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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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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3
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Debbarma R, Tsintzis A, Aspegren M, Souto RS, Lehmann S, Dick K, Leijnse M, Thelander C. Josephson Junction π-0 Transition Induced by Orbital Hybridization in a Double Quantum Dot. PHYSICAL REVIEW LETTERS 2023; 131:256001. [PMID: 38181374 DOI: 10.1103/physrevlett.131.256001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/06/2023] [Accepted: 11/20/2023] [Indexed: 01/07/2024]
Abstract
In this Letter, we manipulate the phase shift of a Josephson junction using a parallel double quantum dot (QD). By employing a superconducting quantum interference device, we determine how orbital hybridization and detuning affect the current-phase relation in the Coulomb blockade regime. For weak hybridization between the QDs, we find π junction characteristics if at least one QD has an unpaired electron. Notably the critical current is higher when both QDs have an odd electron occupation. By increasing the inter-QD hybridization the critical current is reduced, until eventually a π-0 transition occurs. A similar transition appears when detuning the QD levels at finite hybridization. Based on a zero-bandwidth model, we argue that both cases of phase-shift transitions can be understood considering an increased weight of states with a double occupancy in the ground state and with the Cooper pair transport dominated by local Andreev reflection.
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Affiliation(s)
- Rousan Debbarma
- Division of Solid State Physics and NanoLund, Lund University, S-221 00 Lund, Sweden
| | - Athanasios Tsintzis
- Division of Solid State Physics and NanoLund, Lund University, S-221 00 Lund, Sweden
| | - Markus Aspegren
- Division of Solid State Physics and NanoLund, Lund University, S-221 00 Lund, Sweden
| | - Rubén Seoane Souto
- Departamento de Física Teórica de la Materia Condensada, Condensed Matter Physics Center (IFIMAC) and Instituto Nicolás Cabrera, Universidad Autónoma de Madrid, 28049 Madrid, Spain
- Instituto de Ciencia de Materiales de Madrid (ICMM), Consejo Superior de Investigaciones Científicas (CSIC), Sor Juana Inés de la Cruz 3, 28049 Madrid, Spain
| | - Sebastian Lehmann
- Division of Solid State Physics and NanoLund, Lund University, S-221 00 Lund, Sweden
| | - Kimberly Dick
- Division of Solid State Physics and NanoLund, Lund University, S-221 00 Lund, Sweden
- Center for Analysis and Synthesis, Lund University, S-221 00 Lund, Sweden
| | - Martin Leijnse
- Division of Solid State Physics and NanoLund, Lund University, S-221 00 Lund, Sweden
| | - Claes Thelander
- Division of Solid State Physics and NanoLund, Lund University, S-221 00 Lund, Sweden
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4
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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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5
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Senapati T, Karnad AK, Senapati K. Phase biasing of a Josephson junction using Rashba-Edelstein effect. Nat Commun 2023; 14:7415. [PMID: 37973986 PMCID: PMC10654735 DOI: 10.1038/s41467-023-42987-9] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/22/2023] [Accepted: 10/26/2023] [Indexed: 11/19/2023] Open
Abstract
A charge-current-induced shift in the spin-locked Fermi surface leads to a non-equilibrium spin density at a Rashba interface, commonly known as the Rashba-Edelstein effect. Since this is an intrinsically interfacial property, direct detection of the spin moment is difficult. Here we demonstrate that a planar Josephson Junction, realized by placing two closely spaced superconducting electrodes over a Rashba interface, allows for a direct detection of the spin moment as an additional phase in the junction. Asymmetric Fraunhofer patterns obtained for Nb-(Pt/Cu)-Nb nano-junctions, due to the locking of Rashba-Edelstein spin moment to the flux quantum in the junction, provide clear signatures of this effect. This simple experiment offers a fresh perspective on direct detection of spin polarization induced by various spin-orbit effects. In addition, this platform also offers a magnetic-field-controlled phase biasing mechanism in conjunction with the Rashba-Edelstein spin-orbit effect for superconducting quantum circuits.
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Affiliation(s)
- Tapas Senapati
- School of Physical Sciences, National Institute of Science Education and Research (NISER) Bhubaneswar, An OCC of Homi Bhabha National Institute, Jatni, 752050, Odisha, India
| | - Ashwin Kumar Karnad
- Department of Physics, Birla Institute of Technology & Science Pilani - K K Birla Goa Campus, Zuarinagar, 403726, Goa, India
| | - Kartik Senapati
- School of Physical Sciences, National Institute of Science Education and Research (NISER) Bhubaneswar, An OCC of Homi Bhabha National Institute, Jatni, 752050, Odisha, India.
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6
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Mojaveri B, Jafarzadeh Bahrbeig R, Fasihi MA, Babanzadeh S. Enhancing the direct charging performance of an open quantum battery by adjusting its velocity. Sci Rep 2023; 13:19827. [PMID: 37964073 PMCID: PMC10645758 DOI: 10.1038/s41598-023-47193-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/29/2023] [Accepted: 11/10/2023] [Indexed: 11/16/2023] Open
Abstract
The performance of open quantum batteries (QBs) is severely limited by decoherence due to the interaction with the surrounding environment. So, protecting the charging processes against decoherence is of great importance for realizing QBs. In this work we address this issue by developing a charging process of a qubit-based open QB composed of a qubit-battery and a qubit-charger, where each qubit moves inside an independent cavity reservoir. Our results show that, in both the Markovian and non-Markovian dynamics, the charging characteristics, including the charging energy, efficiency and ergotropy, regularly increase with increasing the speed of charger and battery qubits. Interestingly, when the charger and battery move with higher velocities, the initial energy of the charger is completely transferred to the battery in the Markovian dynamics. In this situation, it is possible to extract the total stored energy as work for a long time. Our findings show that open moving-qubit systems are robust and reliable QBs, thus making them a promising candidate for experimental implementations.
