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}).
Significance of an external magnetic field on two-phonon processes in gated lateral semiconductor quantum dots
