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

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 ($N_{\mathrm{L}}$ and $N_{\mathrm{R}}$) 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 $(N_{\mathrm{L}}-N_{\mathrm{R}})$, even though they depend on $(N_{\mathrm{L}}+N_{\mathrm{R}})$.

arXiv comment25 pages [final version - minor typos fixed]

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