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Affiliation(s)
- B Mojaveri
- Department of Physics, Azarbaijan Shahid Madani University, PO Box 51745-406, Tabriz, Iran.
| | - R Jafarzadeh Bahrbeig
- Department of Physics, Azarbaijan Shahid Madani University, PO Box 51745-406, Tabriz, Iran
| | - M A Fasihi
- Department of Physics, Azarbaijan Shahid Madani University, PO Box 51745-406, Tabriz, Iran
| | - S Babanzadeh
- Department of Physics, Azarbaijan Shahid Madani University, PO Box 51745-406, Tabriz, Iran
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7
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Costa A, Baumgartner C, Reinhardt S, Berger J, Gronin S, Gardner GC, Lindemann T, Manfra MJ, Fabian J, Kochan D, Paradiso N, Strunk C. Sign reversal of the Josephson inductance magnetochiral anisotropy and 0-π-like transitions in supercurrent diodes. NATURE NANOTECHNOLOGY 2023; 18:1266-1272. [PMID: 37430040 DOI: 10.1038/s41565-023-01451-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/29/2022] [Accepted: 06/09/2023] [Indexed: 07/12/2023]
Abstract
The recent discovery of the intrinsic supercurrent diode effect, and its prompt observation in a rich variety of systems, has shown that non-reciprocal supercurrents naturally emerge when both space-inversion and time-inversion symmetries are broken. In Josephson junctions, non-reciprocal supercurrent can be conveniently described in terms of spin-split Andreev states. Here we demonstrate a sign reversal of the Josephson inductance magnetochiral anisotropy, a manifestation of the supercurrent diode effect. The asymmetry of the Josephson inductance as a function of the supercurrent allows us to probe the current-phase relation near equilibrium, and to probe jumps in the junction ground state. Using a minimal theoretical model, we can then link the sign reversal of the inductance magnetochiral anisotropy to the so-called 0-π-like transition, a predicted but still elusive feature of multichannel junctions. Our results demonstrate the potential of inductance measurements as sensitive probes of the fundamental properties of unconventional Josephson junctions.
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Affiliation(s)
- A Costa
- Institut für Theoretische Physik, University of Regensburg, Regensburg, Germany
| | - C Baumgartner
- Institut für Experimentelle und Angewandte Physik, University of Regensburg, Regensburg, Germany
| | - S Reinhardt
- Institut für Experimentelle und Angewandte 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
| | - N Paradiso
- Institut für Experimentelle und Angewandte Physik, University of Regensburg, Regensburg, Germany.
| | - C Strunk
- Institut für Experimentelle und Angewandte Physik, University of Regensburg, Regensburg, Germany
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8
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Bargerbos A, Pita-Vidal M, Žitko R, Splitthoff LJ, Grünhaupt L, Wesdorp JJ, Liu Y, Kouwenhoven LP, Aguado R, Andersen CK, Kou A, van Heck B. Spectroscopy of Spin-Split Andreev Levels in a Quantum Dot with Superconducting Leads. PHYSICAL REVIEW LETTERS 2023; 131:097001. [PMID: 37721843 DOI: 10.1103/physrevlett.131.097001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/28/2022] [Accepted: 07/27/2023] [Indexed: 09/20/2023]
Abstract
We use a hybrid superconductor-semiconductor transmon device to perform spectroscopy of a quantum dot Josephson junction tuned to be in a spin-1/2 ground state with an unpaired quasiparticle. Because of spin-orbit coupling, we resolve two flux-sensitive branches in the transmon spectrum, depending on the spin of the quasiparticle. A finite magnetic field shifts the two branches in energy, favoring one spin state and resulting in the anomalous Josephson effect. We demonstrate the excitation of the direct spin-flip transition using all-electrical control. Manipulation and control of the spin-flip transition enable the future implementation of charging energy protected Andreev spin qubits.
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Affiliation(s)
- Arno Bargerbos
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology, 2600 GA Delft, Netherlands
| | - Marta Pita-Vidal
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology, 2600 GA Delft, Netherlands
| | - Rok Žitko
- Jožef Stefan Institute, Jamova 39, SI-1000 Ljubljana, Slovenia
- Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, SI-1000 Ljubljana, Slovenia
| | - Lukas J Splitthoff
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology, 2600 GA Delft, Netherlands
| | - Lukas Grünhaupt
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology, 2600 GA Delft, Netherlands
| | - Jaap J Wesdorp
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology, 2600 GA Delft, Netherlands
| | - Yu Liu
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark
| | - Leo P Kouwenhoven
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology, 2600 GA Delft, Netherlands
| | - Ramón Aguado
- Instituto de Ciencia de Materiales de Madrid (ICMM), Consejo Superior de Investigaciones Cientificas (CSIC), Sor Juana Ines de la Cruz 3, 28049 Madrid, Spain
| | | | - Angela Kou
- Department of Physics and Frederick Seitz Materials Research Laboratory, University of Illinois Urbana-Champaign, Urbana, Illinois 61801, USA
| | - Bernard van Heck
- Leiden Institute of Physics, Leiden University, Niels Bohrweg 2, 2333 CA Leiden, Netherlands
- Dipartimento di Fisica, Università di Roma "La Sapienza", P.le Aldo Moro 5, 00185 Roma, Italy
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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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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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11
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Hadipour M, Haseli S, Dolatkhah H, Rashidi M. Study the charging process of moving quantum batteries inside cavity. Sci Rep 2023; 13:10672. [PMID: 37393354 DOI: 10.1038/s41598-023-37800-y] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/19/2023] [Accepted: 06/28/2023] [Indexed: 07/03/2023] Open
Abstract
In quantum mechanics, quantum batteries are devices that can store energy by utilizing the principles of quantum mechanics. While quantum batteries has been investigated largely theoretical, recent research indicates that it may be possible to implement such a device using existing technologies. The environment plays an important role in the charging of quantum batteries. If a strong coupling exists between the environment and the battery, then battery can be charged properly. It has also been demonstrated that quantum battery can be charged even in weak coupling regime just by choosing a suitable initial state for battery and charger. In this study, we investigate the charging process of open quantum batteries mediated by a common dissipative environment. We will consider a wireless-like charging scenario, where there is no external power and direct interaction between charger and battery. Moreover, we consider the case in which the battery and charger move inside the environment with a particular speed. Our results demonstrate that the movement of the quantum battery inside the environment has a negative effect on the performance of the quantum batteries during the charging process. It is also shown that the non-Markovian environment has a positive effect on improving battery performance.
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Affiliation(s)
- Maryam Hadipour
- Faculty of Physics, Urmia University of Technology, Urmia, Iran
| | - Soroush Haseli
- Faculty of Physics, Urmia University of Technology, Urmia, Iran.
