Optical absorption and conductivity in quasi-two-dimensional crystals from first principles: Application to graphene

This paper gives a theoretical formulation of the electromagnetic response of the quasi-two-dimensional (Q2D) crystals suitable for investigation of optical activity and polariton modes. The response to external electromagnetic field is described by current-current response tensor ${\mathrm{\Pi }}_{\mu \nu }$ calculated by solving the Dyson equation in the random phase approximation (RPA), where current-current interaction is mediated by the photon propagator $D_{\mu \nu }$. The irreducible current-current response tensor ${\mathrm{\Pi }}_{\mu \nu }^0$ is calculated from the {\em ab initio} Kohn-Sham (KS) orbitals. The accuracy of ${\mathrm{\Pi }}_{\mu \nu }^0$ is tested in the long wavelength limit where it gives correct Drude dielectric function and conductivity. The theory is applied to the calculation of optical absorption and conductivity in pristine and doped single layer graphene and successfully compared with previous calculations and measurements.