Quantum Hall effect in monolayer and bilayer black phosphorus

Abstract

We numerically study the quantum Hall effect in both monolayer and bilayer black phosphorus (BP) under an external electric field in the presence of both disorder and a strong perpendicular magnetic field based on the tight-binding model. In the monolayer BP case, the quantized Hall conductivity is similar to that of a two-dimensional electron gas (2DEG), but the positions of all the Hall plateaus shift to the left due to the spectral asymmetry, in agreement with the experimental observations. The width of Hall plateau can be increased by applying a bias voltage to the top and bottom layers of the monolayer BP. The longitudinal conductivity exhibits a strong anisotropy that is large along the armchair direction. In the bilayer BP case, the Hall conductivity remains the same quantization rule as in the case of monolayer BP. Under a certain bias voltage, the plateau is markedly absent, and the LLs spectrum shows the appearance of doubly degenerate branches with a zero-energy level. Eventually, the system undergoes a phase transition from 2DEG to Dirac semimetal, which indicates a biased-induced closure of the bulk energy gap. The two central plateaus with are the most robust against disorder scattering. The longitudinal conductivity remains almost constant around zero energy in the presence of moderate disorder strength.