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

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 ℏ→0, which opens up a gap Egap in the excitation spectrum. The time scale ℏ/Egap∝α−1lnℏ (with α the Lyapunov exponent) is the Ehrenfest time, the characteristic time scale of quantum chaos.