Optical conductivity, Drude weight and plasmons in twisted graphene bilayers

TL;DR

This paper numerically investigates the optical conductivity, Drude weight, and plasmons in twisted graphene bilayers, revealing how these properties depend on twist angle, doping, and temperature, with implications for electronic transport and plasmonic behavior.

Contribution

It introduces a numerical method using the regularized Kramers-Kronig relation to analyze optical properties across arbitrary twist angles and doping levels in twisted bilayer graphene.

Findings

Drude weight follows the density of states shell structure.

Transport gap appears at certain twist angles and finite chemical potential.

Low doping exhibits acoustic interband plasmons and van Hove singularity transitions.

Abstract

We numerically calculate the optical conductivity of twisted graphene bilayers within the continuum model. To obtain the imaginary part, we employ the regularized Kramers-Kronig relation allowing us to discuss arbitrary twist angles, chemical potential and temperature. We find that the Drude weight $D$ as function of the chemical potential $\mu$ closely follows the shell structure of twisted bilayer displayed by the density of states. For certain angles, this results in a transport gap D=0 at finite $\mu$. We also discuss the loss function which, for low doping, is characterized by acoustic interband "plasmons" and transitions close to the van Hove singularities. For larger doping, the plasmon mode of decoupled graphene bilayer is recovered that is damped especially for small wave numbers.