Competing many-body instabilities and unconventional superconductivity in graphene

The band structure of graphene exhibits van Hove singularities (VHSs) at dopings x=±1/8 away from the Dirac point. Near the VHS, interactions effects, enhanced due to the large density of states, can give rise to various many-body phases. We study the competition between many-body instabilities in graphene using the functional renormalization group. We predict a rich phase diagram, which, depending on band structure as well as the range and scale of Coulomb interactions, contains a $d+id$-wave superconducting (SC) phase, or a spin-density-wave phase at the VHS. The $d+id$ state is expected to exhibit quantized charge and spin Hall response, as well as Majorana modes bound to vortices. Nearby the VHS, we find singlet $d+id$-wave and triplet f-wave SC phases.