Excitation spectrum and high-energy plasmons in single-layer and multilayer graphene

In this paper we study the excitation spectrum of single-layer and multilayer graphene beyond the Dirac cone approximation. The dynamical polarizability of graphene is computed using a full pi-band tight-binding model, considering the possibility of interlayer hopping in the calculation. The effect of electron-electron interaction is considered within the random phase approximation. We further discuss the effect of disorder in the spectrum, which leads to a smearing of the absorption peaks. Our results show a redshift of the pi-plasmon dispersion of single-layer graphene with respect to graphite, in agreement with experimental results. The inclusion of interlayer hopping in the kinetic Hamiltonian of multilayer graphene is found to be very important to properly capture the low energy region of the excitation spectrum.