Modeling of the interband transitions in the optical conductivity of doped two-dimensional materials in the terahertz to the infrared frequency range: the case studies of graphene and phosphorene

Abstract

We use Kramers-Kronig analysis and ab initio calculations to develop a simple analytical method for including the effects of high-energy interband electron transitions in the density polarization function of doped graphene and doped phosphorene in the optical limit. The resulting formulas are suitable for applications in the terahertz to the mid-infrared range of frequencies, where the interband electron transitions are shown to give rise to static screening with a suitably chosen in-plane polarizability. In the case of phosphorene, each component of its static polarizability tensor can be computed from a sum-rule–like formula using the ab initio data for the real part of the corresponding component of the full optical interband conductivity tensor of that material.