Excitation gap of a graphene channel with superconducting boundaries

TL;DR

This paper investigates the excitation spectrum and phase-dependent thermal conductance of a graphene SNS junction, revealing neutral Andreev modes with a phase-dependent gap in the undoped case.

Contribution

It provides a theoretical analysis of Andreev modes in graphene SNS junctions, highlighting the phase-dependent excitation gap and its dependence on doping levels.

Findings

Neutral Andreev modes propagate along boundaries in undoped graphene.

The excitation gap depends on the superconducting phase difference.

At high doping, the excitation gap closes, recovering gapless states.

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. 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. The lowest Andreev mode has an excitation gap, which depends on the superconducting phase difference across the SNS graphene channel. At high doping the excitation gap vanishes and the usual gapless density of states of Andreev levels is recovered. We use our results to calculate the superconducting phase dependence of the thermal conductance of the graphene channel.