  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.
