First-principles calculations and model analysis of plasmon excitations in graphene
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 (line width) of Dirac and $π$ 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 $π$ plasmons should be $ω_π(q) = \sqrt{E_g^2 + βq}$ for small $q$'s, where $E_g$ is the band gap at the $M$ point in the Brillouin zone, and $β$ is a fitting parameter. This model is radically different from previous proposals, but in good agreement with our calculated results from first principles.