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REALISTIC MODELS FOR POLARONS

  • Author / Creator
    Chandler, Carl J
  • Electrons interacting with the ions in a solid, or polarons, are some of the most basic condensed matter quasi-particles. They influence the electric conductivity in normal metals, but perhaps most fascinatingly, they mediate the formation of Cooper pairs in low temperature superconductors. The details of this phonon mediation are poorly understood at the level of a microscopic Hamiltonian. The Hamiltonian for basic polaron models has only recently been solved for the single electron, and seems to predict that the polarons in low temperature superconductors would have very large effective masses. This is at odds with the measured small effective masses of many low temperature superconductors in the normal state. In this thesis we examine extensions to the basic Holstein polaron Hamiltonian that provide a more realistic model of what happens in real materials. We also look at the BLF-SSH model, which is the appropriate Hamiltonian for superconductors without optical phonons such as the elemental superconductors. We found that extending the Holstein model to include next nearest neighbour electron hopping and nearest neighbour electron-phonon interactions changed the effective mass slightly, but nowhere near enough to account for the low effective masses that must be present in real materials. The BLF-SSH model was examined in the adiabatic limit and with weak-coupling perturbation theory, but an exact solution was not found. It seems likely that the effective mass for this model is also very large, but an improved algorithm is necessary to prove this. A potential path forward is presented in the appendix.

  • Subjects / Keywords
  • Graduation date
    2016-06:Fall 2016
  • Type of Item
    Thesis
  • Degree
    Doctor of Philosophy
  • DOI
    https://doi.org/10.7939/R3M32NJ5P
  • 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.
  • Language
    English
  • Institution
    University of Alberta
  • Degree level
    Doctoral
  • Department
    • Department of Physics
  • Supervisor / co-supervisor and their department(s)
    • Frank Marsiglio
  • Examining committee members and their departments
    • Joseph Maciejko (Physics)
    • Richard Sydora (Physics)
    • Marc de Montigny (Physics, Campus St. Jean)
    • John Davis (Physics)
    • Mona Berciu (Physics, UBC)