A Strongly Correlated Quantum-Dot Heat Engine with Optimal Performance: An Non-equilibrium Green's function Approach

TL;DR

This paper analytically investigates a strongly correlated quantum dot heat engine using non-equilibrium Green's functions, exploring how Coulomb interactions and system parameters influence thermoelectric performance, with results aligning with recent experiments.

Contribution

It introduces a higher-order approximation beyond Hubbard-1 for analyzing strongly correlated quantum dot heat engines in the infinite-U limit, providing deeper insights into their operation and optimization.

Findings

Higher-order approximation is necessary for Coulomb blockade regime analysis.

The infinite-U limit results align well with experimental data.

System parameters like tunneling and load resistance significantly affect performance.

Abstract

We present an analytical study of a strongly correlated quantum dot-based thermoelectric particle-exchange heat engine for both finite and infinite on-dot Coulomb interaction. Employing Keldysh's non-equilibrium Green's function formalism for different decoupling schemes in the equation of motion, we have analyzed the thermoelectric properties within the non-linear transport regime. As the simplest mean-field approximation is insufficient for analyzing thermoelectric properties in the Coulomb blockade regime, one needs to employ a higher-order approximation to study strongly correlated QD-based heat engines. Therefore initially, we have used the Hubbard-\Romannum{1} approximation to study the quantum dot level position ($\epsilon_d$), thermal gradient ($\Delta T$), and on-dot Coulomb interaction ($U$) dependence of the thermoelectric properties. Furthermore, as a natural extension, we have used an approximation beyond Hubbard-\Romannum{1} in the infinite-$U$ limit (strong on-dot Coulomb repulsion) to provide additional insight into the operation of a more practical quantum dot heat engine. Within this infinite-$U$ limit, we examine the role of the symmetric dot-reservoir tunneling ($\Gamma$) and external serial load resistance ($R$) in optimizing the performance of the strongly correlated quantum dot heat engine. Our infinite-$U$ results show a good quantitative agreement with recent experimental data for a quantum dot coupled to two metallic reservoirs.