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Gao Y, Zhang X, Yi Z, Liu L, Chi F. Thermophase Seebeck Coefficient in Hybridized Superconductor-Quantum-Dot-Superconductor Josephson Junction Side-Coupled to Majorana Nanowire. NANOMATERIALS (BASEL, SWITZERLAND) 2023; 13:2489. [PMID: 37686996 PMCID: PMC10490436 DOI: 10.3390/nano13172489] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/10/2023] [Revised: 09/01/2023] [Accepted: 09/01/2023] [Indexed: 09/10/2023]
Abstract
The dc Josephson current is generated from phase difference between two superconductors separated by a mesoscopic thin film (Josephson junction) without external bias voltage. In the presence of a temperature gradient across the superconductors, a thermal phase is induced under the condition of open circuit. This is very similar to the Seebeck effect in the usual thermoelectric effect, and the thermal phase is thus named as thermophase Seebeck coefficient (TPSC). Here we find obvious enhancement and sign change of the TPSC unique to the Josephson junction composing of two superconductors connected to a semiconductor quantum dot (QD), which is additionally side-coupled to a nanowire hosting Majorana bound states (MBSs), the system denoted by S-MQD-S. These result arise from the newly developed states near the Fermi level of the superconductors due to the QD-MBS hybridization when the dot level is within the superconducting gap. The sign change of the TPSC provides a strong evidence of the existence of MBSs, and is absent if the QD is coupled to regular fermion, such as another QD (system denoted by S-DQD-S). We show that the magnitude and sign of the TPSC are sensitive to the physical quantities including interaction strength between the QD and MBSs, direct overlap between the MBSs, system equilibrium temperature, as well as hopping amplitude between the QD and the superconductors. The obtained results are explained with the help of the current-carrying density of the states (CCDOS), and may be useful in interdisciplinary research areas of Josephson and Majorana physics.
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Affiliation(s)
- Yumei Gao
- School of Electronic and Information Engineering, UEST of China, Zhongshan Institute, Zhongshan 528400, China; (Y.G.); (Z.Y.); (L.L.)
| | - Xiaoyan Zhang
- College of Science, North China Institute of Science and Technology, Beijing 101601, China
| | - Zichuan Yi
- School of Electronic and Information Engineering, UEST of China, Zhongshan Institute, Zhongshan 528400, China; (Y.G.); (Z.Y.); (L.L.)
| | - Liming Liu
- School of Electronic and Information Engineering, UEST of China, Zhongshan Institute, Zhongshan 528400, China; (Y.G.); (Z.Y.); (L.L.)
| | - Feng Chi
- School of Electronic and Information Engineering, UEST of China, Zhongshan Institute, Zhongshan 528400, China; (Y.G.); (Z.Y.); (L.L.)
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2
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Karabassov T, Pashkovskaia VD, Parkhomenko NA, Guravova AV, Kazakova EA, Lvov BG, Golubov AA, Vasenko AS. Density of states in the presence of spin-dependent scattering in SF bilayers: a numerical and analytical approach. BEILSTEIN JOURNAL OF NANOTECHNOLOGY 2022; 13:1418-1431. [PMID: 36540701 PMCID: PMC9732889 DOI: 10.3762/bjnano.13.117] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 06/28/2022] [Accepted: 11/07/2022] [Indexed: 06/17/2023]
Abstract
We present a quantitative study of the density of states (DOS) in SF bilayers (where S is a bulk superconductor and F is a ferromagnetic metal) in the diffusive limit. We solve the quasiclassical Usadel equations in the structure considering the presence of magnetic and spin-orbit scattering. For practical reasons, we propose the analytical solution for the density of states in SF bilayers in the case of a thin ferromagnet and low transparency of the SF interface. This solution is confirmed by numerical calculations using a self-consistent two-step iterative method. The behavior of DOS dependencies on magnetic and spin-orbit scattering times is discussed.
