Plasmonic excitations in Coulomb coupled N-layer graphene structures

We study Dirac plasmons and their damping in spatially separated $N$-layer graphene structures at finite doping and temperatures. The plasmon spectrum consists of one optical excitation with a square-root dispersion and $N-1$ acoustical excitations with linear dispersions, which are undamped at zero temperature within a triangular energy region outside the electron-hole continuum. For any finite number of graphene layers we have found that the energy and weight of the optical plasmon increase in the long wavelength limit, respectively, as square-root and linear functions of $N$. This is in agreement with recent experimental findings. With an increase of the number of multilayer acoustical plasmon modes, the energy and weight of the upper lying branches also exhibit an enhancement with $N$. This increase is strongest for the uppermost acoustical mode so that its energy can exceed at some value of momentum the plasmon energy in an individual graphene sheet. Meanwhile, the energy of the low lying acoustical branches decreases weakly with $N$ as compared with the single acoustical mode in double-layer graphene structures. Our numerical calculations provide a detailed understanding of the overall behavior of the wave vector dependence of the optical and acoustical multilayer plasmon modes and show how their dispersion and damping are modified as a function of temperature, interlayer spacing, and inlayer carrier density in (un)balanced graphene multilayer structures.