Plasmon modes in N-layer bilayer graphene structures

We calculate the plasmon frequency and broadening function in a system consisting of N, up to 5, bilayer graphene sheets at zero temperature. We find that there are one in-phase optical mode and N-1 out-of-phase acoustic ones in plasmon dispersions of the system. With increasing N, the energy of optical and upper-lying acoustical modes increase, while that of the low-lying acoustical branches decreases slightly. For N = 4 and 5, the uppermost acoustical plasmon curve crosses the single-layer plasmon one at some value of momentum outside the electron-hole continuum. In density unbalance systems with N = 3 and 4, the plasmon modes depend remarkably on density values of each layers. This behavior is different from that of graphene multilayer structures.