Zero Mode Operators and Charge-Conjugation Defects in Non-Abelian Fractional Quantum Hall-Superconductor Heterostructures

Abstract

We study zero modes bound to charge-conjugation defects in fractional quantum Hall-superconductor (FQH-SC) heterostructures built from Abelian and non-Abelian FQH states. Although the associated defects are well described by $G$-crossed braided tensor categories, a local operator description of their zero modes is not generally known. We generalize the bulk-to-boundary construction of localized zero mode operators to FQH-SCs with non-Abelian parent topological orders, mapping bulk Wilson operators in the folded theory to localized zero mode operators in the one-dimensional FQH-SC theory. This construction distinguishes zero mode anyons from the local zero mode operators that act on the defect Hilbert space and yields a generalized zero mode algebra. It also determines the fusion-channel dependence of tunneling: tunneling of zero mode operators probes bulk monodromy, while direct zero mode anyon transfer probes $G$-crossed associativity data. Applying this framework, we recover the $\mathbb{Z}_{2m}$ parafermion zero mode structure of fermionic Laughlin FQH-SCs at filling $ν=1/m$, obtain a $\mathbb{Z}_2^{(n)}\times\mathbb{Z}_N$ structure for generalized Moore-Read states at filling $ν=1/m$, with $N=2m$ for fermionic states and $N=m$ for bosonic states, and find a $\mathrm{Fib}\times\mathbb{Z}_N$ structure for the $k=3$ Read-Rezayi state at filling $ν=3/(3M+2)$, with $N=2(3M+2)$ for fermionic states and $N=(3M+2)/2$ for bosonic states. In the Read-Rezayi case, zero mode operator tunneling and direct zero mode anyon transfer yield distinct universal amplitude ratios between the neutral fusion channels, providing a characteristic signature of the underlying Fibonacci defect structure.