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 \PiΠ), 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}).