Plasmon modes in N-layer graphene structures at zero temperature

We investigate the plasmon frequency and the broadening function corresponding to Landau damping in aN-MLG structure consisting ofN, up to 5, MLG sheets at zero temperature. Our results present that plasmon dispersions in the system include an in-phase optical mode and N - 1 out-of-phase acoustic ones. The optical (acoustic) plasmon frequency is higher (lower) than that of MLG at the same parameters. The broadening function of plasmon dispersions is quite similar to that in case of taking into account temperature effects. In addition, the increase in separation between layers increases (decreases) acoustic (optical) plasmon frequency, making plasmon curves become identical at smaller wave vector. Besides, the imbalance in carrier density in graphene sheets affects significantly on plasmon frequencies and plasmon pattern because it separates some plasmon branches far away from the others. However, the number of plasmon branches separated from the others depends mainly on the number of layers containing different carrier density but is independent of the order of these layers in the system.