Thermoelectric performance of a minimally nonlinear voltage probe and voltage-temperature probe heat engine with broken time-reversal symmetry

TL;DR

This paper analyzes the efficiency limits of nonlinear thermoelectric heat engines with broken time-reversal symmetry, revealing universal bounds on efficiency at maximum power that can surpass classical limits, through analytical and numerical methods.

Contribution

It introduces a framework incorporating nonlinear dissipation into thermoelectric models with broken TRS, deriving universal efficiency bounds and analyzing their implications.

Findings

Universal bounds on efficiency at maximum power surpassing Curzon-Ahlborn limit.

Broken TRS and nonlinear dissipation influence engine performance.

Voltage probe generally yields higher power; voltage-temperature probe offers higher efficiency.

Abstract

We investigate the thermoelectric performance of minimally nonlinear irreversible heat engines with broken time-reversal symmetry (TRS), realized through voltage and voltage-temperature probe configurations. Our framework extends the Onsager relations by incorporating a nonlinear power dissipation term into the heat current. We derive and analyze analytical expressions for the efficiency at a given power and the efficiency at maximum power (EMP), expressed in terms of asymmetry parameters and generalized figures of merit. Our analysis reveals that the combined effects of broken TRS and nonlinear dissipation give rise to two universal bounds on the EMP that can surpass the Curzon-Ahlborn (CA) limit. Although these bounds share a similar analytical form, differences in Carnot efficiency and asymmetry parameters lead to distinct operational characteristics, as shown through numerical simulations. We consider a triple-quantum-dot Aharonov-Bohm heat engine incorporating either a voltage probe or a voltage-temperature probe. In both cases, TRS is broken by the magnetic flux. However, the voltage-temperature probe requires an additional anisotropy in the system for its TRS-breaking effects to significantly influence transport. We examine the role of this anisotropy in enhancing performance. Our results show that the EMP and efficiency at a given power can be enhanced by increasing the strength of nonlinear power dissipation, even though the output power remains unchanged. The voltage probe configuration generally yields higher power, while the voltage-temperature probe is more efficient, except in certain regimes where large asymmetries and high figures of merit allow the voltage probe setup to outperform.