Two-loop photon self-energy in pseudoquantum electrodynamics in the presence of a conducting surface

Abstract

In the present paper, we investigate the influence of a grounded perfectly conducting surface on the photon self-energy of a $2+1\mathrm{D}$ system of massless Dirac fermions, whose electron interaction is described by pseudoquantum electrodynamics. We calculate the temporal component of the polarization tensor up to 2-loop perturbation order in the presence of the conducting surface and, applying the Kubo formula, we obtain the longitudinal and optical conductivities of such system. When the distance between the system and the plate tends to infinity, we recover the correspondent results found in the literature. Since pseudoquantum electrodynamics proved to give a good description of the transport properties of graphene, our results can be useful as an alternative way to control the longitudinal and optical conductivities of this material.