- School of Physics, Institute for Research in Fundamental Sciences (IPM), P.O. Box 19395-5531, Tehran, Iran.
| | - Hazhir Dolatkhah
- RCQI, Institute of physics, Slovak Academy of Sciences, Dúbravská Cesta 9, 84511, Bratislava, Slovakia
| | - Maryam Rashidi
- Department of Medical Physics, Faculty of Medicine, Urmia University of Medical Sciences, Urmia, Iran
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12
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Vigliotti L, Cavaliere F, Passetti G, Sassetti M, Traverso Ziani N. Reconstruction-Induced φ0 Josephson Effect in Quantum Spin Hall Constrictions. NANOMATERIALS (BASEL, SWITZERLAND) 2023; 13:1497. [PMID: 37177040 PMCID: PMC10180432 DOI: 10.3390/nano13091497] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/03/2023] [Revised: 04/24/2023] [Accepted: 04/25/2023] [Indexed: 05/15/2023]
Abstract
The simultaneous breaking of time-reversal and inversion symmetry, in connection to superconductivity, leads to transport properties with disrupting scientific and technological potential. Indeed, the anomalous Josephson effect and the superconducting-diode effect hold promises to enlarge the technological applications of superconductors and nanostructures in general. In this context, the system we theoretically analyze is a Josephson junction (JJ) with coupled reconstructed topological channels as a link; such channels are at the edges of a two-dimensional topological insulator (2DTI). We find a robust φ0 Josephson effect without requiring the presence of external magnetic fields. Our results, which rely on a fully analytical analysis, are substantiated by means of symmetry arguments: Our system breaks both time-reversal symmetry and inversion symmetry. Moreover, the anomalous current increases as a function of temperature. We interpret this surprising temperature dependence by means of simple qualitative arguments based on Fermi's golden rule.
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Affiliation(s)
- Lucia Vigliotti
- Dipartimento di Fisica, Università degli Studi di Genova, Via Dodecaneso 33, 16146 Genova, Italy; (M.S.); (N.T.Z.)
| | - Fabio Cavaliere
- Dipartimento di Fisica, Università degli Studi di Genova, Via Dodecaneso 33, 16146 Genova, Italy; (M.S.); (N.T.Z.)
- CNR-SPIN, Via Dodecaneso 33, 16146 Genova, Italy
| | - Giacomo Passetti
- Institut für Theorie der Statistischen Physik, RWTH Aachen University and JARA-Fundamentals of Future Information Technology, 52056 Aachen, Germany;
| | - Maura Sassetti
- Dipartimento di Fisica, Università degli Studi di Genova, Via Dodecaneso 33, 16146 Genova, Italy; (M.S.); (N.T.Z.)
- CNR-SPIN, Via Dodecaneso 33, 16146 Genova, Italy
| | - Niccolò Traverso Ziani
- Dipartimento di Fisica, Università degli Studi di Genova, Via Dodecaneso 33, 16146 Genova, Italy; (M.S.); (N.T.Z.)
- CNR-SPIN, Via Dodecaneso 33, 16146 Genova, Italy
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13
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Turini B, Salimian S, Carrega M, Iorio A, Strambini E, Giazotto F, Zannier V, Sorba L, Heun S. Josephson Diode Effect in High-Mobility InSb Nanoflags. NANO LETTERS 2022; 22:8502-8508. [PMID: 36285780 PMCID: PMC9650771 DOI: 10.1021/acs.nanolett.2c02899] [Citation(s) in RCA: 14] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/26/2022] [Revised: 10/21/2022] [Indexed: 05/27/2023]
Abstract
We report nonreciprocal dissipation-less transport in single ballistic InSb nanoflag Josephson junctions. Applying an in-plane magnetic field, we observe an inequality in supercurrent for the two opposite current propagation directions. Thus, these devices can work as Josephson diodes, with dissipation-less current flowing in only one direction. For small fields, the supercurrent asymmetry increases linearly with external field, and then it saturates as the Zeeman energy becomes relevant, before it finally decreases to zero at higher fields. The effect is maximum when the in-plane field is perpendicular to the current vector, which identifies Rashba spin-orbit coupling as the main symmetry-breaking mechanism. While a variation in carrier concentration in these high-quality InSb nanoflags does not significantly influence the supercurrent asymmetry, it is instead strongly suppressed by an increase in temperature. Our experimental findings are consistent with a model for ballistic short junctions and show that the diode effect is intrinsic to this material.
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Affiliation(s)
- Bianca Turini
- NEST, Istituto Nanoscienze-CNR and Scuola Normale Superiore, 56127Pisa, Italy
| | - Sedighe Salimian
- NEST, Istituto Nanoscienze-CNR and Scuola Normale Superiore, 56127Pisa, Italy
| | | | - Andrea Iorio
- NEST, Istituto Nanoscienze-CNR and Scuola Normale Superiore, 56127Pisa, Italy
| | - Elia Strambini
- NEST, Istituto Nanoscienze-CNR and Scuola Normale Superiore, 56127Pisa, Italy
| | - Francesco Giazotto
- NEST, Istituto Nanoscienze-CNR and Scuola Normale Superiore, 56127Pisa, Italy
| | - Valentina Zannier
- NEST, Istituto Nanoscienze-CNR and Scuola Normale Superiore, 56127Pisa, Italy
| | - Lucia Sorba
- NEST, Istituto Nanoscienze-CNR and Scuola Normale Superiore, 56127Pisa, Italy
| | - Stefan Heun
- NEST, Istituto Nanoscienze-CNR and Scuola Normale Superiore, 56127Pisa, Italy
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14
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Guan XW, He P. New trends in quantum integrability: recent experiments with ultracold atoms. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2022; 85:114001. [PMID: 36170807 DOI: 10.1088/1361-6633/ac95a9] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/05/2022] [Accepted: 09/28/2022] [Indexed: 06/16/2023]
Abstract
Over the past two decades quantum engineering has made significant advances in our ability to create genuine quantum many-body systems using ultracold atoms. In particular, some prototypical exactly solvable Yang-Baxter systems have been successfully realized allowing us to confront elegant and sophisticated exact solutions of these systems with their experimental counterparts. The new experimental developments show a variety of fundamental one-dimensional (1D) phenomena, ranging from the generalized hydrodynamics to dynamical fermionization, Tomonaga-Luttinger liquids, collective excitations, fractional exclusion statistics, quantum holonomy, spin-charge separation, competing orders with high spin symmetry and quantum impurity problems. This article briefly reviews these developments and provides rigorous understanding of those observed phenomena based on the exact solutions while highlighting the uniqueness of 1D quantum physics. The precision of atomic physics realizations of integrable many-body problems continues to inspire significant developments in mathematics and physics while at the same time offering the prospect to contribute to future quantum technology.
