Competing many-body instabilities and unconventional superconductivity   in graphene
  The band structure of graphene exhibits van Hove singularities (VHS) at doping 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 at experimentally accessible temperatures. We study the competition between different many-body instabilities in graphene using functional renormalization group (FRG). We predict a rich phase diagram, which, depending on long range hopping as well as screening strength and absolute scale of the Coulomb interaction, 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. In the vicinity of the VHS, we find singlet d+id-wave as well as triplet f-wave SC phases. 
Maximilian Kiesel and Christian Platt and Werner Hanke and Dmitry A.   Abanin and Ronny Thomale
cond-mat.supr-con