Optical Hall conductivity in bulk and nanostructured graphene beyond the Dirac approximation

TL;DR

This paper introduces a perturbative method for calculating optical Hall conductivity in graphene structures that overcomes computational challenges and reveals unique Hall response features not captured by Dirac approximations.

Contribution

A new perturbative approach for magneto-optical calculations in tight-binding models that avoids large magnetic unit cells and captures novel Hall effects.

Findings

Non-zero optical Hall conductivity at Dirac point energy.

Unique Hall signatures in gapped graphene and antidot lattices.

Predictions are experimentally measurable.

Abstract

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 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 neighbour tight-binding model as well as graphene antidot lattices. In both case, we find unique signatures in the Hall response, that are not captured in continuum (Dirac) approximations. These include a non-zero 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.