Numerical study on collective excitations in graphene

Abstract

Collective excitations in graphene are numerically investigated in the random-phase approximation based on one-particle states in an effective-mass approximation. For plasmons in doped graphene, when the plasmon wave vectors normalized by the Fermi wave vector are the same, the plasmon peak intensities in optical absorption spectra exhibit linear dependencies on the Fermi energy, which are characteristic of two-dimensional Dirac electrons. In the case of nondoped graphene, excitonic collective states to which optical transitions are forbidden appear at energies less than those of interband continuum states. The random-phase approximation with electron-hole attractive interactions well describes both the plasmons and the excitonic states while the Tamm--Dancoff approximation fails to describe the plasmons appropriately.