Screening in graphene antidot lattices

TL;DR

This paper calculates the dynamical polarization function and plasmon dispersion in graphene antidot lattices, revealing complex structures due to minibands and van Hove singularities, with implications for plasmon behavior.

Contribution

It provides the first detailed computation of polarization functions and plasmon dispersion in graphene antidot lattices, including approximation methods for numerical efficiency.

Findings

Polarization functions show complex structures beyond pristine graphene.

Plasmon dispersion follows an approximate square-root law with suppressed frequency.

Approximation schemes agree well with full calculations.

Abstract

We compute the dynamical polarization function for a graphene antidot lattice in the random-phase approximation. The computed polarization functions display a much more complicated structure than what is found for pristine graphene (even when evaluated beyond the Dirac-cone approximation); this reflects the miniband structure and the associated van Hove singularities of the antidot lattice. The polarization functions depend on the azimuthal angle of the {\bf q}-vector. We develop approximations to ease the numerical work, and critically evaluate the performance of the various schemes. We also compute the plasmon dispersion law, and find an approximate square-root dependence with a suppressed plasmon frequency as compared to doped graphene. The plasmon dispersion is nearly isotropic, and the developed approximation schemes agree well with the full calculation.