SciPost Phys. 6, 012 (2019) ·
published 24 January 2019

· pdf
We consider the thermoelectric response of chaotic or disordered quantum dots
in the limit of phasecoherent 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 $(N_{\rm L}+N_{\rm R})$.