Chaos in Andreev Billiards

TL;DR

This paper investigates the classical dynamics of Andreev billiards, a new type of billiard with a normal-superconductor interface, revealing integrability at zero magnetic field and chaos under magnetic influence, with implications for experimental realization.

Contribution

It introduces Andreev billiards as a novel class of billiards and analyzes their integrable and chaotic behavior using tangent map techniques.

Findings

Andreev billiards are integrable at zero magnetic field regardless of shape.

Applying a magnetic field induces chaos in these billiards.

Chaotic behavior is demonstrated in the Bunimovich stadium through Poincaré sections and Lyapunov exponents.

Abstract

A new type of classical billiard - the Andreev billiard - is investigated using the tangent map technique. Andreev billiards consist of a normal region surrounded by a superconducting region. In contrast with previously studied billiards, Andreev billiards are integrable in zero magnetic field, {\it regardless of their shape}. A magnetic field renders chaotic motion in a generically shaped billiard, which is demonstrated for the Bunimovich stadium by examination of both Poincar\'e sections and Lyapunov exponents. The issue of the feasibility of certain experimental realizations is addressed.