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(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 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.