Tight-binding study of the magneto-optical properties of gapped graphene

TL;DR

This paper investigates the magneto-optical properties of gapped graphene using both Dirac and tight-binding models, revealing how a large gap suppresses magnetic effects and highlighting the importance of orbital overlap in optical Hall conductivity.

Contribution

It provides a comparative analysis of Dirac and tight-binding models for gapped graphene's optical properties under magnetic fields, emphasizing the impact of orbital overlap.

Findings

Large gap suppresses magnetic field effects on optical properties

Orbital overlap significantly influences optical Hall conductivity

Dirac and tight-binding models show consistent results in certain regimes

Abstract

We study the optical properties of gapped graphene in presence of a magnetic field. We consider a model based on the Dirac equation, with a gap introduced via a mass term, for which analytical expressions for the diagonal and Hall optical conductivities can be derived. We discuss the effect of the mass term on electron-hole symmetry and $\pi$-$\pi^*$ symmetry and its implications for the optical Hall conductivity. We compare these results with those obtained using a tight-binding model, in which the mass is modeled via a staggered potential and a magnetic field is included via a Peierls substitution. Considering antidot lattices as the source of the mass term, we focus on the limit where the mass term dominates the cyclotron energy. We find that a large gap quenches the effect of the magnetic field. The role of overlap between neighboring $\pi$ orbitals is investigated, and we find that the overlap has pronounced consequences for the optical Hall conductivity that are missed in the Dirac model.