Tunable optical conductivities of ultrathin black phosphorus film in the visible to mid-infrared regime

Abstract

We theoretically study the band structure and photoelectric properties of few-layered black phosphorus based on recent experimental findings [G. W. Zhang et al., Nat. Commun. 8, 14071 (2017)]. According to the experimental findings, it was shown that absorption peaks associated with optical transitions have been observed. For theoretical study, we apply the low-energy k·p method to study the band structure of multi-layer black phosphorus. The optical conductivities σx(ω) and σy(ω) are calculated when the polarized radiation field is applied along the x (armchair)- and y (zigzag)-directions, respectively. Contributions to optical transition from different subbands are considered in the optical conductivity spectrum. Calculation results show that with an increase in the layer number of multi-layer black phosphorus, the band gap becomes small and the subbands evolve into quasi-continuous bands at last. The optical conductivities vary sensitively with changing thickness, doping level, and light polarization.