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

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 d(x2-y2) + id(xy) state, the order parameter at any edge is enhanced and has d(x2-y2)-symmetry, with a decay length strongly increasing with weakening superconductivity. No graphene edge is pair breaking for the d(x2-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.