switzerland
| | - Werner Wegscheider
- Laboratory
for Solid State Physics, ETH Zürich, 8093 Zürich, Switzerland
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9
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Haxell D, Coraiola M, Hinderling M, ten Kate SC, Sabonis D, Svetogorov AE, Belzig W, Cheah E, Krizek F, Schott R, Wegscheider W, Nichele F. Demonstration of the Nonlocal Josephson Effect in Andreev Molecules. NANO LETTERS 2023; 23:7532-7538. [PMID: 37552598 PMCID: PMC10450812 DOI: 10.1021/acs.nanolett.3c02066] [Citation(s) in RCA: 5] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/02/2023] [Revised: 07/24/2023] [Indexed: 08/10/2023]
Abstract
We perform switching current measurements of planar Josephson junctions (JJs) coupled by a common superconducting electrode with independent control over the two superconducting phase differences. We observe an anomalous phase shift in the current-phase relation of a JJ as a function of gate voltage or phase difference in the second JJ. This demonstrates the nonlocal Josephson effect, and the implementation of a φ0-junction which is tunable both electrostatically and magnetically. The anomalous phase shift is larger for shorter distances between the JJs and vanishes for distances much longer than the superconducting coherence length. Results are consistent with the hybridization of Andreev bound states, leading to the formation of an Andreev molecule. Our devices constitute a realization of a tunable superconducting phase source and could enable new coupling schemes for hybrid quantum devices.
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Affiliation(s)
- Daniel
Z. Haxell
- IBM
Research Europe−Zurich, Säumerstrasse 4, 8803 Rüschlikon, Switzerland
| | - Marco Coraiola
- IBM
Research Europe−Zurich, Säumerstrasse 4, 8803 Rüschlikon, Switzerland
| | - Manuel Hinderling
- IBM
Research Europe−Zurich, Säumerstrasse 4, 8803 Rüschlikon, Switzerland
| | | | - Deividas Sabonis
- IBM
Research Europe−Zurich, Säumerstrasse 4, 8803 Rüschlikon, Switzerland
| | | | - Wolfgang Belzig
- Fachbereich
Physik, Universität Konstanz, D-78457 Konstanz, Germany
| | - Erik Cheah
- Solid
State Physics Laboratory, ETH Zürich, 8093 Zürich, Switzerland
| | - Filip Krizek
- Fachbereich
Physik, Universität Konstanz, D-78457 Konstanz, Germany
- Solid
State Physics Laboratory, ETH Zürich, 8093 Zürich, Switzerland
| | - Rüdiger Schott
- Solid
State Physics Laboratory, ETH Zürich, 8093 Zürich, Switzerland
| | | | - Fabrizio Nichele
- IBM
Research Europe−Zurich, Säumerstrasse 4, 8803 Rüschlikon, Switzerland
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10
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Babich I, Kudriashov A, Baranov D, Stolyarov VS. Limitations of the Current-Phase Relation Measurements by an Asymmetric dc-SQUID. NANO LETTERS 2023. [PMID: 37428644 DOI: 10.1021/acs.nanolett.3c01970] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 07/12/2023]
Abstract
Exotic quantum transport phenomena established in Josephson junctions (JJs) are reflected by a nonsinusoidal current-phase relation (CPR). The solidified approach to measuring the CPR is via an asymmetric dc-SQUID with a reference JJ that has a high critical current. We probed this method by measuring CPRs of hybrid JJs based on the 3D topological insulator (TI) Bi2Te2Se with a nanobridge acting as a reference JJ. We captured both highly skewed and sinusoidal critical current oscillations within single devices which contradict the uniqueness of the CPR. This implies that the widely used method provides inaccurate CPR measurement and leads to misinterpretation. It was shown that the accuracy of the CPR measurement is mediated by the asymmetry in derivatives of the CPRs but not in critical currents, as was previously thought. Finally, we provided considerations for an accurate CPR measurement via the most commonly used reference JJs.
