▎ 摘　　要

We present a perturbative method for calculating the optical Hall conductivity in a tight-binding framework based on the Kubo formalism. The method involves diagonalization only of the Hamiltonian in absence of the magnetic field, and thus avoids the computational problems usually arising due to the huge magnetic unit cells required to maintain translational invariance in the presence of a Peierls phase. A recipe for applying the method to numerical calculations of the magneto-optical response is presented. We apply the formalism to the case of ordinary and gapped graphene in a next-nearest-neighbor tight-binding model as well as graphene antidot lattices. In both cases, we find unique signatures in the Hall response that are not captured in continuum (Dirac) approximations. These include a nonzero optical Hall conductivity even when the chemical potential is at the Dirac point energy. Numerical results suggest that this effect should be measurable in experiments. DOI: 10.1103/PhysRevB.86.235438