Optical reflection, transmission and absorption properties of single-layer black phosphorus from a model calculation

Abstract

An effective anisotropic tight-binding model is developed to analytically describe the low-energy electronic structure and optical response of phosphorene (a black phosphorus (BP) monolayer). Within the framework of the model, we derive explicit closed-form expressions, in terms of elementary functions, for the elements of the optical conductivity tensor of phosphorene. These relations provide a convenient parametrization of the highly anisotropic optical response of phosphorene, which allows the reflectance, transmittance, and absorbance of this material to be easily calculated as a function of the frequency of the incident radiation at arbitrary angles of incidence. The results of such a calculation are presented for both a free-standing phosphorene layer and the phosphorene layer deposited on a substrate, and for the two principal cases of polarization of the incident radiation either parallel to or normal to the plane of incidence. Our findings (e.g., a ‘quasi-Brewster’ effect in the reflectance of the phosphorene/ overlayer system) pave the way for developing a new, purely optical method of distinguishing BP monolayers.