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Affiliation(s)
| | | | | | | | - Elena A Kazakova
- Sechenov First Moscow State Medical University, 119991 Moscow, Russia
| | | | - Alexander A Golubov
- Faculty of Science and Technology and MESA Institute for Nanotechnology, University of Twente, 7500 AE Enschede, Netherlands
- Moscow Institute of Physics and Technology, 141700 Dolgoprudny, Russia
| | - Andrey S Vasenko
- HSE University, 101000 Moscow, Russia
- I. E. Tamm Department of Theoretical Physics, P. N. Lebedev Physical Institute, Russian Academy of Sciences, 119991 Moscow, Russia
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3
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Germanese G, Paolucci F, Marchegiani G, Braggio A, Giazotto F. Bipolar thermoelectric Josephson engine. NATURE NANOTECHNOLOGY 2022; 17:1084-1090. [PMID: 36138204 DOI: 10.1038/s41565-022-01208-y] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/02/2022] [Accepted: 07/26/2022] [Indexed: 06/16/2023]
Abstract
Thermoelectric effects in metals are typically small due to the nearly perfect particle-hole symmetry around their Fermi surface. Furthermore, thermo-phase effects and linear thermoelectricity in superconducting systems have been identified only when particle-hole symmetry is explicitly broken, since thermoelectric effects were considered impossible in pristine superconductors. Here, we experimentally demonstrate that superconducting tunnel junctions develop a very large bipolar thermoelectricity in the presence of a sizable thermal gradient thanks to spontaneous particle-hole symmetry breaking. Our junctions show Seebeck coefficients of up to ±300 μV K-1, which is comparable with quantum dots and roughly 105 times larger than the value expected for normal metals at subkelvin temperatures. Moreover, by integrating our junctions into a Josephson interferometer, we realize a bipolar thermoelectric Josephson engine generating phase-tunable electric powers of up to ~140 nW mm-2. Notably, our device implements also the prototype for a persistent thermoelectric memory cell, written or erased by current injection. We expect that our findings will lead to applications in superconducting quantum technologies.
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Affiliation(s)
- Gaia Germanese
- NEST, Istituto Nanoscienze-CNR and Scuola Normale Superiore, Pisa, Italy
- Dipartimento di Fisica, Università di Pisa, Pisa, Italy
| | - Federico Paolucci
- NEST, Istituto Nanoscienze-CNR and Scuola Normale Superiore, Pisa, Italy.
| | | | - Alessandro Braggio
- NEST, Istituto Nanoscienze-CNR and Scuola Normale Superiore, Pisa, Italy
| | - Francesco Giazotto
- NEST, Istituto Nanoscienze-CNR and Scuola Normale Superiore, Pisa, Italy.
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4
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Abstract
Diodes are key elements for electronics, optics, and detection. Their evolution towards low dissipation electronics has seen the hybridization with superconductors and the realization of supercurrent diodes with zero resistance in only one direction. Here, we present the quasi-particle counterpart, a superconducting tunnel diode with zero conductance in only one direction. The direction-selective propagation of the charge has been obtained through the broken electron-hole symmetry induced by the spin selection of the ferromagnetic tunnel barrier: a EuS thin film separating a superconducting Al and a normal metal Cu layer. The Cu/EuS/Al tunnel junction achieves a large rectification (up to ∼40%) already for a small voltage bias (∼200 μV) thanks to the small energy scale of the system: the Al superconducting gap. With the help of an analytical theoretical model we can link the maximum rectification to the spin polarization (P) of the barrier and describe the quasi-ideal Shockley-diode behavior of the junction. This cryogenic spintronic rectifier is promising for the application in highly-sensitive radiation detection for which two different configurations are evaluated. In addition, the superconducting diode may pave the way for future low-dissipation and fast superconducting electronics. Diodes are characterized by mono-directional flow of current, yet this simplicity belies their critical importance in electronics and optics. Here, Strambini et al demonstrate a superconducting quasi-particle equivalent, achieved by the use of a thin ferromagnetic insulator.
