Rayleigh-Schrödinger perturbation theory for electron-phonon interaction in two dimensional quantum dots with asymmetric parabolic potential

Within the framework of the second-order Rayleigh-Schrödinger perturbation theory, we investigate the effects of the interaction of the electron and longitudinal-optical phonons in two-dimensional semiconductive quantum dots with respect to a general potential. We propose a simple expression for the ground state energy, and compare it with those obtained by Landau-Pekar strong coupling theory. It is shown both analytically and numerically that the results obtained from the second-order Rayleigh-Schrödinger perturbation theory could be better than those from Landau-Pekar strong coupling theory when the coupling constant is sufficiently small. Moreover, some interesting problems, such as polarons in quasi-one-dimensional quantum wires, and quasi-zero-dimensional asymmetric or symmetric quantum dots can be easily discussed only by taking different limits. After the numerical calculations, we find that there exists a simple dimensional scaling and symmetry relation for the ground state polaron energy. Furthermore, we apply our results to some weak-coupling polar semiconductors such as GaAs, CdS. It is shown that the polaronic effects are found to be quiet appreciable if the confinement lengths and smaller than a few nanometers