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arXiv:2605.19036

Hidden weak-pairing superconductivity of non-interacting anyons obeying $\frac{1}{3}$ statistics

Zheng-Duo Fan, Ashvin Vishwanath, Zijian Wang

cond-mat.str-elcond-mat.supr-conquant-phSubmitted May 18, 2026• Announced May 20, 2026
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Abstract

We show that a non-interacting gas of charge-$e/3$ anyons with exchange statistics $θ=-π/3$ can superconduct through a hidden weak-pairing mechanism. Such an anyon gas arises naturally in doped fractional Chern insulators at filling $1/3$ or $2/3$, where projective lattice translations enforce three degenerate anyon pockets. Exploiting this three-pocket structure, we develop a flux-attachment construction in which the average statistical flux vanishes, thereby mapping the problem to three species of composite fermions (CFs) in zero effective magnetic field. We show that the anyon statistics itself, encoded in statistical gauge field fluctuations, supplies the pairing glue and drives the CFs into a $p-\mathrm{i}p$ paired state, which corresponds to a $f-\mathrm{i}f$ physical superconductor. The CF strong-pairing phase is adiabatically connected to Laughlin's picture of anyon superconductivity, where charge-$e/3$ anyons bind into charge-$2e/3$ molecules, which then lead to superconductivity. By contrast, the more natural weak-pairing phase of CFs realizes a distinct superconducting phase - its edge is characterized by a chiral central charge $c_-=-1/2$, in contrast to the prediction of integer $c_-$ for the anyon superconductor based on Laughlin's picture, thereby resolving the discrepancy between previous theories and recent numerical results. Our theory provides a natural framework for understanding superconductivity near fractional Chern insulators, as observed in recent experiments. Finally, we discuss extensions of our theory that predict new chiral superconductors adjacent to FCIs at other fillings.

