Ground state properties of magnetic polaron in monolayer black phosphonene

By using the Lee-Low-Pines(LLP)unitary transformation,linear combination operator and variational method,the ground state energy formula of polaron in monolayer black phosphonene on polar substrate in uniform magnetic field is derived,and the effects of magnetic field and substrate material on the ground state energy of the polaron in monolayer black phosene are investigated.The numerical calculation shows that the ground state energy of the polaron increases with the increasing of the magnetic field strength when the vertical distance between the substrate and monolayer black phosphonene and the cutoff wave vector remains unchanged,and decreases with the increasing of the phonon energy of the substrate material.The ground state energy of the polaron on different substrates is different,but the variation law is consistent.When the vertical distance and magnetic field strength remain unchanged,the ground state energy of the polaron increases with the increasing of the cutoff wave vector.These results indicate that the ground state energy of the polaron in the monolayer black phosphonene is related to the external magnetic field and substrate material.