Density of States and Energy Gap in Andreev Billiards

TL;DR

This paper investigates the local density of states in semiclassical Andreev billiards, revealing that a gap near the Fermi energy appears in chaotic billiards but not in regular ones like square or circular billiards.

Contribution

It demonstrates the emergence of an energy gap in chaotic Andreev billiards through numerical analysis, contrasting with the absence of such a gap in regular billiards.

Findings

Energy gap appears in chaotic billiards near Fermi energy.

No gap is observed in square and circular billiards.

Numerical methods effectively distinguish between chaotic and regular billiard spectra.

Abstract

We present numerical results for the local density of states in semiclassical Andreev billiards. We show that the energy gap near the Fermi energy develops in a chaotic billiard. Using the same method no gap is found in similar square and circular billiards.