Thermoelectric coefficients and the figure of merit for large open quantum dots

TL;DR

This paper analyzes the thermoelectric properties of large open quantum dots using random matrix theory, revealing universal behavior and optimal conditions for thermoelectric efficiency at specific temperatures and magnetic fields.

Contribution

It provides the first full distribution analysis of thermoelectric coefficients and figure of merit for large quantum dots under various conditions, highlighting universality and optimal parameters.

Findings

Thermoelectric coefficients peak at half the Thouless energy.

Maximum thermoelectric figure of merit occurs at negligible magnetic field.

Thermoelectric properties are universal, independent of lead asymmetry.

Abstract

We consider the thermoelectric response of chaotic or disordered quantum dots in the limit of phase-coherent transport, statistically described by random matrix theory. We calculate the full distribution of the thermoelectric coefficients (Seebeck $S$ and Peltier $\Pi$), and the thermoelectric figure of merit $ZT$, for large open dots at arbitrary temperature and external magnetic field, when the number of modes in the left and right leads ($N_{\rm L}$ and $N_{\rm R}$) are large. Our results show that the thermoelectric coefficients and $ZT$ are maximal when the temperature is half the Thouless energy, and the magnetic field is negligible. They remain small, even at their maximum, but they exhibit a type of universality at all temperatures, in which they do not depend on the asymmetry between the left and right leads $(N_{\rm L}-N_{\rm R})$, even though they depend on $(N_{\rm L}+N_{\rm R})$.