Dynamical polarizability of graphene beyond the Dirac cone approximation

TL;DR

This paper calculates the dynamical polarizability of graphene considering the entire Brillouin zone, revealing deviations from the Dirac cone approximation at specific energies and directions, impacting the understanding of graphene's plasmon spectrum.

Contribution

It provides a full-zone calculation of graphene's polarizability, including analytical expressions and implications for plasmon behavior beyond the Dirac cone approximation.

Findings

Deviations at $ ablarac{ ext{hbar}\omega=2t$ due to van Hove singularity

Peak splitting in low-energy polarizability depending on wave vector direction

Implications for the plasmon spectrum in graphene

Abstract

We compute the dynamical polarizability of graphene beyond the usual Dirac cone approximation, integrating over the full Brillouin zone. We find deviations at $\hbar\omega=2t$ ($t$ the hopping parameter) which amount to a logarithmic singularity due to the van Hove singularity and derive an approximate analytical expression. Also at low energies, we find deviations from the results obtained from the Dirac cone approximation which manifest themselves in a peak spitting at arbitrary direction of the incoming wave vector $\q$. Consequences for the plasmon spectrum are discussed.