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Affiliation(s)
- Ian Babich
- Advanced Mesoscience and Nanotechnology Centre, Moscow Institute of Physics and Technology, 141700, Dolgoprudny, Russia
| | - Andrei Kudriashov
- Advanced Mesoscience and Nanotechnology Centre, Moscow Institute of Physics and Technology, 141700, Dolgoprudny, Russia
| | - Denis Baranov
- Advanced Mesoscience and Nanotechnology Centre, Moscow Institute of Physics and Technology, 141700, Dolgoprudny, Russia
| | - Vasily S Stolyarov
- Advanced Mesoscience and Nanotechnology Centre, Moscow Institute of Physics and Technology, 141700, Dolgoprudny, Russia
- National University of Science and Technology MISIS, 119049 Moscow, Russia
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11
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Endres M, Kononov A, Arachchige HS, Yan J, Mandrus D, Watanabe K, Taniguchi T, Schönenberger C. Current-Phase Relation of a WTe 2 Josephson Junction. NANO LETTERS 2023; 23:4654-4659. [PMID: 37155691 DOI: 10.1021/acs.nanolett.3c01416] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/10/2023]
Abstract
When a topological insulator is incorporated into a Josephson junction, the system is predicted to reveal the fractional Josephson effect with a 4π-periodic current-phase relation. Here, we report the measurement of a 4π-periodic switching current through an asymmetric SQUID, formed by the higher-order topological insulator WTe2. Contrary to the established opinion, we show that a high asymmetry in critical current and negligible loop inductance are not sufficient by themselves to reliably measure the current-phase relation. Instead, we find that our measurement is heavily influenced by additional inductances originating from the self-formed PdTex inside the junction. We therefore develop a method to numerically recover the current-phase relation of the system and find the 1.5 μm long junction to be best described in the short ballistic limit. Our results highlight the complexity of subtle inductance effects that can give rise to misleading topological signatures in transport measurements.
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Affiliation(s)
- Martin Endres
- Department of Physics, University of Basel, Klingelbergstrasse 82, 4056 Basel, Switzerland
| | - Artem Kononov
- Department of Physics, University of Basel, Klingelbergstrasse 82, 4056 Basel, Switzerland
| | - Hasitha Suriya Arachchige
- Department of Physics and Astronomy, University of Tennessee, Knoxville, Tennessee 37996, United States
| | - Jiaqiang Yan
- Department of Physics and Astronomy, University of Tennessee, Knoxville, Tennessee 37996, United States
- Material Science and Technology Division, Oak Ridge Laboratory, Oak Ridge, Tennessee 37831, United States
| | - David Mandrus
- Department of Physics and Astronomy, University of Tennessee, Knoxville, Tennessee 37996, United States
- Material Science and Technology Division, Oak Ridge Laboratory, Oak Ridge, Tennessee 37831, United States
- Department of Materials Science and Engineering, University of Tennessee, Knoxville, Tennessee 37996, United States
| | - Kenji Watanabe
- Research Center for Functional Materials, National Institute for Materials 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
| | - Christian Schönenberger
- Department of Physics, University of Basel, Klingelbergstrasse 82, 4056 Basel, Switzerland
- Swiss Nanoscience Institute, University of Basel, Klingelbergstrasse 82, 4056 Basel, Switzerland
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12
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Banerjee A, Lesser O, Rahman MA, Thomas C, Wang T, Manfra MJ, Berg E, Oreg Y, Stern A, Marcus CM. Local and Nonlocal Transport Spectroscopy in Planar Josephson Junctions. PHYSICAL REVIEW LETTERS 2023; 130:096202. [PMID: 36930915 DOI: 10.1103/physrevlett.130.096202] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/19/2022] [Accepted: 01/11/2023] [Indexed: 06/18/2023]
Abstract
We report simultaneously acquired local and nonlocal transport spectroscopy in a phase-biased planar Josephson junction based on an epitaxial InAs-Al hybrid two-dimensional heterostructure. Quantum point contacts at the junction ends allow measurement of the 2×2 matrix of local and nonlocal tunneling conductances as a function of magnetic field along the junction, phase difference across the junction, and carrier density. A closing and reopening of a gap was observed in both the local and nonlocal tunneling spectra as a function of magnetic field. For particular tunings of junction density, gap reopenings were accompanied by zero-bias conductance peaks (ZBCPs) in local conductances. End-to-end correlation of gap reopening was strong, while correlation of local ZBCPs was weak. A model of the device, with disorder treated phenomenologically, shows comparable conductance matrix behavior associated with a topological phase transition. Phase dependence helps distinguish possible origins of the ZBCPs.
