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

In this paper we study the excitation spectrum of single- and multi-layer graphene beyond the Dirac cone approximation. The dynamical polarizability of graphene is computed using a full $π$-band tight-binding model, considering the possibility of inter-layer 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 $π$-plasmon dispersion of single-layer graphene with respect to graphite, in agreement with experimental results. The inclusion of inter-layer hopping in the kinetic Hamiltonian of multi-layer graphene is found to be very important to properly capture the low energy region of the excitation spectrum.

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