Polarization and bandgap characteristics of monolayer black phosphoene in magnetic field

Abstract

The effect of magnetic field on the polarization effect of black phosphorene is studied. The ground state energy and the relevant energy bandgap formula of carrier and carrier–phonon interaction system is derived in turn, and the effect of applied magnetic field on ground state energy and bandgap is also investigated, by the method of variational method, LLP unitary transformation method and linear combination operator method. When the substrate is given, the ground state energy and the relevant bandgap of the carrier–phonon interaction system changes with the magnetic induction intensity, phonon energy and cutoff wave vector. It can be shown by numerical calculation: The ground state energy and the relevant bandgap of the Hole and the Hole–phonon interaction system in black phosphorene increases with increase in magnetic induction intensity [Formula: see text]. The ground state energy of the Hole, Hole–phonon system and the relevant bandgap are different when the substrate is different. Under the action of a magnetic field, the ground state energy of the Hole and Hole–phonon system and bandgap decreases with increase in phonon energy and increases with increase in cutoff wave vector when the substrate is fixed.