Conductance and Thermopower of Ballistic Andreev Cavities

TL;DR

This paper investigates how superconductors influence the conductance and thermopower of ballistic chaotic quantum dots, revealing phase-dependent effects and reproducing random matrix theory results through semiclassical analysis.

Contribution

It introduces a trajectory-based semiclassical approach to analyze conductance and thermopower in Andreev cavities, including phase effects and comparison with random matrix theory.

Findings

Superconductors significantly affect conductance based on channel ratios.

Conductance corrections depend on phase difference between two superconductors.

Thermopower is antisymmetric with respect to superconductor phase difference.

Abstract

When coupling a superconductor to a normal conducting region the physical properties of the system are highly affected by the superconductor. We will 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 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 will also see 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.