Polaronic effects in a gaussian quantum dot

Date

2008

Authors

Yanar, S.
Sevim, A.
Boyacioglu, B.
Saglam, M.
Mukhopadhyaya, S.
Chatterjee, A.

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Source Title

Superlattices and microstructures

Print ISSN

0749-6036

Electronic ISSN

Publisher

Elsevier

Volume

43

Issue

3

Pages

208 - 239

Language

English

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Abstract

The 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.

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Published Version (Please cite this version)