Eigenvalues approach for the analysis of plasmon propagation on a graphene layer

Starting from Dirac equation for an idealized graphene layer together with the Lorentz gauge condition, we describe plasmon propagation without making recourse to a classical Kubo-Drude electron model. Two excitation modes are separately considered : 1) excitation by a TM-polarized wave of given vector potential amplitude (voltage source), 2) excitation by current injection (e.g. via a probe)(current source). Losses are accounted for globally by means of a lifetime term. A simple LCR model of the surface admittance emerges that is valid up to several THz and beyond, even under impulsive time-excitation.