Quantum Monte Carlo study of magnetic and superconducting properties of graphene

We apply quantum Monte Carlo technique to address the issue of high controllability of ferromagnetism in graphene and the issue of electron correlation driven superconductivity in graphene, by simulating the t − U − V Hubbard model on a honeycomb lattice. In the region of low electron band filling below the Van Hove singularity, the system shows a short‐range ferromagnetic correlation, which is strengthened slightly by the on‐site Coulomb interaction and markedly by the next nearest‐neighbor hoping integral. The strong dependence of ferromagnetism on the electron band filling can be manipulated by applying electric gate voltage. For V =0 and close to the half filling, we find that pairing with d + id symmetry dominates pairing with extended‐ s symmetry. However, as the system size increases the long‐range part of the d + id pairing correlation decreases and tends to vanish in the thermodynamic limit. An inclusion of nearest‐neighbor interaction V, either repulsive or attractive, has a small effect on the extended‐ s pairing correlation, but strongly suppresses the d + id pairing correlation.