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Gomez-Perez JM, Zhang XP, Calavalle F, Ilyn M, González-Orellana C, Gobbi M, Rogero C, Chuvilin A, Golovach VN, Hueso LE, Bergeret FS, Casanova F. Strong Interfacial Exchange Field in a Heavy Metal/Ferromagnetic Insulator System Determined by Spin Hall Magnetoresistance. NANO LETTERS 2020; 20:6815-6823. [PMID: 32786952 DOI: 10.1021/acs.nanolett.0c02834] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
Spin-dependent transport at heavy metal/magnetic insulator interfaces is at the origin of many phenomena at the forefront of spintronics research. A proper quantification of the different interfacial spin conductances is crucial for many applications. Here, we report the first measurement of the spin Hall magnetoresistance (SMR) of Pt on a purely ferromagnetic insulator (EuS). We perform SMR measurements in a wide range of temperatures and fit the results by using a microscopic model. From this fitting procedure, we obtain the temperature dependence of the spin conductances (Gs, Gr, and Gi), disentangling the contribution of field-like torque (Gi), damping-like torque (Gr), and spin-flip scattering (Gs). An interfacial exchange field of the order of 1 meV acting upon the conduction electrons of Pt can be estimated from Gi, which is at least three times larger than Gr below the Curie temperature. Our work provides an easy method to quantify this interfacial spin-splitting field, which plays a key role in emerging fields such as superconducting spintronics and caloritronics as well as topological quantum computation.
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Affiliation(s)
| | - Xian-Peng Zhang
- Donostia International Physics Center, 20018 Donostia-San Sebastian, Basque Country, Spain
- Centro de Fı́sica de Materiales CFM-MPC (CSIC-UPV/EHU), 20018 Donostia-San Sebastian, Basque Country, Spain
| | | | - Maxim Ilyn
- Centro de Fı́sica de Materiales CFM-MPC (CSIC-UPV/EHU), 20018 Donostia-San Sebastian, Basque Country, Spain
| | - Carmen González-Orellana
- Centro de Fı́sica de Materiales CFM-MPC (CSIC-UPV/EHU), 20018 Donostia-San Sebastian, Basque Country, Spain
| | - Marco Gobbi
- CIC nanoGUNE BRTA, 20018 Donostia-San Sebastian, Basque Country, Spain
- IKERBASQUE, Basque Foundation for Science, 48013 Bilbao, Basque Country, Spain
- Centro de Fı́sica de Materiales CFM-MPC (CSIC-UPV/EHU), 20018 Donostia-San Sebastian, Basque Country, Spain
| | - Celia Rogero
- Donostia International Physics Center, 20018 Donostia-San Sebastian, Basque Country, Spain
- Centro de Fı́sica de Materiales CFM-MPC (CSIC-UPV/EHU), 20018 Donostia-San Sebastian, Basque Country, Spain
| | - Andrey Chuvilin
- CIC nanoGUNE BRTA, 20018 Donostia-San Sebastian, Basque Country, Spain
- IKERBASQUE, Basque Foundation for Science, 48013 Bilbao, Basque Country, Spain
| | - Vitaly N Golovach
- IKERBASQUE, Basque Foundation for Science, 48013 Bilbao, Basque Country, Spain
- Donostia International Physics Center, 20018 Donostia-San Sebastian, Basque Country, Spain
- Centro de Fı́sica de Materiales CFM-MPC (CSIC-UPV/EHU), 20018 Donostia-San Sebastian, Basque Country, Spain
- Departamento de Física de Materiales UPV/EHU, 20018 Donostia-San Sebastian, Basque Country, Spain
| | - Luis E Hueso
- CIC nanoGUNE BRTA, 20018 Donostia-San Sebastian, Basque Country, Spain
- IKERBASQUE, Basque Foundation for Science, 48013 Bilbao, Basque Country, Spain
| | - F Sebastian Bergeret
- Donostia International Physics Center, 20018 Donostia-San Sebastian, Basque Country, Spain
- Centro de Fı́sica de Materiales CFM-MPC (CSIC-UPV/EHU), 20018 Donostia-San Sebastian, Basque Country, Spain
