Semiclassical theory in Andreev billiards: beyond the diagonal approximation

TL;DR

This paper develops a new semiclassical method for analyzing Andreev billiards that extends beyond the diagonal approximation, aiming to better understand the density of states and conductance in these systems.

Contribution

It introduces a novel approach to semiclassical sums in Andreev billiards that surpasses the diagonal approximation, addressing off-diagonal corrections and their effects.

Findings

Method allows calculation beyond the diagonal approximation.

Off-diagonal corrections may explain the density of states gap.

Provides insights into semiclassical analysis of superconducting billiards.

Abstract

Recently semiclassical approximations have been successfully applied to study the effect of a superconducting lead on the density of states and conductance in ballistic billiards. However, the summation over classical trajectories involved in such theories was carried out using the intuitive picture of Andreev reflection rather than the semiclassical reasoning. We propose a method to calculate the semiclassical sums which allows us to go beyond the diagonal approximation in these problems. In particular, we address the question of whether the off-diagonal corrections could explain the gap in the density of states of a chaotic Andreev billiard.