Transparency of graphene and other direct-gap two-dimensional materials

Abstract

The optical properties of graphene are among its remarkable characteristics. Measurements have found that the opacity of a single graphene layer for infrared and visible light is simply equal to $\ensuremath{\pi}$ times the fine-structure constant. Explanations of this beautiful relation have tended to view it as a consequence of the material's Dirac-like band structure. However, in this paper the authors emphasize that the interband absorption rate must be treated by using the underlying nonrelativistic Hamiltonian, not the quasimomentum state label of the bands. They employ both a straightforward model and a tight-binding calculation to show that the opacity of graphene follows not from its celebrated linear dispersion relation but from the fact that it is a two-dimensional material. The same characteristic is therefore present in semiconductor membranes (as revealed by recent experiments) and other two-dimensional systems. This work focuses attention on the universality that reduced dimensionality bestows on optical absorption.