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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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Chi F, Jia QS, Liu J, Gao QG, Yi ZC, Liu LM. Enhancement of the Josephson Current in a Quantum Dot Connected to Majorana Nanowires. NANOMATERIALS (BASEL, SWITZERLAND) 2023; 13:nano13091482. [PMID: 37177026 PMCID: PMC10179805 DOI: 10.3390/nano13091482] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/31/2023] [Revised: 04/22/2023] [Accepted: 04/24/2023] [Indexed: 05/15/2023]
Abstract
We investigate the behavior of the Josephson current in a system composed of a quantum dot (QD) sandwiched between two nanowires by using the nonequilibrium Green's function technique. We consider that the nanowires are in proximity to s-wave superconducror substrates, and Majorana bound states (MBSs) are induced at their ends. It is also assumed that the two nanowires are not aligned in the same orientation, but form a bent angle with respect to each other. It is found that when only one spin state on the QD is coupled to the left nanowire, the Josephson current is the typical sinusoidal function of the phase difference between the two nanowires. If both spin states hybridize to the MBSs with equal coupling strengths, the Josephson current then is not a sinusoidal function of the phase difference. In particular, when the bent angle between the two nanowires is π/2 and the two modes of the MBSs in each nanowire are decoupled from each other, the Josephson current is enhanced by about twenty times in magnitude as compared to the former case. Moreover, the simultaneously enhanced currents of the two spin directions are of the same magnitude but flow in opposite directions and they induce a large pure spin current. Our results also show that this abnormally enhanced Josephson current will be suppressed by a vertical magnetic field applied to the QD.
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Affiliation(s)
- Feng Chi
- School of Electronic and Information Engineering, UEST of China, Zhongshan Institute, Zhongshan 528400, China
| | - Qiang-Sheng Jia
- School of Electronic and Information Engineering, UEST of China, Zhongshan Institute, Zhongshan 528400, China
| | - Jia Liu
- School of Science, Inner Mongolia University of Science and Technology, Baotou 014010, China
| | - Qing-Guo Gao
- School of Electronic and Information Engineering, UEST of China, Zhongshan Institute, Zhongshan 528400, China
| | - Zi-Chuan Yi
- School of Electronic and Information Engineering, UEST of China, Zhongshan Institute, Zhongshan 528400, China
| | - Li-Ming Liu
- School of Electronic and Information Engineering, UEST of China, Zhongshan Institute, Zhongshan 528400, China
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Lima ACP, Ribeiro RCB, Correa JH, Deus F, Figueira MS, Continentino MA. Thermoelectric properties of topological chains coupled to a quantum dot. Sci Rep 2023; 13:1508. [PMID: 36707603 PMCID: PMC9883525 DOI: 10.1038/s41598-023-28491-6] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/12/2022] [Accepted: 01/19/2023] [Indexed: 01/28/2023] Open
Abstract
Topological one-dimensional superconductors can sustain zero energy modes protected by different kinds of symmetries in their extremities. Observing these excitations in the form of Majorana fermions is one of the most intensive quests in condensed matter physics. We are interested in another class of one-dimensional topological systems in this work, namely topological insulators. Which present symmetry-protected end modes with robust properties and do not require the low temperatures necessary for topological superconductivity. We consider a device in the form of a single electron transistor coupled to the simplest kind of topological insulators, namely chains of atoms with hybridized sp orbitals. We study the thermoelectric properties of the device in the trivial, non-trivial topological phases and at the quantum topological transition of the chains. We show that the device's electrical conductance and the Wiedemann-Franz ratio at the topological transition have universal values at very low temperatures. The conductance and thermopower of the device with diatomic sp-chains, at their topological transition, give direct evidence of fractional charges in the system. The former has an anomalous low-temperature behavior, attaining a universal value that is a consequence of the double degeneracy of the system due to the presence of zero energy modes. On the other hand, the system can be tuned to exhibit high values of the thermoelectric figure of merit and the power factor at high temperatures.
