On the basis of Lee–Low–Pines (LLP) unitary transformation, the influence of external magnetic field, Rashba spin–orbit coupling and quantum size effect on the ground-state interaction energy of strong-coupling magnetopolarons in quantum disks (QDs) is studied by using the Tokuda improved linear combine operator method. The results show that the ground-state interaction energy of magnetopolarons consists of four parts: the energy caused by the confinement potential of QDs, interaction energy between the electron and external magnetic field, electron and longitudinal-optical (LO) phonon interaction energy and additional term of Rashba effect originating from phonons. The electron–LO phonon interaction energy Ee- ph and additional term of Rashba effect are always negative; the absolute value |Ee- ph | increases with increasing transverse confinement strength ω0, cyclotron frequency of external magnetic field ωc and electron–LO phonon coupling strength α, but decreases with increasing the thickness of QDs L; the state properties of magnetopolarons are closely linked with the sign of the ground-state interaction energy of magnetopolarons E int and change of E int with ωc, ω0, α and L. In addition, the vibration frequency of magnetopolarons λ increases with increasing ωc, ω0 and α, but decreases with increasing L. For the ground state of magnetopolarons in QDs, the electron–LO phonon interaction plays a significant role, meanwhile, the influence of Rashba spin–orbit coupling effect cannot be ignored.
Effect of spin-orbit coupling on the electron-phonon interaction of the superconductors Pb and Tl