Numerical study of the crossover from free electrons to small polarons

• Author / Creator

  Li, Zhou

• 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.

• Subjects / Keywords

  • Superconductivity
  • Adiabatic limit
  • Polaron
  • Strong coupling
  • Electron-phonon
  • Cold atom
  • Trugman's method
  • Holstein

• Graduation date

  Fall 2012

• Type of Item

  Thesis

• Degree

  Doctor of Philosophy

• DOI

  https://doi.org/10.7939/R3F41N

• License

  This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for non-commercial purposes. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.