Anyon delocalization transitions out of a disordered FQAH insulator

T. Senthil; Zhengyan Darius Shi

REVIEW 3 major objections 4 minor 9 cited by

Anyon delocalization transitions out of a disordered FQAH insulator

T0 review · 3 major / 4 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read Doping the $\nu=2/3$ FQAH insulator with $a_{2/3}$ anyons under smooth disorder drives a direct second-order transition to a chiral topological superconductor, with a universal longitudinal-resistance peak of order $h/e^2$ at the quantum…

desk verdict Solid extension of the clean-limit anyon-doping theory to disorder, with real predictions and one load-bearing symmetry assumption that deserves scrutiny. read the letter →

arxiv 2506.02128 v2 pith:BFUIFNR6 submitted 2025-06-02 cond-mat.str-el

Zhengyan Darius Shi , T. Senthil This is my paper · ORCID

classification cond-mat.str-el

keywords fractionalquantumanomalousHalleffectanyondelocalizationtopologicalsuperconductorvortexglasscriticalpointdisorderJainstateSU(3)symmetry

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper develops a disorder-inclusive theory of what happens when the $\nu=2/3$ lattice Jain fractional quantum anomalous Hall (FQAH) insulator is doped away from its plateau. It claims that when charge-$2/3$ anyons delocalize under a smooth, long-wavelength random potential, the system undergoes a direct second-order transition into a chiral topological superconductor with four chiral Majorana edge modes, and the longitudinal resistance at that quantum critical point has a universal peak of order $h/e^2$. On the superconducting side of the transition, localized anyons are argued to transmute into a zero-field anomalous vortex glass, a random arrangement of Cooper-pair vortices of zero net vorticity, so that dissipationless transport only sets in at a second critical point. If instead the charge-$1/3$ anyon delocalizes, the theory predicts a reentrant integer quantum Hall state with $\rho_{xy}=h/e^2$ at low doping and a Fermi-liquid metal at higher doping. These claims matter because they give concrete transport signatures, universal peak resistances, specific thermal-Hall values, and nonlinear current-voltage curves, that can be used to identify whether the superconductor and reentrant IQAH states seen near $\nu=2/3$ in twisted MoTe$_2$ are indeed anyon-induced.

What carries the argument

The central machinery is the parton construction of the $\nu=2/3$ Jain state, $c=f_1f_2f_3$, with Chern numbers $C_1=-2,\ C_2=C_3=1$ and two emergent gauge fields whose fluxes enforce equal parton densities. Doping with $a_{2/3}$ anyons puts fermions into the three degenerate minima of the $f_3$ band, described by fields $d_I$ ($I=1,2,3$) that see an effective magnetic field; smooth disorder keeps the $d_I$ equivalent and preserves an emergent SU(3) symmetry among them. The key move is to treat the delocalization of these $d_I$ fermions as an SU(3)-symmetric plateau transition with Hall jump $\Delta\sigma^d_{xy}=-3e^2/h$, then use the Ioffe-Larkin composition rule, a series addition of parton and gauge-field conductivities, to convert the critical $d_I$ conductivity into a universal physical resistivity tensor with a universal $\rho_{xx}$ peak. The anomalous vortex glass is derived by duality: localized $a_{2/3}$ anyons become random sources of vorticity $-2\pi$ and $4\pi$ in the Cooper-pair phase, with the net vorticity vanishing.

What would settle it

A low-temperature transport sweep of the doping-tuned $\nu=2/3$ FQAH plateau in a clean moiré device can settle the claim: if the side doped with $a_{2/3}$ anyons shows more than one distinct resistance peak between the plateau and the superconductor, or if the peak height does not saturate to a universal $O(h/e^2)$ value and its width does not shrink as a power of temperature, then the smooth-disorder SU(3) direct-transition mechanism is not what the experiment is measuring.

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Extended reading notes

Core claim

On its own terms, the paper's central claim is that the anyon delocalization transition carries the doped FQAH system into a chiral topological superconductor through a single continuous transition, provided the random potential is smooth enough that disorder respects an emergent SU(3) symmetry among the three valley fermions. The topological superconductor has chiral central charge $c_-=-2$ and zero Hall conductance; at the quantum critical point the resistivity tensor is universal, with a longitudinal peak of order $h/e^2$. The paper further claims that near the onset the superconducting ground state is an anomalous vortex glass: a zero-field vortex glass in which localized $a_{2/3}$ anyons become randomly pinned vortices of strength $-2\pi$ and $+4\pi$ in the Cooper-pair phase, with zero net vorticity. For short-wavelength disorder the SU(3) symmetry is broken and the direct transition is replaced by three separate plateau transitions with intermediate phases carrying neutral $U(1)_{-2}$ topological order and an IQH state with $\sigma_{xy}=-2e^2/h$.

