1204.6245 (Abolhassan Vaezi)

Fractional topological superconductor with fractionalized Majorana
fermions    [PDF]

Abolhassan Vaezi

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 a strongly correlated system. Adding interaction leads to a non-trivial ground-state with nonzero ground-state degeneracy at special filling fraction of excess spinful excitations. In the second model, we start from a fractional topological insulators in which we induce pairing in this system 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 proximity to an s-wave superconductor. We prove that the first two models exhibit Abelian anyons as fractional excitation 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 $d=\sqrt{2m}$ quantum dimension in $\nu=1/m$ filling fraction. Finally, we propose a wavefunction for the fractional topological superconductors of the third type.

View original: http://arxiv.org/abs/1204.6245