  Graphene is at the forefront of condensed matter sciences, because of a
variety of interesting phenomena it supports. If graphene could support high Tc
superconductivity, after doping for example, it will make it even more
valuable. Some authors have suggested possibility of superconductivity in
graphite like systems. However, an early suggestion of one of us (Baskaran) was
unique in the sense it combined Pauling's classic idea of resonating valence
bond physics with band theory to obtain some exciting results for
superconductivity. Black-Schaffer and Doniach took this approach further and
found an unconventional d + id order parameter. To sharpen our theory and get
more convincing and reliable results for superconductivity, we introduce a
correlated variational BCS ground state wavefunction and perform extensive
Monte Carlo study of the repulsive Hubbard model on the honeycomb lattice. We
find that undoped graphene is not a superconductor, consistent with experiments
and also mean field results. Interestingly, an appreciable superconducting
order is obtained around an optimal doping. This result and a supportive slave
particle analysis together suggest the possibility of high temperature
superconductivity in doped graphene.
