Chaos in Andreev Billiards
Ioan Kosztin, Dmitrii L. Maslov, Paul M. Goldbart

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.
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