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Affiliation(s)
- Xi-Wen Guan
- State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, APM, Chinese Academy of Sciences, Wuhan 430071, People's Republic of China
- NSFC-SPTP Peng Huanwu Center for Fundamental Theory, Xi'an 710127, People's Republic of China
- Department of Fundamental and Theoretical Physics, Research School of Physics, Australian National University, Canberra ACT 0200, Australia
| | - Peng He
- Bureau of Frontier Sciences and Education, Chinese Academy of Sciences, Beijing 100864,People's Republic of China
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15
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Jeon KR, Kim JK, Yoon J, Jeon JC, Han H, Cottet A, Kontos T, Parkin SSP. Zero-field polarity-reversible Josephson supercurrent diodes enabled by a proximity-magnetized Pt barrier. NATURE MATERIALS 2022; 21:1008-1013. [PMID: 35798947 DOI: 10.1038/s41563-022-01300-7] [Citation(s) in RCA: 17] [Impact Index Per Article: 8.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/04/2022] [Accepted: 05/26/2022] [Indexed: 06/15/2023]
Abstract
Simultaneous breaking of inversion and time-reversal symmetries in a conductor yields a non-reciprocal electronic transport1-3, known as the diode or rectification effect, that is, low (ideally zero) conductance in one direction and high (ideally infinite) conductance in the other. So far, most of the diode effects observed in non-centrosymmetric polar/superconducting conductors4-7 and Josephson junctions8-10 require external magnetic fields to break the time-reversal symmetry. Here we report zero-field polarity-switchable Josephson supercurrent diodes, in which a proximity-magnetized Pt layer by ferrimagnetic insulating Y3Fe5O12 serves as the Rashba(-type) Josephson barrier. The zero-field diode efficiency of our proximity-engineered device reaches up to ±35% at 2 K, with a clear square-root dependence on temperature. Measuring in-plane field-strength/angle dependences and comparing with Cu-inserted control junctions, we demonstrate that exchange spin-splitting11-13 and Rashba(-type) spin-orbit coupling13-15 at the Pt/Y3Fe5O12 interface are key for the zero-field giant rectification efficiency. Our achievement advances the development of field-free absolute Josephson diodes.
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Affiliation(s)
- Kun-Rok Jeon
- Max Planck Institute of Microstructure Physics, Halle (Saale), Germany.
- Department of Physics, Chung-Ang University (CAU), Seoul, Republic of Korea.
| | - Jae-Keun Kim
- Max Planck Institute of Microstructure Physics, Halle (Saale), Germany
| | - Jiho Yoon
- Max Planck Institute of Microstructure Physics, Halle (Saale), Germany
| | - Jae-Chun Jeon
- Max Planck Institute of Microstructure Physics, Halle (Saale), Germany
| | - Hyeon Han
- Max Planck Institute of Microstructure Physics, Halle (Saale), Germany
| | - Audrey Cottet
- Laboratoire de Physique de l'Ecole Normale Supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université de Paris, Paris, France
| | - Takis Kontos
- Laboratoire de Physique de l'Ecole Normale Supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université de Paris, Paris, France
| | - Stuart S P Parkin
- Max Planck Institute of Microstructure Physics, Halle (Saale), Germany.
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16
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Puliyil S, Banik M, Alimuddin M. Thermodynamic Signatures of Genuinely Multipartite Entanglement. PHYSICAL REVIEW LETTERS 2022; 129:070601. [PMID: 36018679 DOI: 10.1103/physrevlett.129.070601] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/23/2022] [Accepted: 07/19/2022] [Indexed: 06/15/2023]
Abstract
The theory of bipartite entanglement shares profound similarities with thermodynamics. In this Letter we extend this connection to multipartite quantum systems where entanglement appears in different forms with genuine entanglement being the most exotic one. We propose thermodynamic quantities that capture a signature of genuineness in multipartite entangled states. Instead of entropy, these quantities are defined in terms of energy-particularly the difference between global and local extractable works (ergotropies) that can be stored in quantum batteries. Some of these quantities suffice as faithful measures of genuineness and to some extent distinguish different classes of genuinely entangled states. Along with scrutinizing properties of these measures we compare them with the other existing genuine measures, and argue that they can serve the purpose in a better sense. Furthermore, the generality of our approach allows us to define suitable functions of ergotropies capturing the signature of k nonseparability that characterizes qualitatively different manifestations of entanglement in multipartite systems.
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Affiliation(s)
- Samgeeth Puliyil
- School of Physics, IISER Thiruvananthapuram, Vithura, Kerala 695551, India
| | - Manik Banik
- Department of Theoretical Sciences, S.N. Bose National Center for Basic Sciences, Block JD, Sector III, Salt Lake, Kolkata 700106, India
| | - Mir Alimuddin
- School of Physics, IISER Thiruvananthapuram, Vithura, Kerala 695551, India
- Department of Theoretical Sciences, S.N. Bose National Center for Basic Sciences, Block JD, Sector III, Salt Lake, Kolkata 700106, India
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17
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Bobkova IV, Bobkov AM, Silaev MA. Magnetoelectric effects in Josephson junctions. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2022; 34:353001. [PMID: 35709718 DOI: 10.1088/1361-648x/ac7994] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/26/2021] [Accepted: 06/16/2022] [Indexed: 06/15/2023]
Abstract
The review is devoted to the fundamental aspects and characteristic features of the magnetoelectric effects, reported in the literature on Josephson junctions (JJs). The main focus of the review is on the manifestations of the direct and inverse magnetoelectric effects in various types of Josephson systems. They provide a coupling of the magnetization in superconductor/ferromagnet/superconductor JJs to the Josephson current. The direct magnetoelectric effect is a driving force of spin torques acting on the ferromagnet inside the JJ. Therefore it is of key importance for the electrical control of the magnetization. The inverse magnetoelectric effect accounts for the back action of the magnetization dynamics on the Josephson subsystem, in particular, making the JJ to be in the resistive state in the presence of the magnetization dynamics of any origin. The perspectives of the coupling of the magnetization in JJs with ferromagnetic interlayers to the Josephson current via the magnetoelectric effects are discussed.
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Affiliation(s)
- I V Bobkova
- Institute of Solid State Physics, Chernogolovka, Moscow Region 142432, Russia
- Moscow Institute of Physics and Technology, Dolgoprudny 141700, Russia
- National Research University Higher School of Economics, Moscow 101000, Russia
| | - A M Bobkov
- Institute of Solid State Physics, Chernogolovka, Moscow Region 142432, Russia
- Moscow Institute of Physics and Technology, Dolgoprudny 141700, Russia
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18
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Davydova M, Prembabu S, Fu L. Universal Josephson diode effect. SCIENCE ADVANCES 2022; 8:eabo0309. [PMID: 35675396 PMCID: PMC9176746 DOI: 10.1126/sciadv.abo0309] [Citation(s) in RCA: 21] [Impact Index Per Article: 10.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/08/2022] [Accepted: 04/19/2022] [Indexed: 05/27/2023]
Abstract
We propose a universal mechanism for the Josephson diode effect in short Josephson junctions. The proposed mechanism is due to finite Cooper pair momentum and is a manifestation of simultaneous breaking of inversion and time-reversal symmetries. The diode efficiency is up to 40%, which corresponds to an asymmetry between the critical currents in opposite directions Ic+/Ic- ≈ 230%. We show that this arises from both the Doppler shift of the Andreev bound state energies and the phase-independent asymmetric current from the continuum. Last, we propose a simple scheme for achieving finite-momentum pairing, which does not rely on spin-orbit coupling and thus greatly expands existing platforms for the observation of supercurrent diode effects.
