First-principles calculations and model analysis of plasmon excitations in graphene and graphene/hBN heterostructure

Abstract

Plasmon excitations in free-standing graphene and graphene/hexagonal boron nitride (hBN) heterostructure are studied using linear-response time-dependent density functional theory within the random phase approximation. Within a single theoretical framework, we examine both the plasmon dispersion behavior and lifetime (linewidth) of Dirac and $\ensuremath{\pi}$ plasmons on an equal footing. Particular attention is paid to the influence of the hBN substrate and the anisotropic effect. Furthermore, a model-based analysis indicates that the correct dispersion behavior of $\ensuremath{\pi}$ plasmons should be ${\ensuremath{\omega}}_{\ensuremath{\pi}}(q)=\sqrt{{E}_{g}^{2}+\ensuremath{\beta}q\phantom{{}^{l}}}$ for small $q$'s, where ${E}_{g}$ is the band gap at the $M$ point in the Brillouin zone, and $\ensuremath{\beta}$ is a fitting parameter. This model is radically different from previous proposals, but in good agreement with our calculated results from first principles.