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Affiliation(s)
- A Banerjee
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
| | - O Lesser
- Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot, Israel 76100
| | - M A Rahman
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
| | - C Thomas
- Department of Physics and Astronomy, and Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907 USA
| | - T Wang
- Department of Physics and Astronomy, and Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907 USA
| | - M J Manfra
- Department of Physics and Astronomy, and Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907 USA
- School of Materials Engineering, and School of Electrical and Computer Engineering, Purdue University, West Lafayette, Indiana 47907 USA
| | - E Berg
- Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot, Israel 76100
| | - Y Oreg
- Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot, Israel 76100
| | - Ady Stern
- Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot, Israel 76100
| | - C M Marcus
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
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13
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Haxell DZ, Cheah E, Křížek F, Schott R, Ritter MF, Hinderling M, Belzig W, Bruder C, Wegscheider W, Riel H, Nichele F. Measurements of Phase Dynamics in Planar Josephson Junctions and SQUIDs. PHYSICAL REVIEW LETTERS 2023; 130:087002. [PMID: 36898094 DOI: 10.1103/physrevlett.130.087002] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/12/2022] [Revised: 09/15/2022] [Accepted: 01/19/2023] [Indexed: 06/18/2023]
Abstract
We experimentally investigate the stochastic phase dynamics of planar Josephson junctions (JJs) and superconducting quantum interference devices (SQUIDs) defined in epitaxial InAs/Al heterostructures, and characterized by a large ratio of Josephson energy to charging energy. We observe a crossover from a regime of macroscopic quantum tunneling to one of phase diffusion as a function of temperature, where the transition temperature T^{*} is gate-tunable. The switching probability distributions are shown to be consistent with a small shunt capacitance and moderate damping, resulting in a switching current which is a small fraction of the critical current. Phase locking between two JJs leads to a difference in switching current between that of a JJ measured in isolation and that of the same JJ measured in an asymmetric SQUID loop. In the case of the loop, T^{*} is also tuned by a magnetic flux.
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Affiliation(s)
- D Z Haxell
- IBM Research Europe-Zurich, Säumerstrasse 4, 8803 Rüschlikon, Switzerland
| | - E Cheah
- Solid State Physics Laboratory, ETH Zurich, 8093 Zurich, Switzerland
| | - F Křížek
- IBM Research Europe-Zurich, Säumerstrasse 4, 8803 Rüschlikon, Switzerland
- Solid State Physics Laboratory, ETH Zurich, 8093 Zurich, Switzerland
| | - R Schott
- Solid State Physics Laboratory, ETH Zurich, 8093 Zurich, Switzerland
| | - M F Ritter
- IBM Research Europe-Zurich, Säumerstrasse 4, 8803 Rüschlikon, Switzerland
| | - M Hinderling
- IBM Research Europe-Zurich, Säumerstrasse 4, 8803 Rüschlikon, Switzerland
| | - W Belzig
- Fachbereich Physik, Universität Konstanz, D-78457 Konstanz, Germany
| | - C Bruder
- Department of Physics, University of Basel, Klingelbergstrasse 82, CH-4056 Basel, Switzerland
| | - W Wegscheider
- Solid State Physics Laboratory, ETH Zurich, 8093 Zurich, Switzerland
| | - H Riel
- IBM Research Europe-Zurich, Säumerstrasse 4, 8803 Rüschlikon, Switzerland
| | - F Nichele
- IBM Research Europe-Zurich, Säumerstrasse 4, 8803 Rüschlikon, Switzerland
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14
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Souto RS, Leijnse M, Schrade C. Josephson Diode Effect in Supercurrent Interferometers. PHYSICAL REVIEW LETTERS 2022; 129:267702. [PMID: 36608204 DOI: 10.1103/physrevlett.129.267702] [Citation(s) in RCA: 19] [Impact Index Per Article: 9.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/15/2022] [Revised: 10/10/2022] [Accepted: 12/02/2022] [Indexed: 06/17/2023]
Abstract
A Josephson diode is a nonreciprocal circuit element that supports a larger dissipationless supercurrent in one direction than in the other. In this Letter, we propose a class of Josephson diodes based on supercurrent interferometers composed of Andreev bound state Josephson junctions or interacting quantum dot Josephson junctions, which are not diodes themselves but possess nonsinusoidal current-phase relations. We show that such Josephson diodes have several important advantages, like being electrically tunable and requiring only time-reversal breaking by a magnetic flux. We also show that our diodes have a characteristic ac response, revealed by the Shapiro steps. Even the simplest realization of our Josephson diode paradigm that relies on only two junctions can achieve efficiencies of up to ∼40% and, interestingly, far greater efficiencies are achievable by concatenating interferometer loops. We hope that our Letter will stimulate the search for highly tunable Josephson diode effects in Josephson devices based semiconductor-superconductor hybrids, 2d materials, and topological insulators, where nonsinusoidal current-phase relations were recently observed.
