Yanar, S.Sevim, A.Boyacioglu, B.Saglam, M.Mukhopadhyaya, S.Chatterjee, A.2016-02-082016-02-0820080749-6036http://hdl.handle.net/11693/23179The problem of an electron interacting with longitudinal-optical (LO) phonons is investigated in an N-dimensional quantum dot with symmetric Gaussian confinement in all directions using the Rayleigh-Schrödinger perturbation theory, a variant of the canonical transformation method of Lee-Low-Pines, and the sophisticated apparatus of the Feynman-Haken path-integral technique for the entire range of the coupling parameters and the results for N = 2 and N = 3 are obtained as special cases. It is shown that the polaronic effects are quite significant for small dots with deep confining potential well and the parabolic potential is only a poor approximation of the Gaussian confinement. The Feynman-Haken path-integral technique in general gives a good upper bound to the ground state energy for all values of the system parameters and therefore is used as a benchmark for comparison between different methods. It is shown that the perturbation theory yields for the ground state polaron self-energy a simple closed-form analytic expression containing only Gamma functions and in the weak-coupling regime it provides the lowest energy because of an efficient partitioning of the Gaussian potential and the subsequent use of a mean-field kind of treatment. The polarization potential, the polaron radius and the number of virtual phonons in the polaron cloud are obtained using the Lee-Low-Pines-Huybrechts method and their variations with respect to different parameters of the system are discussed.EnglishGaussian confinementPolaronic effectQuantum dotGround stateMathematical transformationsPerturbation techniquesPhononsPolarizationPolaronsGaussian confinementsPolaronic effectsSemiconductor quantum dotsArticle10.1016/j.spmi.2007.11.006