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Hidden weak-pairing superconductivity of non-interacting anyons obeying 13\frac{1}{3}31​ statistics
We show that a non-interacting gas of charge-e/3e/3e/3 anyons with exchange statistics θ=−π/3θ=-π/3θ=−π/3 can superconduct through a hidden weak-pairing mechanism. Such an anyon gas arises naturally in doped fractional Chern insulators at filling 1/31/31/3 or 2/32/32/3, where projective lattice translations enforce three degenerate anyon pockets. Exploiting this three-pocket structure, we develop a flux-attachment construction in which the average statistical flux vanishes, thereby mapping the problem to three species of composite fermions (CFs) in zero effective magnetic field. We show that the anyon statistics itself, encoded in statistical gauge field fluctuations, supplies the pairing glue and drives the CFs into a p−ipp-\mathrm{i}pp−ip paired state, which corresponds to a f−iff-\mathrm{i}ff−if physical superconductor. The CF strong-pairing phase is adiabatically connected to Laughlin's picture of anyon superconductivity, where charge-e/3e/3e/3 anyons bind into charge-2e/32e/32e/3 molecules, which then lead to superconductivity. By contrast, the more natural weak-pairing phase of CFs realizes a distinct superconducting phase - its edge is characterized by a chiral central charge c−=−1/2c_-=-1/2c−​=−1/2, in contrast to the prediction of integer c−c_-c−​ for the anyon superconductor based on Laughlin's picture, thereby resolving the discrepancy between previous theories and recent numerical results. Our theory provides a natural framework for understanding superconductivity near fractional Chern insulators, as observed in recent experiments. Finally, we discuss extensions of our theory that predict new chiral superconductors adjacent to FCIs at other fillings.
We study phases of itinerant anyons when hole-doping Laughlin-like states in fractional Chern insulators (FCIs). In light of the recent observation of time-reversal-broken superconductivity near FCIs in van der Waals materials, a theoretical understanding of doped fractional quantum Hall states on a lattice has been developed by Shi and Senthil [Phys. Rev. X 15, 031069], reviving old ideas about "anyon superconductivity". We test these ideas analytically within an effective parton mean-field theory and numerically with variational Monte Carlo, pointing out that the predicted state depends on whether the Laughlin order at ν=1/mν=1/mν=1/m is described by a U(1), or an SU(m) Chern-Simons field, the latter implying a symmetry between the m parton species. Our results demonstrate that the interplay between band Berry curvature and effective anyon dispersion has crucial implications for which anyonic phase is realized. In the experimentally relevant scenario of hole-doping the ν=1/3ν=1/3ν=1/3 fermionic FCI, our results uncover a mechanism for the formation of an anyon superconducting state of half-integer central charge in the case when the energetically cheapest excitations are the fundamental 1/3 charge anyons, bypassing the need for these anyons to pair into charge-2/3 composites, which has generally been assumed in similar anyon superconductivity constructions.
The ground state of an ideal gas of anyons with statistical angle θ∈(0,π)θ\in(0,π)θ∈(0,π) is a long-standing open problem, with renewed interest from the recent observations of fractional Chern insulators. In this work we construct variational wavefunctions that build in the exact anyon statistics and combine theory-guided composite-boson, composite-fermion and parton wavefunctions with neural-network correlations on the sphere. For spinless and SU(2) semions we confirm the paired anyon superfluid, well below the best crystal states. At θ=π/3θ=π/3θ=π/3 liquids and crystals are closer in energy for the spinless case. For θ=π/3θ=π/3θ=π/3 anyons with SU(3) flavor, we find two candidates. One is a skyrmion Hall crystal, in which the anyons form an integer quantum Hall state in the effective magnetic field from the spin texture. The other is a chiral color superconductor of six-anyon clusters, the color-flavor-locked pairing descendant of a holon metal with SU(3) color gauge symmetry and SU(3) flavor symmetry; its wavefunction is a hyperdeterminant rather than a product of parton determinants. Within our variational ansatz the color superconductor has better energy than both crystals and the color-flavor locked phases with U(1)2^22 and Z3_33​ gauge groups. For twisted MoTe2_22​ this suggests that the reentrant integer quantum anomalous Hall phase is the skyrmion Hall crystal of the doped anyons, and that the observed superconductivity may be the color superconductor, which can undergo a transition to an f+iff+iff+if BCS superconductor with a jump of the chiral central charge by 3.
The quantum-mechanical description of assemblies of particles whose motion is confined to two (or one) spatial dimensions offers many possibilities that are distinct from bosons and fermions. We call such particles anyons. The simplest anyons are parameterized by an angular phase parameter θθθ. θ=0,πθ= 0, πθ=0,π correspond to bosons and fermions respectively; at intermediate values we say that we have fractional statistics. In two dimensions, θθθ describes the phase acquired by the wave function as two anyons wind around one another counterclockwise. It generates a shift in the allowed values for the relative angular momentum. Composites of localized electric charge and magnetic flux associated with an abelian U(1) gauge group realize this behavior. More complex charge-flux constructions can involve non-abelian and product groups acting on a spectrum of allowed charges and fluxes, giving rise to nonabelian and mutual statistics. Interchanges of non-abelian anyons implement unitary transformations of the wave function within an emergent space of internal states. Anyons of all kinds are described by quantum field theories that include Chern--Simons terms. The crossings of one-dimensional anyons on a ring are uni-directional, such that a fractional phase θθθ acquired upon interchange gives rise to fractional shifts in the relative momenta between the anyons. The quasiparticle excitations of fractional quantum Hall states have long been predicted to include anyons. Recently the anyon behavior predicted for quasiparticles in the ν=1/3ν= 1/3ν=1/3 fractional quantum Hall state has been observed both in scattering and in interferometric experiments. Excitations within designed systems, notably including superconducting circuits, can exhibit anyon behavior. Such systems are being developed for possible use in quantum information processing.
The quantum-mechanical description of assemblies of particles whose motion is confined to two (or one) spatial dimensions offers many possibilities that are distinct from bosons and fermions. We call such particles anyons. The simplest anyons are parameterized by an angular phase parameter θ. θ = 0, π correspond to bosons and fermions, respectively; at intermediate values, we say that we have fractional statistics. In two dimensions, θ describes the phase acquired by the wave function as two anyons wind around one another counterclockwise. It generates a shift in the allowed values for the relative angular momentum. Composites of localized electric charge and magnetic flux associated with an abelian U(1) gauge group realize this behavior. More complex charge-flux constructions can involve nonabelian and product groups acting on a spectrum of allowed charges and fluxes, giving rise to nonabelian and mutual statistics. Interchanges of nonabelian anyons implement unitary transformations of the wave function within an emergent space of internal states. Anyons of all kinds are described by quantum field theories that include Chern–Simons terms. The crossings of one-dimensional anyons on a ring are unidirectional, such that a fractional phase θ acquired upon interchange gives rise to fractional shifts in the relative momenta between the anyons. The quasiparticle excitations of fractional quantum Hall states have long been predicted to include anyons. Recently, the anyon behavior predicted for quasiparticles in the ν = 1/3 fractional quantum Hall state has been observed in both scattering and interferometric experiments. Excitations within designed systems, notably including superconducting circuits, can exhibit anyon behavior. Such systems are being developed for possible use in quantum information processing.
We propose doping SU(3)SU(3)SU(3)-symmetric spin liquids as a route toward charge-6e6e6e superconductivity. This generalizes the idea of constructing charge-4e4e4e superconductivity from doped SU(4)SU(4)SU(4)-symmetric phases. As a concrete platform, we study a bilayer triangular-lattice Hubbard model with SU(3)SU(3)SU(3) spin symmetry and interlayer antiferromagnetic exchange. Using complementary parton constructions, we analyze doped Z3\mathbb{Z}_3Z3​ quantum spin liquid and SU(3)SU(3)SU(3)-related chiral spin liquids. Doping a Z3\mathbb{Z}_3Z3​ quantum spin liquid can produce an orthogonal metal with a gauge invariant fermi surface of charge-3e3e3e fermionic trions. Pairing these trions gives a time-reversal-symmetric charge-6e6e6e superconductor. Doping Abelian SU(3)1SU(3)_1SU(3)1​ and SU(6)1SU(6)_1SU(6)1​ chiral spin liquids yields chiral charge-6e6e6e superconductors with and without residual Abelian topological order, respectively. Doping a non-Abelian SU(3)2SU(3)_2SU(3)2​ chiral spin liquid leads to a non-Abelian chiral charge-6e6e6e superconductor intertwined with SO(3)−3SO(3)_{-3}SO(3)−3​ topological order and supporting non-Abelian h/(6e)h/(6e)h/(6e) superconducting vortices. We also identify several other phases, including Z3\mathbb{Z}_3Z3​ orthogonal metal, quantum anomalous Hall (crystal) phases enriched by Z3\mathbb{Z}_3Z3​ or Z2\mathbb{Z}_2Z2​ topological order, SU(3)SU(3)SU(3)-breaking charge-2e2e2e superconductors, composite fermi liquid coupled to non-Abelian gauge field, and descendant chiral spin liquids. Our results identify doped SU(3)SU(3)SU(3) spin liquids as a natural setting where symmetry, fractionalization, and topology cooperate to produce charge-6e6e6e superconductivity.