Polarons in a cylindrical quantum well wire with finite confining potential

The polaron self-energy and the correction to the electron effective mass in a cylindrical quantum well wire (QWW) are studied by the perturbation approach. The interactions of electrons with different phonon modes in the QWW system, including the confined longitudinal optical phonon modes, in the wire (LO1), in the barrier materials (LO2) and in the interface optical (IO) phonon modes, are considered. The result shows that the LO1 phonon's contribution to the polaron self-energy increases gradually as the radius of the wire increases, and finally reaches that of the three-dimensional limit, while the LO2 phonon contributes only when the radius of the wire is very small. Also, the contribution of the IO phonon modes first increases quickly as the wire radius increases and soon reaches a maximum, then reduces to zero monotonically.