Screening in graphene antidot lattices

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.

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• Dielectric function, screening, and plasmons of graphene in the presence of spin-orbit interactions
• Screening and Collective Modes in Disordered Graphene Antidot Lattices
• Kinetic theory of spin-polarized systems in electric and magnetic fields with spin-orbit coupling: II. RPA response functions and collective modes
• Dielectric properties of graphene on transition metal dichalcogenide substrate