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Affiliation(s)
- Margarita Davydova
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
| | - Saranesh Prembabu
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
| | - Liang Fu
- Corresponding author. (M.D.); (L.F.)
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19
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Ilić S, Bergeret FS. Theory of the Supercurrent Diode Effect in Rashba Superconductors with Arbitrary Disorder. PHYSICAL REVIEW LETTERS 2022; 128:177001. [PMID: 35570454 DOI: 10.1103/physrevlett.128.177001] [Citation(s) in RCA: 24] [Impact Index Per Article: 12.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/26/2022] [Revised: 03/22/2022] [Accepted: 03/31/2022] [Indexed: 06/15/2023]
Abstract
We calculate the nonreciprocal critical current and quantify the supercurrent diode effect in two-dimensional Rashba superconductors with arbitrary disorder, using the quasiclassical Eilenberger equation. The nonreciprocity is caused by the helical superconducting state, which appears when both inversion and time-reversal symmetries are broken. In the absence of disorder, we find a very strong diode effect, with the nonreciprocity exceeding 40% at optimal temperatures, magnetic fields, and spin-orbit coupling. We establish that the effect persists even in the presence of strong disorder. We show that the sign of the diode effect changes as magnetic field and disorder are increased, reflecting the changes in the nature of the helical state.
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Affiliation(s)
- S Ilić
- Centro de Física de Materiales (CFM-MPC), Centro Mixto CSIC-UPV/EHU, Manuel de Lardizabal 5, E-20018 San Sebastián, Spain
| | - F S Bergeret
- Centro de Física de Materiales (CFM-MPC), Centro Mixto CSIC-UPV/EHU, Manuel de Lardizabal 5, E-20018 San Sebastián, Spain
- Donostia International Physics Center (DIPC), Manuel de Lardizabal 4, E-20018 San Sebastián, Spain
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20
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Telesio F, Carrega M, Cappelli G, Iorio A, Crippa A, Strambini E, Giazotto F, Serrano-Ruiz M, Peruzzini M, Heun S. Evidence of Josephson Coupling in a Few-Layer Black Phosphorus Planar Josephson Junction. ACS NANO 2022; 16:3538-3545. [PMID: 35099941 PMCID: PMC8945388 DOI: 10.1021/acsnano.1c09315] [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: 10/21/2021] [Accepted: 01/26/2022] [Indexed: 06/14/2023]
Abstract
Setting up strong Josephson coupling in van der Waals materials in close proximity to superconductors offers several opportunities both to inspect fundamental physics and to develop cryogenic quantum technologies. Here we show evidence of Josephson coupling in a planar few-layer black phosphorus junction. The planar geometry allows us to probe the junction behavior by means of external gates, at different carrier concentrations. Clear signatures of Josephson coupling are demonstrated by measuring supercurrent flow through the junction at milli-Kelvin temperatures. Manifestation of a Fraunhofer pattern with a transverse magnetic field is also reported, confirming the Josephson coupling. These findings represent evidence of proximity Josephson coupling in a planar junction based on a van der Waals material beyond graphene and will expedite further studies, exploiting the peculiar properties of exfoliated black phosphorus thin flakes.
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Affiliation(s)
- Francesca Telesio
- NEST,
Istituto Nanoscienze-CNR and Scuola Normale Superiore, Piazza San Silvestro 12, 56127 Pisa, Italy
| | | | - Giulio Cappelli
- NEST,
Istituto Nanoscienze-CNR and Scuola Normale Superiore, Piazza San Silvestro 12, 56127 Pisa, Italy
| | - Andrea Iorio
- NEST,
Istituto Nanoscienze-CNR and Scuola Normale Superiore, Piazza San Silvestro 12, 56127 Pisa, Italy
| | - Alessandro Crippa
- NEST,
Istituto Nanoscienze-CNR and Scuola Normale Superiore, Piazza San Silvestro 12, 56127 Pisa, Italy
| | - Elia Strambini
- NEST,
Istituto Nanoscienze-CNR and Scuola Normale Superiore, Piazza San Silvestro 12, 56127 Pisa, Italy
| | - Francesco Giazotto
- NEST,
Istituto Nanoscienze-CNR and Scuola Normale Superiore, Piazza San Silvestro 12, 56127 Pisa, Italy
| | | | | | - Stefan Heun
- NEST,
Istituto Nanoscienze-CNR and Scuola Normale Superiore, Piazza San Silvestro 12, 56127 Pisa, Italy
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21
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Baumgartner C, Fuchs L, Costa A, Picó-Cortés J, Reinhardt S, Gronin S, Gardner GC, Lindemann T, Manfra MJ, Faria Junior PE, Kochan D, Fabian J, Paradiso N, Strunk C. Effect of Rashba and Dresselhaus spin-orbit coupling on supercurrent rectification and magnetochiral anisotropy of ballistic Josephson junctions. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2022; 34:154005. [PMID: 35051919 DOI: 10.1088/1361-648x/ac4d5e] [Citation(s) in RCA: 12] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/01/2021] [Accepted: 01/20/2022] [Indexed: 06/14/2023]
Abstract
Simultaneous breaking of inversion- and time-reversal symmetry in Josephson junction (JJ) leads to a possible violation of theI(φ) = -I(-φ) equality for the current-phase relation. This is known as anomalous Josephson effect and it produces a phase shiftφ0in sinusoidal current-phase relations. In ballistic JJs with non-sinusoidal current phase relation the observed phenomenology is much richer, including the supercurrent diode effect and the magnetochiral anisotropy (MCA) of Josephson inductance. In this work, we present measurements of both effects on arrays of JJs defined on epitaxial Al/InAs heterostructures. We show that the orientation of the current with respect to the lattice affects the MCA, possibly as the result of a finite Dresselhaus component. In addition, we show that the two-fold symmetry of the Josephson inductance reflects in the activation energy for phase slips.
