Electronic Properties of Graphene Multilayers

We determine numerically the tight-binding band structure, the density of states and the plasmon spectrum of N stacked graphene layers beyond the Dirac cone approximation. We calculate the polarizability in the random phase approximation and determine the dielectric function $\epsilon$({\bf q},$\omega)$. This allows to determine the acoustic and optical modes of the plasmon spectrum. Because we do not limit ourselves to the Dirac cone approximation we cannot use the semi-analytic approach usually proposed for graphene in the literature. Instead we use a combination of numerical procedures to determine the collective modes of graphene multilayer.