Effect of electron-phonon interaction on spectroscopies in graphene

TL;DR

This paper investigates how electron-phonon interactions influence the electronic density of states, optical conductivity, and quasiparticle properties in graphene, revealing unique phonon-induced features due to graphene's Dirac electron dynamics.

Contribution

It provides a detailed analysis of electron-phonon effects on graphene's spectroscopic properties, highlighting differences from metals with constant density of states.

Findings

Phonon structures persist in graphene's DOS due to its linear energy dependence.

Optical conductivity exhibits a shift in the energy scale and spectral weight transfer caused by electron-phonon interactions.

Universal conductivity is reduced at high energies, with phonon-assisted features and suppressed interband transitions.

Abstract

We calculate the effect of the electron-phonon interaction on the electronic density of states (DOS), the quasiparticle properties and on the optical conductivity of graphene. In metals with DOS constant on the scale of phonon energies, the electron-phonon renormalizations drop out of the dressed DOS, however, due to the Dirac nature of the electron dynamics in graphene, the band DOS is linear in energy and phonon structures remain, which can be emphasized by taking an energy derivative. There is a shift in the chemical potential and in the position in energy of the Dirac point. Also, the DOS can be changed from a linear dependence out of value zero at the Dirac point to quadratic out of a finite value. The optical scattering rate $1/\tau$ sets the energy scale for the rise of the optical conductivity from its universal DC value $4e^2/\pi h$ (expected in the simplest theory when chemical potential and temperature are both $\ll 1/2\tau$) to its universal AC background value $(\sigma_0=\pi e^2/2h)$. As in ordinary metals the DC conductivity remains unrenormalized while its AC value is changed. The optical spectral weight under the intraband Drude is reduced by a mass renormalization factor as is the effective scattering rate. Optical weight is transferred to an Holstein phonon-assisted side band. Due to Pauli blocking the interband transitions are sharply suppressed, but also nearly constant, below twice the value of renormalized chemical potential and also exhibit a phonon-assisted contribution. The universal background conductivity is reduced below $\sigma_0$ at large energies.