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PreprintCC BY 4.0arXiv

1/3-Flux Bound States in Multicomponent Superconductor Exhibiting Non-Abelian Statistics of ℤ3 Parafermions

  • Xing-Yu Wu
  • Y. H. Wang
  • X. C. Xie
  • Yijia Wu
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Abstract

Multicomponent superconductors (MSCs) are predicted to host magnetic flux quanta carrying arbitrary fractions of the superconducting flux quantum. Recent advances have raised the expectation that 1/3 flux quanta may emerge in MSCs with C3 rotational symmetry. Electrons bound to such fractional flux are long regarded to form anyons, yet their explicit braiding statistics remain unexplored. We propose that these 1/3-flux bound states (1/3-FBSs) exhibit the intriguing non-Abelian statistics of ℤ3 parafermions. Under no-double-occupancy constraint, two successive braiding operations of 1/3-FBSs are equivalent to a single ℤ3 parafermion braiding operation. The parafermion parity encoding the braiding outcome can be read out via the fermionic occupation number of the 1/3-FBSs. Combined with a crossed-Andreev-reflection-induced Hadamard gate, one can realize the complete set of ℤ3 parafermion braiding operations.

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Cite

BibTeXRIS
BibTeX
@misc{wu202613flux,
  title = {{$1/3$-Flux Bound States in Multicomponent Superconductor Exhibiting Non-Abelian Statistics of $\mathbb Z_3$ Parafermions}},
  author = {Xing-Yu Wu and Y. H. Wang and X. C. Xie and Yijia Wu},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.08326},
  eprint = {2609.08326},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.08326},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - 1/3-Flux Bound States in Multicomponent Superconductor Exhibiting Non-Abelian Statistics of ℤ_3 Parafermions
AU  - Xing-Yu Wu
AU  - Y. H. Wang
AU  - X. C. Xie
AU  - Yijia Wu
PY  - 2026
DA  - 2026/09/15
PB  - arXiv
DO  - 10.48550/arxiv.2609.08326
UR  - https://arxiv.org/abs/2609.08326
AB  - Multicomponent superconductors (MSCs) are predicted to host magnetic flux quanta carrying arbitrary fractions of the superconducting flux quantum. Recent advances have raised the expectation that 1/3 flux quanta may emerge in MSCs with C_3 rotational symmetry. Electrons bound to such fractional flux are long regarded to form anyons, yet their explicit braiding statistics remain unexplored. We propose that these 1/3-flux bound states (1/3-FBSs) exhibit the intriguing non-Abelian statistics of ℤ_3 parafermions. Under no-double-occupancy constraint, two successive braiding operations of 1/3-FBSs are equivalent to a single ℤ_3 parafermion braiding operation. The parafermion parity encoding the braiding outcome can be read out via the fermionic occupation number of the 1/3-FBSs. Combined with a crossed-Andreev-reflection-induced Hadamard gate, one can realize the complete set of ℤ_3 parafermion braiding operations.
ER  -