Non-equilibrium thermoelectric transport across normal metal–quantum dot–superconductor hybrid system within the Coulomb blockade regime

Abstract

A detailed investigation of the non-equilibrium steady-state electric and thermoelectric transport properties of a quantum dot coupled to the normal metallic and s-wave superconducting reservoirs (N-QD-S) are provided within the Coulomb blockade regime. Using non-equilibrium Keldysh Green’s function formalism, initially, various model parameter dependence of thermoelectric transport properties are analysed within the linear response regime. It is observed that the single-particle tunnelling close to the superconducting gap edge can generate a relatively large thermopower and figure of merit. Moreover, the Andreev tunnelling plays a significant role in the suppression of thermopower and figure of merit within the gap region. Further, within the non-linear regime, we discuss two different situations, i.e., the finite voltage biasing between isothermal reservoirs and the finite thermal gradient in the context of thermoelectric heat engine. In the former case, it is shown that the sub-gap Andreev heat current can become finite beyond the linear response regime and play a vital role in asymmetric heat dissipation and thermal rectification effect for low voltage biasing. The rectification of heat current is enhanced for strong on-dot Coulomb interaction and at low background thermal energy. In the latter case, we study the variation of thermovoltage, thermopower, maximum power output, and corresponding efficiency with the applied thermal gradient. These results illustrate that hybrid superconductor-quantum dot nanostructures are a promising candidate for low-temperature thermal applications.

Phase and Thermal Driven Transport across T-Shaped Double Quantum Dot Josephson Junction

“…At finite temperature the average superconducting pairing correlation terms i.e. d † iσ d † iσ and d iσ d iσ are negligible and only average occupation n diσ need to be calculated self-consistently [40,43,44]. Thus within the HF mean field approximation the Hamiltonian in equation ( 4) is simplified as…”

“…Recently, very few studies has been conducted on the thermal transport properties of quantum dot-based Josephson junctions i.e when both the leads are superconducting [40,41]. Further, the thermoelectric transport properties of systems where the quantum dot is coupled between normal metal and BCS superconductor (N-QD-S) [42,43,44] and ferromagnet and BCS superconductor (F-QD-S) [45,46,47,48] have been studied recently. Further the thermoelectric transport properties of multi-dot and multi-terminal systems with one superconducting lead are also gaining attention [49,50,51,52,53].…”

Superior thermoelectric properties through triangular triple quantum dots (TTQD) attached to one metallic and one superconducting lead

“…30,[48][49][50][51][52] The few recent studies on two-terminal devices have conrmed that the thermoelectric properties of QD hybrid systems coupled to one conventional lead (metallic or ferromagnetic lead) and one superconducting lead, are remarkably better than those coupled to two conventional leads. 16,28,29,45,47,53 It has been found that the thermoelectric efficiency of the former can even reach several times or even tens of times that of the latter, by comprehensively regulating the superconducting gap, interdot coupling and asymmetric parameters, which can also be additionally enhanced by the interference effect and interdot Coulomb interaction. This is mainly attributed to the unique tunnelling mechanism and high density of states distribution near superconducting gap edges.…”

“…The very high density of states near superconducting gap edges changes rapidly with energy, which is mainly responsible for the high thermopower and low thermal conductivity near the superconducting gap edges. However, recent studies have mainly focused on single quantum dot, 16,47 double quantum dot 28,53 and parallel coupled triple quantum dot systems, 29,45 the thermoelectric properties of TTQD coupling to one metallic-metallic and one superconducting lead have not been studied yet.…”

Nonlocal quantum heat engines made of hybrid superconducting devices

“…Recent approaches to this problem exploit tunnel junctions between unequal superconducting electrodes using nonlinearities [4][5][6] or single-electron transistors [7][8][9], hybrid normal-superconductor junctions including quantum dot energy filters [10][11][12][13][14][15], spin-dependent scattering [16][17][18][19][20][21][22][23][24][25][26], photon-assisted tunneling [27], or interference phenomena [28,29]. The gapped density of states has also been successfully used for cooling [30,31] and for power sources [32,33].…”