Wavefunctions for Anyon Superconductors
Abstract
Anyon superconductivity arises from the condensation of mobile anyons rather than from a conventional Cooper instability, yet a systematic wavefunction description remains lacking. We develop a hierarchy-wavefunction construction for superconducting states derived from parent topological orders and identify their off-diagonal long-range order, condensate charge, chiral central charge, and residual topological order through the plasma analogy and topological field theories. We construct Abelian and non-Abelian examples descending from the semion state, a ν=2/3 hierarchy state, the ν=1/3 Laughlin state, ν=1 integer quantum Hall state, and Pfaffian state. Remarkably, for the semion case, the superconducting many-semion wavefunction is equivalent to a state of fermionized anyons filling two effective Landau levels, recovering Laughlin's original construction of semion superconductor. Finally, we show that hierarchy wavefunctions emerge naturally in the dilute, long-distance limit of the anyon-Hilbert-space formulation, which applies to ideal Chern bands and moiré bands of twisted bilayer MoTe2. Our results establish a unified wavefunction-level framework linking anyon condensation, superconducting order, and topological field theory.
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BibTeX
@misc{seo2026wavefunctions,
title = {{Wavefunctions for Anyon Superconductors}},
author = {Donghae Seo and Taegon Lee and Gil Young Cho},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.04187},
eprint = {2609.04187},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.04187},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Wavefunctions for Anyon Superconductors
AU - Donghae Seo
AU - Taegon Lee
AU - Gil Young Cho
PY - 2026
DA - 2026/09/03
PB - arXiv
DO - 10.48550/arxiv.2609.04187
UR - https://arxiv.org/abs/2609.04187
AB - Anyon superconductivity arises from the condensation of mobile anyons rather than from a conventional Cooper instability, yet a systematic wavefunction description remains lacking. We develop a hierarchy-wavefunction construction for superconducting states derived from parent topological orders and identify their off-diagonal long-range order, condensate charge, chiral central charge, and residual topological order through the plasma analogy and topological field theories. We construct Abelian and non-Abelian examples descending from the semion state, a ν=2/3 hierarchy state, the ν=1/3 Laughlin state, ν=1 integer quantum Hall state, and Pfaffian state. Remarkably, for the semion case, the superconducting many-semion wavefunction is equivalent to a state of fermionized anyons filling two effective Landau levels, recovering Laughlin's original construction of semion superconductor. Finally, we show that hierarchy wavefunctions emerge naturally in the dilute, long-distance limit of the anyon-Hilbert-space formulation, which applies to ideal Chern bands and moiré bands of twisted bilayer MoTe_2. Our results establish a unified wavefunction-level framework linking anyon condensation, superconducting order, and topological field theory.
ER -