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 $\nu =2/3$ 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 $\pm |q_N|$ 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 $\nu =1/3$) 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.

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• Edge states
• Fractional quantum Hall effect
• Quantum transport
• Superconducting fluctuations
• Topological phases of matter
• Disordered systems
• Quantum fluids & solids
• Luttinger liquid model
• Renormalization group