Edge properties of the chiral d-wave superconducting state in doped graphene

TL;DR

This study explores how edges influence the chiral d-wave superconducting state in doped graphene, revealing enhanced edge order parameters, the absence of zero-energy edge states, and the emergence of Majorana fermions under certain conditions.

Contribution

It provides new insights into edge effects on chiral d-wave superconductivity in graphene, including the behavior of edge modes and conditions for Majorana fermion appearance.

Findings

Edge order parameter is enhanced and has d_{x^2-y^2} symmetry.

No zero-energy localized edge states are found.

Majorana fermions can appear at edges with Rashba spin-orbit coupling and Zeeman field.

Abstract

We investigate the effect of edges on the intrinsic electron-electron interaction driven d-wave superconducting state in graphene doped close to the van Hove singularity. While the bulk is in a chiral $d_{x^2-y^2}+id_{xy}$ state, the order parameter at any edge is enhanced and has $d_{x^2-y^2}$-symmetry, with a decay length strongly increasing with weakening superconductivity. No graphene edge is pair breaking for the $d_{x^2-y^2}$ state and we never find any localized zero-energy edge states. We find two chiral edge modes which carry a spontaneous, but not quantized, quasiparticle current related to the zero-energy momentum. Moreover, for realistic values of the Rashba spin-orbit coupling, a Majorana fermion appears at the edge when tuning a Zeeman field.