The transparency of graphene and other direct-gap two dimensional materials

TL;DR

This paper clarifies the optical transparency of graphene and similar 2D materials by emphasizing the role of canonical momentum coupling and density of states, challenging previous models based solely on linear dispersion.

Contribution

It introduces a physically consistent explanation for the optical properties of graphene, applicable to other 2D materials, focusing on canonical momentum and density of states rather than dispersion relations.

Findings

Optical transparency of graphene is explained by canonical momentum coupling.

The model predicts a van Hove singularity peak at higher energies.

The absorption spectrum shows asymmetry consistent with experimental data.

Abstract

Graphene and other two-dimensional materials display remarkable optical properties, including a simple light transparency of $T \approx 1 - \pi \alpha$ for light in the visible region. Most theoretical rationalizations of this "universal" opacity employ a model coupling light to the electron's crystal momentum and put emphasis on the linear dispersion of the graphene bands. However, such a formulation of interband absorption is not allowable within band structure theory, because it conflates the crystal momentum label with the canonical momentum operator. We show that the physical origin of the optical behavior of graphene can be explained within a straightforward picture with the correct use of canonical momentum coupling. Its essence lies in the two-dimensional character of the density of states rather than in the precise dispersion relation, and therefore the discussion is applicable to other systems such as semiconductor membranes. At higher energies the calculation predicts a peak corresponding to a van Hove singularity as well as a specific asymmetry in the absorption spectrum of graphene, in agreement with previous results.