Ehrenfest-time-dependent excitation gap in a chaotic Andreev billiard

Abstract

A semiclassical theory is developed for the appearance of an excitation gap in a ballistic chaotic cavity connected by a point contact to a superconductor. Diffraction at the point contact is a singular perturbation in the limit $\hbar\to 0$, which opens up a gap $E_{\rm gap}$ in the excitation spectrum. The time scale $\hbar/E_{\rm gap}\proptoα^{-1}\ln\hbar$ (with $α$ the Lyapunov exponent) is the Ehrenfest time, the characteristic time scale of quantum chaos.