Parafermions in fractional Chern insulator-superconductor heterostructures: the role of spin polarization
Abstract
Most proposals for Z3 parafermions in fractional quantum Hall-superconductor structures used the spin-unpolarized ν= 2/3 Halperin (1,1,2) state. The fractional quantum anomalous Hall (FQAH) states of twisted MoTe2 and rhombohedral graphene are believed to be spin- and valley-polarized Jain states, with the same topological order but a different spin structure. We analyze a trench between two polarized ν= 2/3 edges. Among the pairing and tunneling bilinears of the edge-mode electrons, exactly two of each have zero conformal spin. Pairing is compatible only with the neutral-mode superconductivity channel and tunneling only with neutral-mode backscattering, whereas in the unpolarized state singlet pairing and tunneling select the same channel. Since the two channels condense the same neutral anyon up to a local operator, the domain walls carry Z3 parafermions, with 3 protected states per pair, whether or not the neutral channel changes between regions; fixing the fermion parity does not enlarge this count. Before the neutral gap forms, pairing is at best marginal for repulsive inter-edge coupling unless an attractive neutral coupling favors its channel; once the gap has formed, both charge terms are relevant for an inter-edge Coulomb coupling below 7/25 of the intra-edge one. The superconductor must supply even-frequency, equal-spin, intravalley pairing, which an s-wave singlet superconductor with only Ising spin-orbit coupling does not provide at leading order, whereas chiral p+ip and f+if states do. The Z3 label is carried by a quasiparticle of the FQAH state, so no process confined to a junction whose tunneling segments are not FQAH can change it, and we expect a 6π-periodic Josephson current with or without fixed fermion parity.
Related
- Parafermions in polarized ν=2/3 Fractional Quantum (Anomalous) Hall Heterostructures
- Direct transition from a fractional Chern insulator to a topological superconductor
- Is the fractional Chern insulator-superconductor transition in twisted MoTe2 direct?
- Zero Mode Operators and Charge-Conjugation Defects in Non-Abelian Fractional Quantum Hall-Superconductor Heterostructures
- Topological and kinetic origins of fractional thermal conductance at the topological insulator--superconductor interface
BibTeX
@misc{amire2026parafermions,
title = {{Parafermions in fractional Chern insulator-superconductor heterostructures: the role of spin polarization}},
author = {Aaron Amire},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.01486},
eprint = {2610.01486},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.01486},
}
RIS
TY - UNPB
TI - Parafermions in fractional Chern insulator-superconductor heterostructures: the role of spin polarization
AU - Aaron Amire
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.01486
UR - https://arxiv.org/abs/2610.01486
AB - Most proposals for Z_3 parafermions in fractional quantum Hall-superconductor structures used the spin-unpolarized ν= 2/3 Halperin (1,1,2) state. The fractional quantum anomalous Hall (FQAH) states of twisted MoTe_2 and rhombohedral graphene are believed to be spin- and valley-polarized Jain states, with the same topological order but a different spin structure. We analyze a trench between two polarized ν= 2/3 edges. Among the pairing and tunneling bilinears of the edge-mode electrons, exactly two of each have zero conformal spin. Pairing is compatible only with the neutral-mode superconductivity channel and tunneling only with neutral-mode backscattering, whereas in the unpolarized state singlet pairing and tunneling select the same channel. Since the two channels condense the same neutral anyon up to a local operator, the domain walls carry Z_3 parafermions, with 3 protected states per pair, whether or not the neutral channel changes between regions; fixing the fermion parity does not enlarge this count. Before the neutral gap forms, pairing is at best marginal for repulsive inter-edge coupling unless an attractive neutral coupling favors its channel; once the gap has formed, both charge terms are relevant for an inter-edge Coulomb coupling below 7/25 of the intra-edge one. The superconductor must supply even-frequency, equal-spin, intravalley pairing, which an s-wave singlet superconductor with only Ising spin-orbit coupling does not provide at leading order, whereas chiral p+ip and f+if states do. The Z_3 label is carried by a quasiparticle of the FQAH state, so no process confined to a junction whose tunneling segments are not FQAH can change it, and we expect a 6π-periodic Josephson current with or without fixed fermion parity.
ER -