Edge Properties and Majorana Fermions in the Proposed Chiral d-Wave Superconducting State of Doped Graphene

Annica M. Black-Schaffer

doi:10.1103/PhysRevLett.109.197001

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Edge Properties and Majorana Fermions in the Proposed Chiral d-Wave Superconducting State of Doped Graphene

Annica M. Black-Schaffer

DOI 10.1103/PhysRevLett.109.197001 · Physical Review Letters

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Abstract

We investigate the effect of edges on the intrinsic d-wave superconducting state in graphene doped close to the van Hove singularity. While the bulk is in a chiral dx2−y2+idxy state, the order parameter at any edge is enhanced and has dx2−y2-symmetry, with a decay length strongly increasing with weakening superconductivity. No graphene edge is pair breaking for the dx2−y2 state, and there are no 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.