Opacity of graphene independent of light frequency and polarization due to the topological charge of the Dirac points

TL;DR

This paper explains that graphene's opacity, approximately equal to π times the fine-structure constant, is topologically protected and independent of light frequency and polarization, revealing the topological charge visually.

Contribution

It demonstrates that the opacity of graphene and similar topological materials is topologically protected and directly related to the topological charge of Dirac points, independent of light properties.

Findings

Graphene's opacity is approximately π times the fine-structure constant.

Opacity remains roughly independent of light frequency and polarization.

Topological surface states in 3D insulators also exhibit this opacity, visible in infrared.

Abstract

The opacity of graphene is known to be approximately given by the fine-structure constant $\alpha$ times $\pi$. We point out the fact that the opacity is roughly independent of the frequency and polarization of the light can be attributed to the topological charge of the Dirac points. As a result, one can literally see the topological charge by naked eyes from the opacity of graphene, and moreover it implies that the fine-structure constant is topologically protected. A similar analysis suggests that 3D topological insulator thin films of any thickness also have opacity $\pi\alpha$ in the infrared region owing to the topological surface states, indicating that one can see the surface states by naked eyes through an infrared lens. For 3D Dirac or Weyl semimetals, the optical absorption power is linear to the frequency in the infrared region, with a linearity given by the fine-structure constant and the topological charge of Weyl points.