Graphene Andreev Billiards

TL;DR

This paper investigates the energy spectra of graphene-based Andreev billiards, demonstrating a mapping to normal metal billiards and deriving a semiclassical quantization rule, with results matching well with exact calculations.

Contribution

It introduces a semiclassical quantization rule for graphene Andreev billiards and shows their spectra align with those of normal metal-superconductor systems.

Findings

Semiclassical and exact spectra agree well

Mapping to normal metal-superconductor billiards

Effective quantization rule derived

Abstract

We studied the energy levels of graphene based Andreev billiards consisting of a superconductor region on top of a monolayer graphene sheet. For the case of Andreev retro-reflection we show that the graphene based Andreev billiard can be mapped to the normal metal-superconducting billiards with the same geometry. We also derived a semiclassical quantization rule in graphene based Andreev billiards. The exact and the semiclassically obtained spectrum agree very well both for the case of Andreev retro-reflection and specular Andreev reflection.