| | - Fèlix Casanova
- CIC nanoGUNE BRTA, 20018 Donostia-San Sebastian, Basque Country, Spain
- IKERBASQUE, Basque Foundation for Science, 48013 Bilbao, Basque Country, Spain
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6
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Marchegiani G, Braggio A, Giazotto F. Nonlinear Thermoelectricity with Electron-Hole Symmetric Systems. PHYSICAL REVIEW LETTERS 2020; 124:106801. [PMID: 32216390 DOI: 10.1103/physrevlett.124.106801] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/10/2019] [Revised: 02/05/2020] [Accepted: 02/14/2020] [Indexed: 06/10/2023]
Abstract
In the linear regime, thermoelectric effects between two conductors are possible only in the presence of an explicit breaking of the electron-hole symmetry. We consider a tunnel junction between two electrodes and show that this condition is no longer required outside the linear regime. In particular, we demonstrate that a thermally biased junction can display an absolute negative conductance, and hence thermoelectric power, at a small but finite voltage bias, provided that the density of states of one of the electrodes is gapped and the other is monotonically decreasing. We consider a prototype system that fulfills these requirements, namely, a tunnel junction between two different superconductors where the Josephson contribution is suppressed. We discuss this nonlinear thermoelectric effect based on the spontaneous breaking of electron-hole symmetry in the system, characterize its main figures of merit, and discuss some possible applications.
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Affiliation(s)
- G Marchegiani
- NEST Istituto Nanoscienze-CNR and Scuola Normale Superiore, I-56127 Pisa, Italy
| | - A Braggio
- NEST Istituto Nanoscienze-CNR and Scuola Normale Superiore, I-56127 Pisa, Italy
| | - F Giazotto
- NEST Istituto Nanoscienze-CNR and Scuola Normale Superiore, I-56127 Pisa, Italy
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7
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Fornieri A, Giazotto F. Towards phase-coherent caloritronics in superconducting circuits. NATURE NANOTECHNOLOGY 2017; 12:944-952. [PMID: 28984310 DOI: 10.1038/nnano.2017.204] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/04/2016] [Accepted: 09/04/2017] [Indexed: 06/07/2023]
Abstract
The emerging field of phase-coherent caloritronics (from the Latin word calor, heat) is based on the possibility of controlling heat currents by using the phase difference of the superconducting order parameter. The goal is to design and implement thermal devices that can control energy transfer with a degree of accuracy approaching that reached for charge transport by contemporary electronic components. This can be done by making use of the macroscopic quantum coherence intrinsic to superconducting condensates, which manifests itself through the Josephson effect and the proximity effect. Here, we review recent experimental results obtained in the realization of heat interferometers and thermal rectifiers, and discuss a few proposals for exotic nonlinear phase-coherent caloritronic devices, such as thermal transistors, solid-state memories, phase-coherent heat splitters, microwave refrigerators, thermal engines and heat valves. Besides being attractive from the fundamental physics point of view, these systems are expected to have a vast impact on many cryogenic microcircuits requiring energy management, and possibly lay the first stone for the foundation of electronic thermal logic.
