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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 γ and determine the critical value γc below which no SPs exist. The quality factor of TM SPs, for single-band and two-band transitions, is proportional to the square of αλSP/γ, with α being the fine-structure constant and λSP being the plasmon wavelength. In addition, we show that impurity scattering suppresses TE SPs.

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