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Affiliation(s)
- C Baumgartner
- Institut für Experimentelle und Angewandte Physik, University of Regensburg, 93040 Regensburg, Germany
| | - L Fuchs
- Institut für Experimentelle und Angewandte Physik, University of Regensburg, 93040 Regensburg, Germany
| | - A Costa
- Institut für Theoretische Physik, University of Regensburg, 93040 Regensburg, Germany
| | - Jordi Picó-Cortés
- Institut für Theoretische Physik, University of Regensburg, 93040 Regensburg, Germany
| | - S Reinhardt
- Institut für Experimentelle und Angewandte Physik, University of Regensburg, 93040 Regensburg, Germany
| | - S Gronin
- Microsoft Quantum Purdue, Purdue University, West Lafayette, Indiana 47907 United States of America
- Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907 United States of America
| | - G C Gardner
- Microsoft Quantum Purdue, Purdue University, West Lafayette, Indiana 47907 United States of America
- Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907 United States of America
| | - T Lindemann
- Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907 United States of America
- Department of Physics and Astronomy, Purdue University, West Lafayette, Indiana 47907 United States of America
| | - M J Manfra
- Microsoft Quantum Purdue, Purdue University, West Lafayette, Indiana 47907 United States of America
- Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907 United States of America
- Department of Physics and Astronomy, Purdue University, West Lafayette, Indiana 47907 United States of America
- School of Materials Engineering, Purdue University, West Lafayette, Indiana 47907 United States of America
- School of Electrical and Computer Engineering, Purdue University, West Lafayette, Indiana 47907 United States of America
| | - P E Faria Junior
- Institut für Theoretische Physik, University of Regensburg, 93040 Regensburg, Germany
| | - D Kochan
- Institut für Theoretische Physik, University of Regensburg, 93040 Regensburg, Germany
| | - J Fabian
- Institut für Theoretische Physik, University of Regensburg, 93040 Regensburg, Germany
| | - N Paradiso
- Institut für Experimentelle und Angewandte Physik, University of Regensburg, 93040 Regensburg, Germany
| | - C Strunk
- Institut für Experimentelle und Angewandte Physik, University of Regensburg, 93040 Regensburg, Germany
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22
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Song R, Zhang P, Hao N. Phase-Manipulation-Induced Majorana Mode and Braiding Realization in Iron-Based Superconductor Fe(Te,Se). PHYSICAL REVIEW LETTERS 2022; 128:016402. [PMID: 35061489 DOI: 10.1103/physrevlett.128.016402] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/01/2021] [Revised: 12/21/2021] [Accepted: 12/22/2021] [Indexed: 06/14/2023]
Abstract
A recent experiment reported the evidence of dispersing one-dimensional Majorana mode trapped by the crystalline domain walls in FeSe_{0.45}Te_{0.55}. Here, we perform the first-principles calculations to show that iron atoms in the domain wall spontaneously form the ferromagnetic order in line with orientation of the wall. The ferromagnetism can impose a π phase difference between the domain-wall-separated surface superconducting regimes under the appropriate width and magnetization of the wall. Accordingly, the topological surface superconducting state of FeSe_{0.45}Te_{0.55} can give rise to one-dimensional Majorana modes trapped by the wall. More interestingly, we further propose a surface junction in the form of FeSe_{0.45}Te_{0.55}-ferromagnet-FeSe_{0.45}Te_{0.55}, which can be adopted to create and fuse the Majorana zero modes through controlling the width or magnetization of the interior ferromagnetic barrier. The braiding and readout of Majorana zero modes can be realized by the designed device. Such surface junction has the potential application in the superconducting topological quantum computation.
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Affiliation(s)
- Rui Song
- HEDPS, Center for Applied Physics and Technology and School of Physics, Peking University, Beijing 100871, China
- HEDPS, Center for Applied Physics and Technology and School of Engineering, Peking University, Beijing 100871, China
- Anhui Key Laboratory of Condensed Matter Physics at Extreme Conditions, High Magnetic Field Laboratory, HFIPS, Anhui, Chinese Academy of Sciences, and University of Science and Technology of China, Hefei, China
| | - Ping Zhang
- HEDPS, Center for Applied Physics and Technology and School of Engineering, Peking University, Beijing 100871, China
- School of Physics and Physical Engineering, Qufu Normal University, Qufu 273165, China
- Institute of Applied Physics and Computational Mathematics, Beijing 100088, China
- Beijing Computational Science Research Center, Beijing 100084, China
| | - Ning Hao
- Anhui Key Laboratory of Condensed Matter Physics at Extreme Conditions, High Magnetic Field Laboratory, HFIPS, Anhui, Chinese Academy of Sciences, and University of Science and Technology of China, Hefei, China
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23
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Baumgartner C, Fuchs L, Costa A, Reinhardt S, Gronin S, Gardner GC, Lindemann T, Manfra MJ, Faria Junior PE, Kochan D, Fabian J, Paradiso N, Strunk C. Supercurrent rectification and magnetochiral effects in symmetric Josephson junctions. NATURE NANOTECHNOLOGY 2022; 17:39-44. [PMID: 34795437 DOI: 10.1038/s41565-021-01009-9] [Citation(s) in RCA: 54] [Impact Index Per Article: 27.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/19/2021] [Accepted: 08/16/2021] [Indexed: 05/28/2023]
Abstract
Transport is non-reciprocal when not only the sign, but also the absolute value of the current depends on the polarity of the applied voltage. It requires simultaneously broken inversion and time-reversal symmetries, for example, by an interplay of spin-orbit coupling and magnetic field. Hitherto, observation of nonreciprocity was tied to resistivity, and dissipationless non-reciprocal circuit elements were elusive. Here we engineer fully superconducting non-reciprocal devices based on highly transparent Josephson junctions fabricated on InAs quantum wells. We demonstrate supercurrent rectification far below the transition temperature. By measuring Josephson inductance, we can link the non-reciprocal supercurrent to an asymmetry of the current-phase relation, and directly derive the supercurrent magnetochiral anisotropy coefficient. A semiquantitative model explains well the main features of our experimental data. Non-reciprocal Josephson junctions have the potential to become for superconducting circuits what pn junctions are for traditional electronics, enabling new non-dissipative circuit elements.
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Affiliation(s)
- Christian Baumgartner
- Institut für Experimentelle und Angewandte Physik, University of Regensburg, Regensburg, Germany
| | - Lorenz Fuchs
- Institut für Experimentelle und Angewandte Physik, University of Regensburg, Regensburg, Germany
| | - Andreas Costa
- Institut für Theoretische Physik, University of Regensburg, Regensburg, Germany
| | - Simon Reinhardt
- Institut für Experimentelle und Angewandte Physik, University of Regensburg, Regensburg, Germany
| | - Sergei Gronin
- Microsoft Quantum Purdue, Purdue University, West Lafayette, IN, USA
- Birck Nanotechnology Center, Purdue University, West Lafayette, IN, USA
| | - Geoffrey C Gardner
- Microsoft Quantum Purdue, Purdue University, West Lafayette, IN, USA
- Birck Nanotechnology Center, Purdue University, West Lafayette, IN, USA
| | - Tyler Lindemann
- Birck Nanotechnology Center, Purdue University, West Lafayette, IN, USA
- Department of Physics and Astronomy, Purdue University, West Lafayette, IN, USA
| | - Michael J Manfra
- Microsoft Quantum Purdue, Purdue University, West Lafayette, IN, USA
- 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
- School of Electrical and Computer Engineering, Purdue University, West Lafayette, IN, USA
| | | | - Denis Kochan
- Institut für Theoretische Physik, University of Regensburg, Regensburg, Germany
| | - Jaroslav Fabian
- Institut für Theoretische Physik, University of Regensburg, Regensburg, Germany
| | - Nicola Paradiso
- Institut für Experimentelle und Angewandte Physik, University of Regensburg, Regensburg, Germany.
