Non-equilibrium thermoelectric transport across normal metal-Quantum dot-Superconductor hybrid system within the Coulomb blockade regime

TL;DR

This paper investigates non-equilibrium thermoelectric transport in a normal metal-quantum dot-superconductor system within the Coulomb blockade regime, revealing significant effects of Andreev tunneling and Coulomb interactions on thermoelectric properties and heat rectification.

Contribution

It provides a detailed analysis of thermoelectric transport in N-QD-S systems using non-equilibrium Green's functions, highlighting the roles of Andreev processes and Coulomb interactions in both linear and nonlinear regimes.

Findings

Single-particle tunneling near the superconducting gap enhances thermopower.

Andreev tunneling suppresses thermopower within the gap.

Sub-gap Andreev heat current influences thermal rectification and heat dissipation.

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 promising candidatess for low-temperature thermal applications.