Work

$1/3$-Flux Bound States in Multicomponent Superconductor Exhibiting Non-Abelian Statistics of $\mathbb {Z}_3$ Parafermions

Year: 2026

Type: preprint

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 $C_3$ 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 $\mathbb{Z}_3$ parafermions. Under no-double-occupancy constraint, two successive braiding operations of $1/3$-FBSs are equivalent to a single $\mathbb Z_3$ 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 $\mathbb{Z}_3$ parafermion braiding operations.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.08326

Authors: Wu, Xing-Yu, Wang, Y. H., Xie, X. C., Wu, Yijia

Institutions: Fudan University, State Key Laboratory of Surface Physics, Shanghai Research Center for Quantum Sciences

Language: English

Topic: Topological Materials and Phenomena

Subfield: Condensed Matter Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: green

Funders: National Natural Science Foundation of China, Fudan University, National Science and Technology Major Project

Awards: G102552572, G1208052468, G4635499152, G8590833815, G8600829791, G939132664

OpenAlex ID: W7212076272

Cites: 3

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