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Numerical study of the crossover from free electrons to small polarons Open Access


Other title
Trugman's method
adiabatic limit
cold atom
strong coupling
Type of item
Degree grantor
University of Alberta
Author or creator
Li, Zhou
Supervisor and department
Marsiglio, Frank (Department of Physics)
Examining committee member and department
Chen, Jie (Department of Electrical and Computer Engineering)
Sydora, Richard (Department of Physics)
Freeman, Mark (Department of Physics)
Beach, Kevin (Department of Physics)
Freericks, James (Department of Physics)
Department of Physics

Date accepted
Graduation date
Doctor of Philosophy
Degree level
The electron-phonon interaction is one of the fundamental interactions in almost all condensed matter materials. In conventional superconductors, the electron-phonon interaction is the glue that attracts two electrons to one another to form a pair. A strong electron-phonon interaction leads to the concept of a polaron, which is an electron with lattice distortions around it. The small polaron is a polaron with spatial extent comparable to an interatomic dimension of the solid. Evidence for polarons has been identified in many experiments in superconductors and semiconductors. In this thesis we present exact calculations of the polaron. Specifically we have refined Trugman's method to solve the ground state of an electron-phonon coupled system in the whole parameter regime, and we also generalized this method to treat spin-orbit coupled systems. The most difficult regimes, which is the strong-coupling regime and the small phonon frequency limit, have been solved by these refinements. There are three representative kinds of electron-phonon interaction, the Holstein model, the Fr"ohlich model and the BLF-SSH model. In this thesis we have addressed the first and the third one. The second one, the Fr"ohlich model, is very similar to the Holstein model but the interaction is nonlocal. For the Holstein model we have observed the expected smooth crossover from free electrons to small polarons, while for the BLF-SSH model, we have studied the weak coupling regime with perturbation theory and derived a new analytical result for the one-dimensional problem.
Permission is hereby granted to the University of Alberta Libraries to reproduce single copies of this thesis and to lend or sell such copies for private, scholarly or scientific research purposes only. Where the thesis is converted to, or otherwise made available in digital form, the University of Alberta will advise potential users of the thesis of these terms. The author reserves all other publication and other rights in association with the copyright in the thesis and, except as herein before provided, neither the thesis nor any substantial portion thereof may be printed or otherwise reproduced in any material form whatsoever without the author's prior written permission.
Citation for previous publication
Zhou Li, 2010, Phys. Rev. B 81, 115114.Zhou Li, 2011, Phys. Rev. B 83, 195104.Zhou Li, 2011, Phys. Rev. B 83, 045104.

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