Quantized Transport of ν=2/3 Fractional Quantum Hall Edge with Disordered Superconducting Proximity

Quantum Hall edge states in proximity to a superconductor (SC) usually acquire a nonquantized electron-to-hole conversion probability in transport, due to nonuniversal SC couplings and disorders. With counterpropagating modes, we show that the situation can be the opposite in the ν=2/3 fractional quantum Hall (FQH) edge states with SC proximity, where disordered SC couplings can reconstruct the edge states into an infinite set of stable phases with quantized electron-to-hole conversion probability along a long edge. Each phase is dominated by a disordered SC coupling that tunnels ±|q_{N}| Cooper pairs, which can take values |q_{N}|=1, 4, 15, etc. We predict that this gives rise to a quantized downstream resistance R_{d}=h/(2q_{N}^{2}e^{2}) in an FQH-SC junction, serving as a quantized electrical transport signature beyond the Hall conductance. Higher-order nonlinear transport due to irrelevant Cooper pair tunneling or vortex dissipation is further studied, which becomes dominant when the edge is in a normal phase. Our results apply to both the single-layer state (as a particle-hole conjugate of ν=1/3) and the bilayer Halperin-(112) state, revealing a rich landscape of disorder-stabilized phases in FQH edge states with SC proximity, and may as well apply to fractional Chern insulators recently observed at the same filling.