Load-bearing premise

The direct transition claim rests on the assumption that the disorder potential varies only on long wavelengths, so that the three valley-fermion flavors remain exactly equivalent to one another; the paper itself states that short-wavelength disorder splits the transition into three separate ones.

Editorial extensions

If this is right

On the $a_{2/3}$ doping side with smooth disorder, the FQAH plateau gives way at $\mu_{c1}$ to a superconducting state through a direct continuous transition; at $T=0$ the critical point has a universal longitudinal resistance peak of order $h/e^2$, broadened at finite temperature with width $\sim T^{1/(\bar\nu z)}$ and $\bar\nu z \ge 2$.
The resulting superconductor has $c_-=-2$ and no electron spectral weight below the $a_{1/3}$ gap, and it is reached from the FQAH by transmuting anyons into vortices.
For $\mu_{c1}<\mu<\mu_{c2}$, the ground state is an anomalous vortex glass at zero field, with nonzero linear resistance at any $T>0$ due to vortex creep and nonlinear current-voltage characteristics below a current scale $J_T\sim T^{1+1/|\theta|}$ with $\theta\approx0.5$.
Short-wavelength disorder forbids the direct transition: the evolution passes through three intermediate phases, a neutral $U(1)_{-2}$ topological insulator, then an IQH state with $\sigma_{xy}=-2e^2/h$, with each intervening critical point having a universal $O(h/e^2)$ resistivity tensor.
On the $a_{1/3}$ doping side, disorder stabilizes a reentrant IQH state with $\rho_{xy}=h/e^2$ at low doping, replacing the clean charge-ordered Fermi liquid, and at higher doping there is a transition to a Fermi-liquid metal.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

A microscopic calculation of the relative excitation gaps of the $a_{1/3}$ and $a_{2/3}$ anyons in twisted MoTe$_2$ would settle which doping side realizes anyon-induced superconductivity and which realizes the reentrant IQH state; the paper treats this energetics as input rather than deriving it.
The same parton construction should apply to other lattice Jain states at $\nu=p/(2p+1)$; if so, the number of equivalent valley flavors and the size of the Hall jump would change, turning the universal-peak prediction into a family of predictions that future material searches could test.
Measuring the temperature dependence of the resistance-peak width would give a quantitative probe of the universality class: extracting $\bar\nu z$ would test whether the transition is indeed the SU(3)-symmetric plateau transition rather than a generic disordered transition.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Here's my read. This is a serious, mostly solid theory paper that takes the clean-limit anyon-doping framework from Shi and Senthil's earlier work and pushes it into the disordered regime. The genuinely new results are the dirty-limit phase diagrams, the split into three transitions for short-wavelength disorder, and the prediction of an anomalous vortex glass at zero field near the FQAH–SC boundary. The universal resistance peak at the anyon delocalization critical point is a concrete, falsifiable signature. The Chern–Simons response calculations and the appendices are internally consistent; the vortex transmutation argument is explicit, and the bosonic mapping is a nice sanity check. The authors are also honest about the tMoTe2 comparison: they flag the Streda slope discrepancy and the small-vs-large carrier density question, and they acknowledge the concurrent work of Nosov et al. That's good practice.

The main soft spot, and it's a real one, is the SU(3)-symmetric smooth-disorder assumption that underlies the direct FQAH-to-superconductor transition. The paper argues that smooth disorder has no intervalley Fourier weight, so off-diagonal W_IJ is excluded. That's fine for a scalar potential. But smooth strain or twist-angle variations generate valley-diagonal potentials with different coefficients for the three d_I fermions, and the paper does not show such perturbations are irrelevant at the dirty plateau-transition fixed point. If relevant, the single transition with Δσ_xy = -3 splits into the multiple transitions the paper itself describes for short-wavelength disorder. So the direct transition and its universal single peak are less generic than the abstract suggests. The short-wavelength story, with the intermediate U(1)_-2 and IQH phases, is more robust.

A second, minor soft spot: the anomalous vortex glass is argued via a plausible energy comparison and a dual model, but it is not a controlled derivation. That's probably acceptable for a physics paper, but a referee should push on whether the AVG region can actually be wide enough to observe.

