Excitation gap of a graphene channel with superconducting boundaries

Abstract

We calculate the density of states of electron-hole excitations in a superconductor normal-metal superconductor (SNS) junction in graphene, in the long-junction regime that the superconducting gap is much larger than the Thouless energy ET=hv/d (with v the carrier velocity in graphene and d the separation of the NS boundaries). If the normal region is undoped, the excitation spectrum consists of neutral modes that propagate along the boundaries transporting energy but no charge. These Andreev modes are a coherent superposition of electron states from the conduction band and hole states from the valence band, coupled by specular Andreev reflection at the superconductor.