| | - Christoph Strunk
- Institut für Experimentelle und Angewandte Physik, University of Regensburg, Regensburg, Germany
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24
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Zakavati S, Tabesh FT, Salimi S. Bounds on charging power of open quantum batteries. Phys Rev E 2021; 104:054117. [PMID: 34942849 DOI: 10.1103/physreve.104.054117] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/24/2020] [Accepted: 10/19/2021] [Indexed: 11/07/2022]
Abstract
In general, quantum systems most likely undergo open-system dynamics due to their smallness and sensitivity. Energy storage devices, so-called quantum batteries, are not excluded from this phenomenon. Here, we study fundamental bounds on the power of open quantum batteries from the geometric point of view. By defining an activity operator, a tight upper bound on the charging power is derived for the open quantum batteries in terms of the fluctuations of the activity operator and the quantum Fisher information. The variance of the activity operator may be interpreted as a generalized thermodynamic force, while the quantum Fisher information describes the speed of evolution in the state space of the battery. The thermodynamic interpretation of the upper bound is discussed in detail. As an example, a model for the battery, taking into account the environmental effects, is proposed, and the effect of dissipation and decoherence during the charging process on both the stored work and the charging power is investigated. Our results show that the upper bound is saturated in some time intervals. Also, the maximum value of both the stored work and the corresponding power is achieved in the non-Markovian underdamped regime.
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Affiliation(s)
- Shadab Zakavati
- Department of Physics, University of Kurdistan, P.O. Box 66177-15175, Sanandaj, Iran
| | - Fatemeh T Tabesh
- Department of Physics, University of Kurdistan, P.O. Box 66177-15175, Sanandaj, Iran
| | - Shahriar Salimi
- Department of Physics, University of Kurdistan, P.O. Box 66177-15175, Sanandaj, Iran
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25
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Yao Y, Cai R, Yu T, Ma Y, Xing W, Ji Y, Xie XC, Yang SH, Han W. Giant oscillatory Gilbert damping in superconductor/ferromagnet/superconductor junctions. SCIENCE ADVANCES 2021; 7:eabh3686. [PMID: 34826245 PMCID: PMC8626077 DOI: 10.1126/sciadv.abh3686] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 03/04/2021] [Accepted: 10/06/2021] [Indexed: 06/13/2023]
Abstract
Interfaces between materials with differently ordered phases present unique opportunities for exotic physical properties, especially the interplay between ferromagnetism and superconductivity in the ferromagnet/superconductor heterostructures. The investigation of zero- and π-junctions has been of particular interest for both fundamental physical science and emerging technologies. Here, we report the experimental observation of giant oscillatory Gilbert damping in the superconducting niobium/nickel-iron/niobium junctions with respect to the nickel-iron thickness. This observation suggests an unconventional spin pumping and relaxation via zero-energy Andreev bound states that exist not only in the niobium/nickel-iron/niobium π-junctions but also in the niobium/nickel-iron/niobium zero-junctions. Our findings could be important for further exploring the exotic physical properties of ferromagnet/superconductor heterostructures and potential applications of ferromagnet π-junctions in quantum computing, such as half-quantum flux qubits.
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Affiliation(s)
- Yunyan Yao
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
- Collaborative Innovation Center of Quantum Matter, Beijing 100871, China
| | - Ranran Cai
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
- Collaborative Innovation Center of Quantum Matter, Beijing 100871, China
| | - Tao Yu
- Max Planck Institute for the Structure and Dynamics of Matter, 22761 Hamburg, Germany
| | - Yang Ma
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
- Collaborative Innovation Center of Quantum Matter, Beijing 100871, China
| | - Wenyu Xing
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
- Collaborative Innovation Center of Quantum Matter, Beijing 100871, China
| | - Yuan Ji
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
- Collaborative Innovation Center of Quantum Matter, Beijing 100871, China
| | - Xin-Cheng Xie
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
- Collaborative Innovation Center of Quantum Matter, Beijing 100871, China
- CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences, Beijing 100190, China
- Beijing Academy of Quantum Information Sciences, Beijing 100193, China
| | | | - Wei Han
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
- Collaborative Innovation Center of Quantum Matter, Beijing 100871, China
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26
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Bobkova IV, Bobkov AM, Silaev MA. Dynamic Spin-Triplet Order Induced by Alternating Electric Fields in Superconductor-Ferromagnet-Superconductor Josephson Junctions. PHYSICAL REVIEW LETTERS 2021; 127:147701. [PMID: 34652200 DOI: 10.1103/physrevlett.127.147701] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/27/2021] [Accepted: 09/01/2021] [Indexed: 06/13/2023]
Abstract
Dynamic states offer extended possibilities to control the properties of quantum matter. Recent efforts are focused on studying the ordered states which appear exclusively under the time-dependent drives. Here, we demonstrate a class of systems which feature dynamic spin-triplet superconducting order stimulated by the alternating electric field. The effect is based on the interplay of ferromagnetism, interfacial spin-orbital coupling, and the condensate motion driven by the field, which converts hidden static p-wave order, produced by the joint action of the ferromagnetism and the spin-orbital coupling, into dynamic s-wave equal-spin-triplet correlations. We demonstrate that the critical current of Josephson junctions hosting these states is proportional to the electromagnetic power, supplied either by the external irradiation or by the ac current source. Based on these unusual properties we propose the scheme of a Josephson transistor which can be switched by the ac voltage and demonstrates an even-numbered sequence of Shapiro steps. Combining the photoactive Josephson junctions with recently discovered Josephson phase batteries we find photomagnetic SQUID devices which can generate spontaneous magnetic fields while being exposed to irradiation.
