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Collective Modes of Massive Dirac Fermions in Armchair Graphene Nanoribbons

We report the plasmon dispersion characteristics of intrinsic and extrinsic armchair graphene nanoribbons of atomic width N = 5 using a p_z-orbital tight binding model with third-nearest-neighbor (3nn) coupling. The coupling parameters are obtained by fitting the 3nn dispersions to that of an extended Huckel theory. The resultant massive Dirac Fermion system has a band gap E_g \approx 64 meV. The extrinsic plasmon dispersion relation is found to approach a common dispersion curve as the chemical potential $μ$ increases, whereas the intrinsic plasmon dispersion relation is found to have both energy and momentum thresholds. We also report an analytical model for the extrinsic plasmon group velocity in the q \rightarrow 0 limit.