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Foell, Charles A.

Physics

2006

MS

In this thesis we present the theory of a new type of multicomponent polaron. This "vector polaron" is found to have the following properties: (I) it has a non-trivial internal structure, manifested by a spatial variation in the electronic and vibrational character; (2) it can have low energy internal degrees of freedom; and (3) it can be classified into a minimum of three types. We elucidate the fundamental nature of the vector polaron by considering a one dimensional model of an electron in a doubly (or nearly) degenerate band interacting with two classical elastic distortion fields via Holstein and Jahn-Teller coupling. Effective equations of motion for the electron envelopes are shown to be coupled nonlinear Schrödinger equations. We identify three types of stable vector polarons for our range of a parameters in this model. A Rayleigh-Ritz variational calculation is performed to obtain upper bounds on polaron energies in which kinematic corrections from the elastic distortions are included. From these energies, analytic expressions for effective masses are extracted and subsequently compared to results from other polaron models. We also obtain analytic expressions for the binding energies and effective masses for small coupling using Rayleigh-Schrödinger perturbation theory.