Effects of temperature, doping and anisotropy of energy surfaces on behaviors of plasmons in graphene

A numerical scheme based on the tight-binding description for pz-electrons in graphene was developed to study the formation and behaviors of plasmons in this two-dimensional electron system. The random phase approximation has been used to calculate the dielectric function for arbitrary temperature and doping level. We show that at zero-doping, only one kind of plasmons of long wavelength is observed at sufficiently high temperature. At finite doping, such plasmons exist even at zero temperature, but strongly damped, due to the interplay between the intra- and inter-band transition processes. Particularly, we show a significant dependence of the plasmon spectrum on the wave-vector direction in the regime of high doping, which is the reflection of the anisotropy of the energy surfaces far from the Dirac point.