Non-universal features in the quasi-particle excitation spectra of Andreev billiards and wires

Abstract

We study non-universal features of the quasi-particle excitation spectra of normal-conducting mesoscopic structures, whose classical dynamics are chaotic, and which are coupled to a superconducting lead. In the first part we demonstrate the importance of non-universal contributions in Andreev billiards when the ergodic time of the billiard is of the same order as the mean escape time. Non-universality introduces additional oscillations in the quasi-particle excitation spectrum which are related to the decaying modes of the classical evolution operator in the closed billiard. In the second part we demonstrate that in a long rough wire coupled to a superconductor classical anomalous diffusion modifies the energy scale below which universality holds as a function of the geometrical parameters in comparison to billiards with a narrow superconducting lead.