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Affiliation(s)
- I V Bobkova
- Institute of Solid State Physics, Chernogolovka, Moscow region, 142432 Russia
- Moscow Institute of Physics and Technology, Dolgoprudny 141700, Russia
- National Research University Higher School of Economics, Moscow 101000, Russia
| | - A M Bobkov
- Institute of Solid State Physics, Chernogolovka, Moscow region, 142432 Russia
| | - M A Silaev
- Moscow Institute of Physics and Technology, Dolgoprudny 141700, Russia
- Department of Physics, Nanoscience Center, University of Jyväskylä, 40014 Jyväskylä, Finland
- Institute for Physics of Microstructures, Russian Academy of Sciences, 603950 Nizhny Novgorod, GSP-105, Russia
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27
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Idzuchi H, Pientka F, Huang KF, Harada K, Gül Ö, Shin YJ, Nguyen LT, Jo NH, Shindo D, Cava RJ, Canfield PC, Kim P. Unconventional supercurrent phase in Ising superconductor Josephson junction with atomically thin magnetic insulator. Nat Commun 2021; 12:5332. [PMID: 34504077 PMCID: PMC8429564 DOI: 10.1038/s41467-021-25608-1] [Citation(s) in RCA: 11] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/24/2021] [Accepted: 08/22/2021] [Indexed: 11/23/2022] Open
Abstract
In two-dimensional (2D) NbSe2 crystal, which lacks inversion symmetry, strong spin-orbit coupling aligns the spins of Cooper pairs to the orbital valleys, forming Ising Cooper pairs (ICPs). The unusual spin texture of ICPs can be further modulated by introducing magnetic exchange. Here, we report unconventional supercurrent phase in van der Waals heterostructure Josephson junctions (JJs) that couples NbSe2 ICPs across an atomically thin magnetic insulator (MI) Cr2Ge2Te6. By constructing a superconducting quantum interference device (SQUID), we measure the phase of the transferred Cooper pairs in the MI JJ. We demonstrate a doubly degenerate nontrivial JJ phase (ϕ), formed by momentum-conserving tunneling of ICPs across magnetic domains in the barrier. The doubly degenerate ground states in MI JJs provide a two-level quantum system that can be utilized as a new dissipationless component for superconducting quantum devices. Our work boosts the study of various superconducting states with spin-orbit coupling, opening up an avenue to designing new superconducting phase-controlled quantum electronic devices. Van der Waals structures provide a new platform to explore novel physics of superconductor/ferromagnet interfaces. Here, NbSe2 Josephson junction with Cr2Ge2Te6 enables non-trivial Josephson phase by spin-dependent interaction, boosting the study of superconducting states with spin-orbit coupling and phase-controlled quantum electronic device.
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Affiliation(s)
- H Idzuchi
- Department of Physics, Harvard University, Cambridge, MA, USA.,WPI Advanced Institute for Materials Research and Center for Science and Innovation in Spintronics, Tohoku University, Sendai, Japan
| | - F Pientka
- Department of Physics, Harvard University, Cambridge, MA, USA.,Institut für Theoretische Physik, Goethe-Universität, Frankfurt am Main, Germany
| | - K-F Huang
- Department of Physics, Harvard University, Cambridge, MA, USA
| | - K Harada
- Center for Emergent Matter Science (CEMS), RIKEN, Hatoyama, Saitama, Japan
| | - Ö Gül
- Department of Physics, Harvard University, Cambridge, MA, USA
| | - Y J Shin
- Department of Physics, Harvard University, Cambridge, MA, USA.,Center for Functional Nanomaterials, Brookhaven National Laboratory, Upton, NY, USA
| | - L T Nguyen
- Department of Chemistry, Princeton University, Princeton, NJ, USA
| | - N H Jo
- Department of Physics and Astronomy, Iowa State University, Ames, IA, USA.,Ames Laboratory, Iowa State University, Ames, IA, USA
| | - D Shindo
- Center for Emergent Matter Science (CEMS), RIKEN, Hatoyama, Saitama, Japan
| | - R J Cava
- Department of Chemistry, Princeton University, Princeton, NJ, USA
| | - P C Canfield
- Department of Physics and Astronomy, Iowa State University, Ames, IA, USA.,Ames Laboratory, Iowa State University, Ames, IA, USA
| | - P Kim
- Department of Physics, Harvard University, Cambridge, MA, USA.
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28
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Preliminary demonstration of a persistent Josephson phase-slip memory cell with topological protection. Nat Commun 2021; 12:5200. [PMID: 34465775 PMCID: PMC8408200 DOI: 10.1038/s41467-021-25209-y] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/12/2021] [Accepted: 07/09/2021] [Indexed: 11/08/2022] Open
Abstract
Superconducting computing promises enhanced computational power in both classical and quantum approaches. Yet, scalable and fast superconducting memories are not implemented. Here, we propose a fully superconducting memory cell based on the hysteretic phase-slip transition existing in long aluminum nanowire Josephson junctions. Embraced by a superconducting ring, the memory cell codifies the logic state in the direction of the circulating persistent current, as commonly defined in flux-based superconducting memories. But, unlike the latter, the hysteresis here is a consequence of the phase-slip occurring in the long weak link and associated to the topological transition of its superconducting gap. This disentangles our memory scheme from the large-inductance constraint, thus enabling its miniaturization. Moreover, the strong activation energy for phase-slip nucleation provides a robust topological protection against stochastic phase-slips and magnetic-flux noise. These properties make the Josephson phase-slip memory a promising solution for advanced superconducting classical logic architectures or flux qubits. Superconducting computing promises enhanced computational power, but scalable and fast superconducting memories are still not implemented. Here, the authors demonstrate a superconducting memory cell based on hysteretic phase-slip transition, without degradation up to ~1 K over several days.
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29
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Golod T, Hovhannisyan RA, Kapran OM, Dremov VV, Stolyarov VS, Krasnov VM. Reconfigurable Josephson Phase Shifter. NANO LETTERS 2021; 21:5240-5246. [PMID: 34114467 PMCID: PMC8289326 DOI: 10.1021/acs.nanolett.1c01366] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/06/2021] [Revised: 06/08/2021] [Indexed: 06/01/2023]
Abstract
Phase shifter is one of the key elements of quantum electronics. In order to facilitate operation and avoid decoherence, it has to be reconfigurable, persistent, and nondissipative. In this work, we demonstrate prototypes of such devices in which a Josephson phase shift is generated by coreless superconducting vortices. The smallness of the vortex allows a broad-range tunability by nanoscale manipulation of vortices in a micron-size array of vortex traps. We show that a phase shift in a device containing just a few vortex traps can be reconfigured between a large number of quantized states in a broad [-3π, +3π] range.
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Affiliation(s)
- Taras Golod
- Department
of Physics, Stockholm University, AlbaNova University Center, SE-10691 Stockholm, Sweden
| | - Razmik A. Hovhannisyan
- Department
of Physics, Stockholm University, AlbaNova University Center, SE-10691 Stockholm, Sweden
- Moscow
Institute of Physics and Technology, 141700 Dolgoprudny, Russia
| | - Olena M. Kapran
- Department
of Physics, Stockholm University, AlbaNova University Center, SE-10691 Stockholm, Sweden
| | | | | | - Vladimir M. Krasnov
- Department
of Physics, Stockholm University, AlbaNova University Center, SE-10691 Stockholm, Sweden
- Moscow
Institute of Physics and Technology, 141700 Dolgoprudny, Russia
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