Conductance and thermopower of ballistic Andreev cavities

When coupling a superconductor to a normal conducting region the physical properties of the system are highly affected by the superconductor. We investigate the effect of one or two superconductors on the conductance of a ballistic chaotic quantum dot to leading order in the total channel number using trajectory-based semiclassics. The results show that the effect of one superconductor on the conductance is of the order of the number of channels and that the sign of the quantum correction from the Drude conductance depends on the particular ratios of the numbers of channels of the superconducting and normal conducting leads. In the case of two superconductors with the same chemical potential, we additionally study how the conductance and the sign of quantum corrections are affected by their phase difference. As far as random matrix theory results exist these are reproduced by our calculations. Furthermore, in the case that the chemical potential of the superconductors is the same as that of one of the two normal leads the conductance shows, under certain conditions, similar effects as a normal metal-superconductor junction. The semiclassical framework is also able to treat the thermopower of chaotic Andreev billiards consisting of one chaotic dot, two normal leads, and two superconducting islands and shows it to be antisymmetric in the phase difference of the superconductors.