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Affiliation(s)
- A. C. P. Lima
- grid.418228.50000 0004 0643 8134Centro Brasileiro de Pesquisas Físicas, Rua Dr. Xavier Sigaud, 150, Urca, Rio de Janeiro, RJ 22290-180 Brazil
| | - R. C. Bento Ribeiro
- grid.418228.50000 0004 0643 8134Centro Brasileiro de Pesquisas Físicas, Rua Dr. Xavier Sigaud, 150, Urca, Rio de Janeiro, RJ 22290-180 Brazil
| | - J. H. Correa
- grid.441911.80000 0001 1818 386XUniversidad Tecnológica Del Perú, Nathalio Sanchez, 125, 15046 Lima, Peru
| | - Fernanda Deus
- grid.412211.50000 0004 4687 5267Universidade do Estado do Rio de Janeiro, Rodovia Presidente Dutra km 298, Resende, RJ 27537-000 Brazil
| | - M. S. Figueira
- grid.411173.10000 0001 2184 6919Instituto de Física, Universidade Federal Fluminense, Av. Litorânea s/N, Niterói, RJ 24210-340 Brazil
| | - Mucio A. Continentino
- grid.418228.50000 0004 0643 8134Centro Brasileiro de Pesquisas Físicas, Rua Dr. Xavier Sigaud, 150, Urca, Rio de Janeiro, RJ 22290-180 Brazil
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Ricco LS, Sanches JE, Marques Y, de Souza M, Figueira MS, Shelykh IA, Seridonio AC. Topological isoconductance signatures in Majorana nanowires. Sci Rep 2021; 11:17310. [PMID: 34453069 PMCID: PMC8397770 DOI: 10.1038/s41598-021-96415-3] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/07/2021] [Accepted: 08/04/2021] [Indexed: 11/23/2022] Open
Abstract
We consider transport properties of a hybrid device composed by a quantum dot placed between normal and superconducting reservoirs, and coupled to a Majorana nanowire: a topological superconducting segment hosting Majorana bound states (MBSs) at the opposite ends. It is demonstrated that if highly nonlocal and nonoverlapping MBSs are formed in the system, the zero-bias Andreev conductance through the dot exhibits characteristic isoconductance profiles with the shape depending on the spin asymmetry of the coupling between the dot and the topological superconductor. Otherwise, for overlapping MBSs with less degree of nonlocality, the conductance is insensitive to the spin polarization and the isoconductance signatures disappear. This allows to propose an alternative experimental protocol for probing the nonlocality of the MBSs in Majorana nanowires.
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Affiliation(s)
- L S Ricco
- Science Institute, University of Iceland, Dunhagi-3, 107, Reykjavik, Iceland.
