Direction-dependent electronic phase transition in magnetic field-induced gated phosphorene

A detailed physical meaning of the electronic phase transition in monolayer black phosphorus (BP) has been addressed in the presence of local gate voltage and Zeeman magnetic field. The main features of this transition characterize through the electronic density of states (DOS) in the vicinity of the Fermi level. The numerical calculations have been performed within the continuum approximation of tight-binding model and the Green's function method. The anisotropy crystal structure of BP causes different behaviors in each component of DOS. First, we have confirmed the Zeeman effect, i.e. the splitting of Van Hove singularities. Then, our results show that the electronic band gap of phosphorene along the x-direction decreases with weak magnetic fields when the gate voltage is absent and the system transits to the semimetallic phase at strong regimes, whereas there is no phase transition along the y-direction. Interestingly, turning on the gate, phase transition independent of the direction does not occur at both weak and strong magnetic fields. Another remarkable point refers to the increase of the band gap with gate voltage at both directions, leading to the semimetallic-semiconductor transition along the x-direction at strong magnetic fields. Tuning the band gap by the gate voltage and magnetic field are useful for future applications of BP.