Low frequency optical conductivity in graphene and in other scale-invariant two-band systems

TL;DR

This paper analyzes the optical conductivity in two-band, scale-invariant systems like graphene, revealing a universal power law dependence on frequency determined by system dimension and dynamical exponent.

Contribution

It derives a general power law formula for optical conductivity in non-interacting two-band systems with pseudospin-momentum locking, highlighting universal behavior in 2D systems.

Findings

2D systems with pseudospin-momentum locking have frequency-independent conductivity.

Optical conductivity follows a power law with exponent (d-2)/z.

Results apply to systems like graphene at half filling.

Abstract

We investigate optical transitions of non-interacting electron systems consisting of two symmetric energy bands touching each other at the Fermi energy (e.g. graphene at half filling). Optical conductivity is obtained using Kubo formula at zero temperature. We show that for particles whose pseudospin direction is determined solely by the direction of their momentum, the optical conductivity has power law frequency dependence with the exponent $(d-2)/z$ where $d$ is the dimension of the system and $z$ is the dynamical exponent. According to our result two-dimensional systems with the above pseudospin characteristics always exhibit frequency-independent optical conductivity.