Quantized Transport of Disordered Superconducting Fractional Quantum Hall Edge (II): the ν=5/2 Case Study

Identifying the ground state of the experimentally realized fractional quantum Hall (FQH) system at filling factor 5/2 remains a central open question. Numerical studies favor the non-Abelian Pfaffian (Pf) and its particle-hole conjugate, the anti-Pfaffian (APf), while thermal conductance measurements suggest the particle-hole Pfaffian (PH-Pf) as another candidate. We propose coupling the 5/2 FQH edge to a superconductor and show that disordered superconducting proximity can reconstruct the edge into a hierarchy of stable phases characterized by quantized electron-to-hole conversion probabilities along the boundary. We further outline an experimental protocol in which the predicted electric conductances are different for the three different Pfaffian states.