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      Self-consistent study of Abelian and non-Abelian order in a two-dimensional topological superconductor

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      GOERTZEN-THESIS.pdf (8.804Mb)
      Date
      2016-01-27
      Author
      Goertzen, Stephanie
      Type
      Thesis
      Degree Level
      Masters
      Metadata
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      Abstract
      We perform microscopic mean-field studies of topological order in a two-dimensional topological superconductor in the Bogoliubov-de Gennes (BdG) formalism. By adopting a two-dimensional s-wave topological superconductivity (TSC) model on a minimal tight-binding system, we solve the BdG equations self-consistently to obtain not only the superconducting order parameter, but also the Hartree potential. By computing the Thouless, Kohmoto, Nightingale, and den Nijs (TKNN) number and investigating the bulk-boundary correspondence, we study the nature of Abelian and non-Abelian TSC in terms of self-consistent solutions to the BdG equations. In particular, we examine the effects of temperature and a single non-magnetic impurity deposited in the centre of the system and how they vary depending on topology. We find that the non-Abelian phase exhibits signs of unconventional superconductivity, and by examining the behaviour of this phase under both low and high Zeeman field conditions, we show that the magnitude of the Zeeman field largely dictates the susceptibility of the system to temperature. Furthermore, we investigate the possible interplay of charge density waves (CDW) and TSC. By self-consistently solving for the mean fields, we show that TSC and topological CDW are degenerate ground states---with the same excitation spectrum in the presence of surfaces---and thus can coexist in the Abelian phase. The effects of a non-magnetic impurity, which tends to pin the phase of charge density modulations, are examined in the context of topological CDW.
      Degree
      Master of Science (M.Sc.)
      Department
      Physics and Engineering Physics
      Program
      Physics
      Supervisor
      Tanaka, Kaori
      Committee
      Dick, Rainer; Yao, Yansun; Sowa, Artur
      Copyright Date
      December 2015
      URI
      http://hdl.handle.net/10388/ETD-2015-12-2398
      Subject
      topological superconductivity
      Majorana fermion
      TKNN number
      non-Abelian statistics
      charge density wave
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