Abstract

We show that the d+id superconducting state, which has no known experimental realizations, can be realized in strongly doped graphene. We consider graphene that is doped to theMpoint ofthe Brilliouin zone, where the Fermi surface nesting and the divergent density of states can produce interaction driven instabilities to exotic phases with high energy scales. Analyzing the competition between various ordering tendencies within a renormalisation group framework, we find that the leading instability is to d-wave superconductivity, for any choice of weak repulsive interactions. The dx2−y2 and dxy superconducting states have the same critical temperature Tc. Analysis of the competition of these orders below Tc reveals that both orders co-exist to produce d+id superconductivity.