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Affiliation(s)
- Antonio Fornieri
- NEST, Istituto Nanoscienze-CNR and Scuola Normale Superiore, Piazza San Silvestro 12, I-56127 Pisa, Italy
- Center for Quantum Devices and Station Q Copenhagen, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
| | - Francesco Giazotto
- NEST, Istituto Nanoscienze-CNR and Scuola Normale Superiore, Piazza San Silvestro 12, I-56127 Pisa, Italy
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8
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Kleeorin Y, Meir Y, Giazotto F, Dubi Y. Large Tunable Thermophase in Superconductor - Quantum Dot - Superconductor Josephson Junctions. Sci Rep 2016; 6:35116. [PMID: 27734919 PMCID: PMC5062082 DOI: 10.1038/srep35116] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/15/2016] [Accepted: 09/22/2016] [Indexed: 11/09/2022] Open
Abstract
In spite of extended efforts, detecting thermoelectric effects in superconductors has proven to be a challenging task, due to the inherent superconducting particle-hole symmetry. Here we present a theoretical study of an experimentally attainable Superconductor - Quantum Dot - Superconductor (SC-QD-SC) Josephson Junction. Using Keldysh Green's functions we derive the exact thermo-phase and thermal response of the junction, and demonstrate that such a junction has highly tunable thermoelectric properties and a significant thermal response. The origin of these effects is the QD energy level placed between the SCs, which breaks particle-hole symmetry in a gradual manner, allowing, in the presence of a temperature gradient, for gate controlled appearance of a superconducting thermo-phase. This thermo-phase increases up to a maximal value of ±π/2 after which thermovoltage is expected to develop. Our calculations are performed in realistic parameter regimes, and we suggest an experimental setup which could be used to verify our predictions.
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Affiliation(s)
- Yaakov Kleeorin
- Department of Physics, Ben-Gurion University of the Negev, Beer Sheva, 84105, Israel
| | - Yigal Meir
- Department of Physics, Ben-Gurion University of the Negev, Beer Sheva, 84105, Israel
- The Ilse Katz Institute for Nanoscale Science and Technology, Ben-Gurion University of the Negev, Beer Sheva, 84105, Israel
| | - Francesco Giazotto
- NEST Istituto Nanoscienze-CNR and Scuola Normale Superiore, I-56127 Pisa, Italy
| | - Yonatan Dubi
- The Ilse Katz Institute for Nanoscale Science and Technology, Ben-Gurion University of the Negev, Beer Sheva, 84105, Israel
- Department of Chemistry, Ben-Gurion University of the Negev, Beer Sheva, 84105, Israel
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9
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Beckmann D. Spin manipulation in nanoscale superconductors. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2016; 28:163001. [PMID: 27001949 DOI: 10.1088/0953-8984/28/16/163001] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
The interplay of superconductivity and magnetism in nanoscale structures has attracted considerable attention in recent years due to the exciting new physics created by the competition of these antagonistic ordering phenomena, and the prospect of exploiting this competition for superconducting spintronics devices. While much of the attention is focused on spin-polarized supercurrents created by the triplet proximity effect, the recent discovery of long range quasiparticle spin transport in high-field superconductors has rekindled interest in spin-dependent nonequilibrium properties of superconductors. In this review, the experimental situation on nonequilibrium spin injection into superconductors is discussed, and open questions and possible future directions of the field are outlined.
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Affiliation(s)
- D Beckmann
- Karlsruhe Institute of Technology (KIT), Institute of Nanotechnology, 76021 Karlsruhe, Germany
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10
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Kolenda S, Wolf MJ, Beckmann D. Observation of Thermoelectric Currents in High-Field Superconductor-Ferromagnet Tunnel Junctions. PHYSICAL REVIEW LETTERS 2016; 116:097001. [PMID: 26991193 DOI: 10.1103/physrevlett.116.097001] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/18/2015] [Indexed: 06/05/2023]
Abstract
We report on the experimental observation of spin-dependent thermoelectric currents in superconductor-ferromagnet tunnel junctions in high magnetic fields. The thermoelectric signals are due to a spin-dependent lifting of the particle-hole symmetry, and are found to be in excellent agreement with recent theoretical predictions. The maximum Seebeck coefficient inferred from the data is about -100 μV/K, much larger than commonly found in metallic structures. Our results directly prove the coupling of spin and heat transport in high-field superconductors.
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Affiliation(s)
- S Kolenda
- Institute of Nanotechnology, Karlsruhe Institute of Technology, Karlsruhe, Germany
| | - M J Wolf
- Institute of Nanotechnology, Karlsruhe Institute of Technology, Karlsruhe, Germany
| | - D Beckmann
- Institute of Nanotechnology, Karlsruhe Institute of Technology, Karlsruhe, Germany
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