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Temperature-dependent Plasmons and Their Damping Rates for Graphene with a Finite Energy Bandgap

We obtained numerical and closed-form analytic expressions for finite-temperature plasmon dispersion relations for intrinsic graphene in the presence of a finite energy gap in the energy spectrum. The calculations were carried out using the random-phase approximation. The analytic results have been derived in the high temperature regime and long-wavelength limit. We have found that the plasmon damping rate decreases in the presence of a band gap. Our method of calculation could also be applied to silicene and other buckled honeycomb lattice structures. The finite-temperature plasmon dispersion relations are presented when a single graphene layer is Coulomb coupled to a semi infinite conductor. Both cases of gapless and gapped monolayer graphene have been investigated when a thick substrate is in their proximity. Both the plasmon excitation frequency and damping rate are linear functions of the in-plane wave vector in the long wavelength limit when a monolayer interacts with a conducting substrate which is not the case for free-standing pristine or gapped graphene.