Optical conductivity of black phosphorus

Black phosphorus (BP) is a two-dimensional layered material composed of phosphorus atoms. Recently, it was demonstrated that external perturbations such as electric field close the band gap or even induce a band inversion in few-layer BP, resulting in the insulator phase with a finite energy gap or the Dirac semimetal phase characterized by two separate Dirac nodes. At the transition between the two phases, a semi-Dirac state appears in which energy disperses linearly along one direction and quadratically along the other direction. In this work, we study the optical conductivity of few-layer BP using a lattice model and the corresponding continuum model, incorporating the effects of an external electric field and finite temperature. We find that the low-frequency optical conductivity scales as a different power-law depending on the phase, which can be used as an experimental signature. We also demonstrate the change of the material parameters as an external field increases and its consequence on the power law behavior of the optical conductivity.