Quantum field theoretical description for the reflectivity of graphene

Abstract

We derive the polarization tensor of graphene at nonzero temperature in $(2+1)$-dimensional space-time. The obtained tensor coincides with the previously known result at all Matsubara frequencies, but, in contrast, it admits analytic continuation to the real frequency axis satisfying all physical requirements. Using the obtained representation for the polarization tensor, we develop a quantum field theoretical description for the reflectivity of graphene. The analytic asymptotic expressions for the reflection coefficients and reflectivities at low and high frequencies are derived for both independent polarizations of the electromagnetic field. The dependencies of the reflectivities on the frequency and angle of incidence are investigated. Numerical computations using the exact expressions for the polarization tensor are performed and application regions for the analytic asymptotic results are determined.