Influence of Impurity Scattering on Surface Plasmons in Graphene in the Lindhard Approximation

We study the influence of impurity scattering on transverse magnetic (TM) and transverse electric (TE) surface plasmons (SPs) in graphene using the Lindhard approximation. We show how the behaviour and domains of TM SPs are affected by the impurity strength gamma and determine the critical value gamma c below which no SPs exist. The quality factor of TM SPs, for single-band and two-band transitions, is proportional to the square of alpha lambda SP/gamma, with alpha being the fine-structure constant and lambda SP being the plasmon wavelength. In addition, we show that impurity scattering suppresses TE SPs.