Induced superconductivity distinguishes chaotic from integrable billiards

TL;DR

This paper demonstrates that proximity-induced superconductivity creates a spectral gap in chaotic billiards but not in integrable rectangular billiards, highlighting fundamental differences in their quantum behaviors.

Contribution

It introduces a theoretical distinction between chaotic and integrable billiards based on their spectral response to superconducting proximity using random-matrix theory.

Findings

Chaotic billiards develop a spectral gap due to superconductivity.

Integrable billiards remain gapless when coupled to a superconductor.

Spectral behavior distinguishes chaotic from integrable quantum systems.

Abstract

Random-matrix theory is used to show that the proximity to a superconductor opens a gap in the excitation spectrum of an electron gas confined to a billiard with a chaotic classical dynamics. In contrast, a gapless spectrum is obtained for a non-chaotic rectangular billiard, and it is argued that this is generic for integrable systems.