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Paper   IPM / P / 12344
School of Physics
  Title:   Fractional Topological Superconductor with Fractionalized Majorana Fermions
  Author(s):  A. Vaezi
  Status:   Preprint
  Journal:
  Year:  2012
  Supported by:  IPM
  Abstract:
We present three different models for describing fractional topological superconductors. In the simplest model, we study an imbalanced Fermi gas subject to a pairing potential. We tune parameters such that the superconducting band becomes as flat as possible. Due to the flatness of the band structure and the imbalance between spin-up an spin-down electrons, the system becomes strongly correlated. Adding interaction leads to a non-trivial ground-state with degenerate ground-state at special filling fractions of excess spinful excitations. In the second model, we start from a fractional topological insulators in which we induce pairing by putting it on top of an s-wave superconducting substrate. The third model is at a flat band fractional Chern insulator or a conventional fractional quantum Hall ferro-magnet whose quasi-particles are paired up in the proximity of an s-wave superconductor. We argue that the first two models exhibit Abelian anyons as their fractional excitations and have a non-trivial topological order. More interestingly, using several different approaches, we show that the third model leads to a non-Abelian fractional topological superconductor whose edge state is a fractionalized Majorana fermions. Additionally, the low energy excitations around vortices in the bulk are fractionalized Majorana zero modes with d=√{2m} quantum dimension in ν = 1/m filling fraction. A wave-function for the fractional topological superconductors of the third type has been proposed. Finally, we discuss the connection between the third model and the \mathbbZN rotor model which has been shown to give non-Abelian anyons with quantum dimension d=√N.

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