Quantized Transport of $\nu = 2/3$ Fractional Quantum Hall Edge with Disordered Superconducting Proximity

Quantum Hall edge states in proximity to a superconductor (SC) usually acquire a non-quantized electron-to-hole conversion probability in transport, due to non-universal SC couplings and disorders. With counter-propagating 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 $R_d = h/(2q^2_Ne^2)$ 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.