Graphene in a Uniform Magnetic Field

We study monolayer graphene in a uniform magnetic field in the absence and presence of interactions. In the non-interacting limit for 1/q flux quanta per unit cell, the central two bands have 2q Dirac points in the Brillouin zone for nearest neighbor hopping. The Dirac points can be gapped out with a 2^nd nearest neighbor hopping (t₂) and the central two bands pick up large Chern numbers. If we break the inversion symmetry by introducing a staggered potential (m) Chern number of the central bands becomes 1. Competition between t₂ and m leads to a topological phase transition.

In the case of interacting graphene, there are at least three different competing phases when we consider Hubbard interaction and nearest neighbor spin-spin interaction. In the continuum limit, the theory has been studied before. It has been found that there exist four competing phases namely, ferromagnetic, antiferromagnetic, charge density wave, and Kekule distortion phase[1]. In our study, we attempt to understand all the phases in the lattice model. We investigate if there are phases in the lattice model not found in the continuum limit.

[1] M. Kharitonov, PRB 85, 155439(2012)