The Properties Of Valley Polaron In Monolayer Transition Metal Dichalcogenides

Using the method of combining the linear combination operator,the Lee-Low-Pines(LLP)transformation,variational method and Pekar variational method theoretically study the renormalization of the effective mass of polaron in monolayer transition metal dichalcogenides on different polar substrates originating from the electron-optical phonon coupling in the Frohlich polaron model,in which in which both of the surface optical phonons modes induced by the polar substrate and the intrinsic longitudinal optical phonons modes have been taken into account.We focus on the effects of the optical phonon mode cut-off wave vector k,the intrinsic polarizability parameters ?0 of the monolayer transition metal chalcogenide,the internal distance z0 between the polar substrate and the monolayer transition metal chalcogenide,and the electron spin(but ignore the influence of spin orbit coupling)on the effctive mass renormalization and ground state energy of the valley polaron,and give some feasible schemes on the electron mobility of monolayer transition metal chalcogenides and band gap modulation.The mainly results are:Firstly,In the presence or absence of magnetic field,the effective mass and ground state energy of the valley polaron can be significantly changed by replacing different polar substrates or adjusting the internal distance z0 between the monolayer transition metal chalcogenide and the polar substrate,in which The range of effective mass and ground state energy increases with the increase of polarizability parameter ? of polar substrate,and decreases with the increase of internal distance z0.Polar substrate plays an important role in changing the mobility and band gap modulation of monolayer transition metal chalcogenides.Secondly,In the presence or absence of magnetic field,the effective mass and ground state energy of the valley polaron increase with the increase of the intrinsic polarizability parameter ?0,but the increase amplitude is small.The material also plays a role in changing the mobility and band gap modulation of the monolayer transition metal chalcogenides.Thirdly,In the presence or absence of magnetic field,the effective mass and ground state energy of the valley polaron of monolayer transition metal chalcogenide change obviously with the cut-off wave vector k.in which the effective mass increases with the increase of k,increases sharply at k<4×109m-1,and then vary smoothly when the cut-off wave vector k>4×109m-1,and the ground state energy decreases with the increase of k,increases sharply at k<4×109m-1,and then vary smoothly when the cut-off wave vector k>4×109m-1,this implies that only the phonon modes with the small wave vector are strongly coupled with electron and give the dominate contributions to the correction of the zero LLs,which is also consistent with the recent theoretical results based on first-principle calculation.Fourthly,The effect of electron spin on the effective mass and ground state energy of the valley polaron of monolayer transition metal chalcogenide is not obvious(in this paper,only the electron spin is considered,but not the spin orbit coupling).Therefore,the contribution of electron spin to the mobility and band gap modulation of monolayer transition metal chalcogenide is small,which can not be considered in practical operation.