Effect of Holstein phonons on the electronic properties of graphene

TL;DR

This paper investigates how Holstein phonons influence the electronic properties of graphene, finding minimal effects on Fermi velocity and optical conductivity, thus supporting the validity of the Boltzmann approach for this system.

Contribution

It provides a detailed analysis of Holstein phonon effects on graphene's electronic properties using self-energy calculations and optical conductivity, concluding their negligible impact.

Findings

Fermi velocity renormalization of about 1%

Negligible effects of Holstein phonons on optical conductivity

Validation of Boltzmann approach for high-energy optical phonons

Abstract

We obtain the self-energy of the electronic propagator due to the presence of Holstein polarons within the first Born approximation. This leads to a renormalization of the Fermi velocity of one percent. We further compute the optical conductivity of the system at the Dirac point and at finite doping within the Kubo-formula. We argue that the effects due to Holstein phonons are negligible and that the Boltzmann approach which does not include inter-band transition and can thus not treat optical phonons due to their high energy of $\hbar\omega_0\sim0.1-0.2$eV, remains valid.