Optical conductivity of black phosphorus with a tunable electronic structure

Black phosphorus (BP) is a two-dimensional layered material composed of phosphorus atoms. Recently, it was demonstrated that external perturbations such as an electric field close the band gap in few-layer BP, and can even induce a band inversion, resulting in an insulator phase with a finite energy gap or a 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. 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 a power law that differs depending on the phase, which can be utilized as an experimental signature of few-layer BP in different phases. We also systematically analyze the evolution of the material parameters as the electric field increases, and the consequence on the power-law behavior of the optical conductivity.