Repulsive interactions enhance the coupling of superconductors to fractional quantum Hall edges

We study helical gapless modes arising on the edges of Abelian fractional quantum Hall liquids proximity coupled to a superconductor. This setup can be utilized to create non-Abelian parafermion zero modes if the coupling to the superconductor opens a gap in the helical modes. However, when the coupling to the superconductor is weak it is ineffective and does not open a gap due to the competition with the repulsive interactions stabilizing the fractional quantum Hall liquid. We therefore investigate the possibility for obtaining a gapped phase at strong coupling to the superconductor. To this end, we use an effective wire construction model for the quantum Hall liquid and employ renormalization group methods to obtain the phase diagram of the system. Surprisingly, at strong coupling we find a gapped phase which is stabilized by strong repulsive interactions in the bulk of the quantum Hall fluids. To investigate the possibility for obtaining a gap in the intermediate coupling regime, we identify a duality transformation that maps between the weak coupling and strong coupling regimes. We find conditions on the existence of a gap in the intermediate coupling regime by investigating self-dual points of the model.