Thermoelectric study of dissipative quantum dot heat engines

TL;DR

This study investigates the thermoelectric behavior of a dissipative quantum dot heat engine, analyzing how electron-phonon interactions and phonon bath couplings affect efficiency and heat flow direction.

Contribution

It provides a detailed analysis of thermoelectric performance considering out-of-equilibrium phonons and strong phonon-bath coupling in quantum dot heat engines.

Findings

n-type heat engine outperforms p-type in thermoelectric efficiency

dot temperature deviates from bath temperature with stronger electron-phonon coupling

phonon heat currents are controlled by the dot temperature, affecting performance

Abstract

This paper examines the thermoelectric response of a dissipative quantum dot heat engine based on the Anderson-Holstein model in two relevant operating limits: (i) when the dot phonon modes are out of equilibrium, and (ii) when the dot phonon modes are strongly coupled to a heat bath. In the first case, a detailed analysis of the physics related to the interplay between the quantum dot level quantization, the on-site Coulomb interaction and the electron-phonon coupling on the thermoelectric performance reveals that an n-type heat engine performs better than a p-type heat engine. In the second case, with the aid of the dot temperature estimated by incorporating a {\it{thermometer bath}}, it is shown that the dot temperature deviates from the bath temperature as electron-phonon interaction becomes stronger. Consequently, it is demonstrated that the dot temperature controls the direction of phonon heat currents, thereby influencing the thermoelectric performance. Finally, the conditions on the maximum efficiency with varying phonon couplings between the dot and all the other macroscopic bodies are analyzed in order to reveal the nature of the optimum junction.