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Affiliation(s)
- Rubén Seoane Souto
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark
- Division of Solid State Physics and NanoLund, Lund University, S-22100 Lund, Sweden
| | - Martin Leijnse
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark
- Division of Solid State Physics and NanoLund, Lund University, S-22100 Lund, Sweden
| | - Constantin Schrade
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark
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15
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Moehle C, Rout PK, Jainandunsing NA, Kuiri D, Ke CT, Xiao D, Thomas C, Manfra MJ, Nowak MP, Goswami S. Controlling Andreev Bound States with the Magnetic Vector Potential. NANO LETTERS 2022; 22:8601-8607. [PMID: 36279222 PMCID: PMC9650727 DOI: 10.1021/acs.nanolett.2c03130] [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: 08/07/2022] [Revised: 10/16/2022] [Indexed: 06/16/2023]
Abstract
Tunneling spectroscopy measurements are often used to probe the energy spectrum of Andreev bound states (ABSs) in semiconductor-superconductor hybrids. Recently, this spectroscopy technique has been incorporated into planar Josephson junctions (JJs) formed in two-dimensional electron gases, a potential platform to engineer phase-controlled topological superconductivity. Here, we perform ABS spectroscopy at the two ends of planar JJs and study the effects of the magnetic vector potential on the ABS spectrum. We show that the local superconducting phase difference arising from the vector potential is equal in magnitude and opposite in sign at the two ends, in agreement with a model that assumes localized ABSs near the tunnel barriers. Complemented with microscopic simulations, our experiments demonstrate that the local phase difference can be used to estimate the relative position of localized ABSs separated by a few hundred nanometers.
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Affiliation(s)
- Christian
M. Moehle
- QuTech
and Kavli Institute of Nanoscience, Delft
University of Technology, 2600 GADelft, The Netherlands
| | - Prasanna K. Rout
- QuTech
and Kavli Institute of Nanoscience, Delft
University of Technology, 2600 GADelft, The Netherlands
| | - Nayan A. Jainandunsing
- QuTech
and Kavli Institute of Nanoscience, Delft
University of Technology, 2600 GADelft, The Netherlands
| | - Dibyendu Kuiri
- Academic
Centre for Materials and Nanotechnology, AGH University of Science and Technology, 30-059Krakow, Poland
| | - Chung Ting Ke
- QuTech
and Kavli Institute of Nanoscience, Delft
University of Technology, 2600 GADelft, The Netherlands
| | - Di Xiao
- Department
of Physics and Astronomy, Purdue University, West Lafayette, Indiana47907, United States
| | - Candice Thomas
- Department
of Physics and Astronomy, Purdue University, West Lafayette, Indiana47907, United States
| | - Michael J. Manfra
- Department
of Physics and Astronomy, Purdue University, West Lafayette, Indiana47907, United States
- Elmore
School of Electrical and Computer Engineering, Purdue University, West Lafayette, Indiana47907, United States
- School
of Materials Engineering, Purdue University, West Lafayette, Indiana47907, United States
- Microsoft
Quantum Lab West Lafayette, West
Lafayette, Indiana47907, United States
| | - Michał P. Nowak
- Academic
Centre for Materials and Nanotechnology, AGH University of Science and Technology, 30-059Krakow, Poland
| | - Srijit Goswami
- QuTech
and Kavli Institute of Nanoscience, Delft
University of Technology, 2600 GADelft, The Netherlands
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16
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Portolés E, Iwakiri S, Zheng G, Rickhaus P, Taniguchi T, Watanabe K, Ihn T, Ensslin K, de Vries FK. A tunable monolithic SQUID in twisted bilayer graphene. NATURE NANOTECHNOLOGY 2022; 17:1159-1164. [PMID: 36280761 DOI: 10.1038/s41565-022-01222-0] [Citation(s) in RCA: 9] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/11/2022] [Accepted: 09/05/2022] [Indexed: 06/16/2023]
Abstract
Magic-angle twisted bilayer graphene (MATBG) hosts a number of correlated states of matter that can be tuned by electrostatic doping1-4. Transport5,6 and scanning-probe7-9 experiments have shown evidence for band, correlated and Chern insulators along with superconductivity. This variety of in situ tunable states has allowed for the realization of tunable Josephson junctions10-12. However, although phase-coherent phenomena have been measured10-12, no control of the phase difference of the superconducting condensates has been demonstrated so far. Here we build on previous gate-defined junction realizations and form a superconducting quantum interference device13 (SQUID) in MATBG, where the superconducting phase difference is controlled through the magnetic field. We observe magneto-oscillations of the critical current, demonstrating long-range coherence of superconducting charge carriers with an effective charge of 2e. We tune to both asymmetric and symmetric SQUID configurations by electrostatically controlling the critical currents through the junctions. This tunability allows us to study the inductances in the device, finding values of up to 2 μH. Furthermore, we directly probe the current-phase relation of one of the junctions of the device. Our results show that complex devices in MATBG can be realized and used to reveal the properties of the material. We envision our findings, together with the established history of applications SQUIDs have14-16, will foster the development of a wide range of devices such as phase-slip junctions17 or high kinetic inductance detectors18.
