Parafermionic bound states under uncorrelated edge disorder

Determine whether spatially varying pinning phases generated by completely uncorrelated disorder on the two edges can support parafermionic bound states, and characterize how residual low-energy excitations affect the localization and observable signatures of those states.

Background

The paper analyzes spin-polarized ν=2/3 fractional quantum Hall edges coupled by tunneling and crossed Andreev reflection. In the presence of edge-correlated disorder, disorder averaging preserves a tunneling/pairing channel and can produce an effective double sine-Gordon theory supporting stable Z3 parafermion zero modes.

For completely uncorrelated disorder on the two edges, inter-edge couplings average to zero at first order. The resulting replica-generated interactions may produce an Anderson-localized, Bose-glass-like state with a mobility gap rather than a spectral gap. Although the charge fields may be locally pinned, their pinning phases vary spatially, and the paper does not resolve whether such disordered pinning can retain parafermionic bound states or how remaining low-energy excitations would influence their localization and experimental observability.