Coherent Thermoelectric Effects in Mesoscopic Andreev Interferometers

We investigate thermoelectric transport through Andreev interferometers. We show that the ratio of the thermal and the charge conductance exhibits large oscillations with the phase difference $\phi$ between the two superconducting contacts, and that the Wiedemann-Franz law holds only when $\phi=\pi$. A large average thermopower furthermore emerges whenever there is an asymmetry in the dwell times to reach the superconducting contacts. When this is the case, the thermopower is odd in $\phi$. In contrast, when the average times to reach either superconducting contact are the same, the average thermopower is zero, however mesoscopic effects (analogous to universal conductance fluctuations) lead to a sample-dependent thermopower which is systematically even in $\phi$.