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Affiliation(s)
- Elías Portolés
- Solid State Physics Laboratory, ETH Zurich, Zurich, Switzerland.
| | - Shuichi Iwakiri
- Solid State Physics Laboratory, ETH Zurich, Zurich, Switzerland
| | - Giulia Zheng
- Solid State Physics Laboratory, ETH Zurich, Zurich, Switzerland
| | - Peter Rickhaus
- Solid State Physics Laboratory, ETH Zurich, Zurich, Switzerland
| | - Takashi Taniguchi
- International Center for Materials Nanoarchitectonics, National Institute for Materials Science, Tsukuba, Japan
| | - Kenji Watanabe
- Research Center for Functional Materials, National Institute for Materials Science, Tsukuba, Japan
| | - Thomas Ihn
- Solid State Physics Laboratory, ETH Zurich, Zurich, Switzerland
- Quantum Center, ETH Zurich, Zurich, Switzerland
| | - Klaus Ensslin
- Solid State Physics Laboratory, ETH Zurich, Zurich, Switzerland.
- Quantum Center, ETH Zurich, Zurich, Switzerland.
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17
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Park S, Lee W, Jang S, Choi YB, Park J, Jung W, Watanabe K, Taniguchi T, Cho GY, Lee GH. Steady Floquet-Andreev states in graphene Josephson junctions. Nature 2022; 603:421-426. [PMID: 35296842 DOI: 10.1038/s41586-021-04364-8] [Citation(s) in RCA: 8] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/30/2021] [Accepted: 12/16/2021] [Indexed: 01/12/2023]
Abstract
Engineering quantum states through light-matter interaction has created a paradigm in condensed-matter physics. A representative example is the Floquet-Bloch state, which is generated by time-periodically driving the Bloch wavefunctions in crystals. Previous attempts to realize such states in condensed-matter systems have been limited by the transient nature of the Floquet states produced by optical pulses1-3, which masks the universal properties of non-equilibrium physics. Here we report the generation of steady Floquet-Andreev states in graphene Josephson junctions by continuous microwave application and direct measurement of their spectra by superconducting tunnelling spectroscopy. We present quantitative analysis of the spectral characteristics of the Floquet-Andreev states while varying the phase difference of the superconductors, the temperature, the microwave frequency and the power. The oscillations of the Floquet-Andreev-state spectrum with phase difference agreed with our theoretical calculations. Moreover, we confirmed the steady nature of the Floquet-Andreev states by establishing a sum rule of tunnelling conductance4, and analysed the spectral density of Floquet states depending on Floquet interaction strength. This study provides a basis for understanding and engineering non-equilibrium quantum states in nanodevices.
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Affiliation(s)
- Sein Park
- Department of Physics, Pohang University of Science and Technology, Pohang, Republic of Korea
| | - Wonjun Lee
- Department of Physics, Pohang University of Science and Technology, Pohang, Republic of Korea.,Center for Artificial Low Dimensional Electronic Systems, Institute for Basic Science (IBS), Pohang, Republic of Korea
| | - Seong Jang
- Department of Physics, Pohang University of Science and Technology, Pohang, Republic of Korea
| | - Yong-Bin Choi
- Department of Physics, Pohang University of Science and Technology, Pohang, Republic of Korea
| | - Jinho Park
- Department of Physics, Pohang University of Science and Technology, Pohang, Republic of Korea
| | - Woochan Jung
- Department of Physics, Pohang University of Science and Technology, Pohang, Republic of Korea
| | - Kenji Watanabe
- Research Center for Functional Materials, National Institute for Materials Science, Tsukuba, Japan
| | - Takashi Taniguchi
- International Center for Materials Nanoarchitectonics, National Institute for Materials Science, Tsukuba, Japan
| | - Gil Young Cho
- Department of Physics, Pohang University of Science and Technology, Pohang, Republic of Korea. .,Center for Artificial Low Dimensional Electronic Systems, Institute for Basic Science (IBS), Pohang, Republic of Korea. .,Asia Pacific Center for Theoretical Physics, Pohang, Republic of Korea.
| | - Gil-Ho Lee
- Department of Physics, Pohang University of Science and Technology, Pohang, Republic of Korea. .,Asia Pacific Center for Theoretical Physics, Pohang, Republic of Korea.
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