Fractional topological superconductivity on quantum Hall edges

Certain types of topological superconductors can support localized zero-modes which can be used to for topological quantum computing applications. The most well studied examples are systems supporting Majorana fermion zero-modes. Fractional topological superconductors (FTS) arise when fractional quasiparticles bind to form Cooper pairs. These exotic phases of matter support parafermion zero-modes, which have richer non-Abelian statistics than their Majorana fermion counterparts.

Fractional quasiparticles can be found in fractional quantum Hall (FQH) liquids. Thus, FTSs can be experimentally realized by proximity coupling counter propagating FQH edges to more standard superconductors. Such a proximity coupling is challenging to obtain, since FQH liquids require strong electronic repulsion and strong magnetic fields, both of which suppress superconductivity. In this talk, I will show that despite these challenges fractional topological superconductivity can be observed experimentally.

First, I show that for Laughlin FQH with filling fraction ν=1/m, FTSs are stabilized by sufficiently strong repulsive interactions in the bulk of Laughlin fluids, and I will present the phase diagram and parameter regime in which FTSs can be found. I will also discuss how the presence of vortices in the external superconductors affects manifestations of fractional topological superconductivity in transport signatures. Our results show that although the vortices act as a dissipative bath that can absorb electrons, an exotic phase harboring parafermion zero modes can still be observed. Our results also explain the qualitatively different transport signatures for integer and fractional filling fractions as seen in recent experimental measurements.