Graphene Andreev Billiards

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.

5 pages, 3 figures

References in corpus (11)

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• The electronic properties of graphene
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• Excitation gap of a graphene channel with superconducting boundaries
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• Andreev billiards
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