Effect Of Hydrogen-like Impurities On The Properties Of The Black Phosphorene

This article takes the monolayer black phosphorene(MBP)doped with hydrogen-like impurities on polar substrates as the research object.The polarization properties of the black phosphorene and the influence of hydrogen-like impurities on its properties were studied by the methods of LLP unitary transformation,linear combination operator and variation.The following main conclusions are obtained:Firstly,the properties of ground state energy of bound polaron in the black phosphorene were studied by the methods of variation,LLP unitary transformation and linear combination operator.The numerical results show that the bound polaron energy in the black phosphorene decreases with the increase of phonon energy,increases with the increase of cutoff wave vector,decreases with coulomb potential,and lower than that the energy without coulomb potential.Secondly,the temperature effect of energy and band gap of bound polaron in the black phosphorene were studied by the methods of variation,LLP unitary transformation and linear combination operator The numerical results show that the bound polaron energy and the relevant energy band gap remain constant at low temperature,increase with the increase of temperature at higher temperature;decrease with an increase of phonon energy and increases with greater values of cutoff wave vector.The bound polaron energy will gradually decrease with an increase of coulomb potential,and the bound polaron energy is lower than the polaron energy.The base spacing increases gradually and the bound polaron energy decreases gradually.Thirdly,the ground state energy and the relevant energy band gap of bound magnetic polaron in the black phosphorene were also studied remain by variation,LLP unitary transformation and linear combination operator method.The numerical results show that the ground state energy of bound magnetic polaron and the relevant energy band gap were increase with greater magnetic induction intensity,decrease with an increase of phonon energy,increases with the increase of cutoff wave vector.The energy of bound magnetic polaron decreases with increasing coulomb potential.The bound polaron energy were lower than the polaron energy.Finally,the properties of the average number of phonons in bound polarons in the black phosphorene were studied by variation,LLP unitary transformation and linear combination operator method.The numerical results show that the average number of phonons was constant at lower temperature and increase with increasing temperature,decrease with an increase of phonon energy,and increase with the increase of cutoff wave vector.Compared with the average number of phonons of the polaron,the average number of phonons in the bound polaron is less.The results show that hydrogen-like impurities,polar substrates,temperature,and external magnetic fields have important effects on the polarization properties of monolayer black phosphorene,which has a certain theoretical guiding effect on the further research and application of black phosphorene.