| | - J E Sanches
- School of Engineering, Department of Physics and Chemistry, São Paulo State University (Unesp), 15385-000, Ilha Solteira, SP, Brazil
| | - Y Marques
- Department of Physics, ITMO University, 197101, St. Petersburg, Russia
| | - M de Souza
- Department of Physics, São Paulo State University (Unesp), IGCE, 13506-970, Rio Claro, SP, Brazil
| | - M S Figueira
- Instituto de Física, Universidade Federal Fluminense, 24210-340, Niterói, Rio de Janeiro, Brazil
| | - I A Shelykh
- Science Institute, University of Iceland, Dunhagi-3, 107, Reykjavik, Iceland
- Department of Physics, ITMO University, 197101, St. Petersburg, Russia
| | - A C Seridonio
- School of Engineering, Department of Physics and Chemistry, São Paulo State University (Unesp), 15385-000, Ilha Solteira, SP, Brazil
- Department of Physics, São Paulo State University (Unesp), IGCE, 13506-970, Rio Claro, SP, Brazil
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Chi F, Fu ZG, Liu J, Li KM, Wang Z, Zhang P. Thermoelectric Effect in a Correlated Quantum Dot Side-Coupled to Majorana Bound States. NANOSCALE RESEARCH LETTERS 2020; 15:79. [PMID: 32297030 PMCID: PMC7158981 DOI: 10.1186/s11671-020-03307-y] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/26/2019] [Accepted: 03/24/2020] [Indexed: 05/27/2023]
Abstract
We theoretically study the thermoelectric effect in a hybrid device composed by a topological semiconducting nanowire hosting Majorana bound states (MBSs) and a quantum dot (QD) connected to the left and right non-magnetic electrodes held at different temperatures. The electron-electron Coulomb interactions in the QD are taken into account by the non-equilibrium Green's function technique. We find that the sign change of the thermopower, which is useful for detecting the MBSs, will occur by changing the QD-MBS hybridization strength, the direct overlap between the MBSs at the opposite ends of the nanowire, and the system temperature. Large value of 100% spin-polarized or pure spin thermopower emerges even in the absence of Zeeman splitting in the QD or magnetic electrodes because the MBSs are coupled to electrons of only one certain spin direction in the QD due to the chiral nature of the Majorana fermions. Moreover, the magnitude of the thermopower will be obviously enhanced by the existence of MBSs.
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Affiliation(s)
- Feng Chi
- School of Electronic and Information Engineering, University of Electronic Science and Technology of China, Zhongshan Institute, Shiqi District Xueyuan Road No. 1, Zhongshan, 528402, China
| | - Zhen-Guo Fu
- Institute of Applied Physics and Computational Mathematics, No. 6 Huayuan Road, Haidian District, Beijing, 100088, China.
| | - Jia Liu
- School of Science, Inner Mongolia University of Science and Technology, Kundu District Alding Road No. 7, Baotou, 014010, China
| | - Ke-Man Li
- School of Science, Inner Mongolia University of Science and Technology, Kundu District Alding Road No. 7, Baotou, 014010, China
| | - Zhigang Wang
- Institute of Applied Physics and Computational Mathematics, No. 6 Huayuan Road, Haidian District, Beijing, 100088, China
| | - Ping Zhang
- Institute of Applied Physics and Computational Mathematics, No. 6 Huayuan Road, Haidian District, Beijing, 100088, China
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Álamo M, Muñoz E. Thermoelectric Efficiency of a Topological Nano-Junction. ENTROPY 2018; 20:e20050366. [PMID: 33265456 PMCID: PMC7512887 DOI: 10.3390/e20050366] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 03/24/2018] [Revised: 05/10/2018] [Accepted: 05/11/2018] [Indexed: 11/21/2022]
Abstract
We studied the non-equilibrium current, transport coefficients and thermoelectric performance of a nano-junction, composed by a quantum dot connected to a normal superconductor and a topological superconductor leads, respectively. We considered a one-dimensional topological superconductor, which hosts two Majorana fermion states at its edges. Our results show that the electric and thermal currents across the junction are highly mediated by multiple Andreev reflections between the quantum dot and the leads, thus leading to a strong nonlinear dependence of the current on the applied bias voltage. Remarkably, we find that our system reaches a sharp maximum of its thermoelectric efficiency at a finite bias, when an external magnetic field is imposed upon the junction. We propose that this feature can be used for accurate temperature sensing at the nanoscale.
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Affiliation(s)
- Manuel Álamo
- Physics Institute, Pontificia Universidad Católica de Chile, Vicuña Mackenna 4860, Santiago 7820436, Chile
| | - Enrique Muñoz
- Physics Institute, Pontificia Universidad Católica de Chile, Vicuña Mackenna 4860, Santiago 7820436, Chile
- Research Center for Nanotechnology and Advanced Materials CIEN-UC, Pontificia Universidad Católica de Chile, Vicuña Mackenna 4860, Santiago 7820436, Chile
- Correspondence: ; Tel.: +56-2-23547625
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