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Paper IPM / P / 12344  


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 spinup an spindown electrons, the system becomes strongly correlated. Adding interaction leads to a nontrivial groundstate with degenerate groundstate 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 swave superconducting substrate. The third model is at a flat band fractional Chern insulator or a conventional fractional quantum Hall ferromagnet whose quasiparticles are paired up in the proximity of an swave superconductor. We argue that the first two models exhibit Abelian anyons as their fractional excitations and have a nontrivial topological order. More interestingly, using several different approaches, we show that the third model leads to a nonAbelian 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 wavefunction for the fractional topological superconductors of the third type has been proposed. Finally, we discuss the connection between the third model and the \mathbbZ_{N} rotor model which has been shown to give nonAbelian anyons with quantum dimension d=√N.
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