Bottom line: the paper deserves a serious referee slot. The central framework holds up; the caveats are addressable rather than fatal. Anyone working on doped FQAH systems or disordered topological phases will want to read it. I'd suggest the referee focus on the SU(3) assumption and ask whether the direct transition survives generic long-wavelength disorder, and on whether the AVG has a finite window in the doping axis.

Referee Report

3 major / 4 minor

Summary. The paper develops a theory of doping-induced transitions out of the ν=2/3 lattice Jain FQAH state in the presence of quenched disorder, extending the authors' earlier clean-limit parton analysis. The central scenario is that doping in charge-2/3 anyons, combined with smooth long-wavelength disorder, produces a direct continuous transition from an anyon glass to a chiral topological superconductor, characterized by a universal longitudinal resistance peak and, very close to the transition, an anomalous vortex glass. For short-wavelength disorder the same evolution is argued to split into three transitions separated by intermediate insulating topological phases. Doping in charge-1/3 anyons is instead argued to yield a reentrant integer quantum Hall state. The framework is applied to recent twisted MoTe2 experiments, with explicit cautions about unresolved experimental ambiguities.

Significance. If the central claims hold, the paper provides a concrete and falsifiable framework for interpreting the transport anomalies observed near the ν=2/3 FQAH plateau in twisted MoTe2: a universal resistance peak at the anyon delocalization transition, an anomalous vortex glass regime with non-linear I-V response, and a reentrant integer quantum Hall state. The paper contains explicit Chern-Simons derivations of vortex transmutation and a useful bosonic mapping, and it is commendably explicit about several limitations, including the uncertain carrier density interpretation and the need for microscopic anyon energetics. The main value is the identification of a sharp experimental signature—a universal ρ_xx peak—attached to a specific anyon-delocalization scenario, rather than a fully microscopic derivation of the tMoTe2 phase diagram.

major comments (3)

[Doping the a_{2/3} anyon: dirty limit, Eq. (9)] The claim that long-wavelength disorder necessarily preserves an emergent SU(3) symmetry among the three d_I species is too strong. Smoothness (small Fourier momentum) excludes intervalley couplings W_IJ with q of order K_I−K_J, but it does not exclude valley-diagonal random potentials W_I(r) d_I^† d_I with spatially dependent and unequal coefficients. Such terms are generated by smooth strain or twist-angle disorder through valley-dependent deformation potentials and pseudo-gauge fields—indeed the paper itself invokes random twist angle as a plausible dominant disorder source in footnote 6. These terms break the SU(3) symmetry while remaining long-wavelength, so by the paper's own logic for short-wavelength disorder (Fig. 4) they would generically split the single Δσ_xy^d=−3 transition into multiple transitions. The direct FQAH–superconductor transition and the associated single universal ρ_xx peak therefore require a symmetry assumption about the disorder ensemble, not merely smoothness. The manuscript should either demonstrate that such valley-dependent diagonal perturbations are irrelevant at the dirty plateau-transition fixed point, or explicitly restrict the direct-transition claim to exactly SU(3)-symmetric disorder and discuss whether that is realistic for tMoTe2.
[Doping the a_{2/3} anyon: dirty limit, Eqs. (10)–(11)] The paper asserts a universal value of the critical resistivity tensor ρ_c at μ_c1, but it does not actually compute or constrain the critical conductivity tensor σ_d of the SU(3)-symmetric plateau transition. The Ioffe-Larkin relation only converts σ_d to ρ_c; universality of ρ_c follows only if both σ_xx^d and σ_xy^d take universal values at the critical point. For the ordinary IQH plateau transition the critical σ_xy is not fixed by symmetry unless particle-hole symmetry is imposed, and for the three-flavor transition the critical tensor is even less constrained. The 'universal peak' is therefore a universal statement only in the weak sense of being O(h/e^2) and material-independent, not a computed number. The manuscript should either provide a derivation or numerical reference for the critical σ_d of this transition class, or temper the language so that the predicted observable is the existence and scaling of the peak rather than a precisely universal height.
[Doping the a_{1/3} anyon: dirty limit] The transition from the a_{1/3} anyon glass to the reentrant IQH state is not analyzed with the same control as the a_{2/3} case. The text states that the smooth-disorder transition is 'about which very little is understood', and for short-wavelength disorder the route is justified only by 'it is natural to encounter a plateau transition' in which the total Hall conductance jumps by 1. Since the paper uses this scenario to explain the ν<2/3 side of the tMoTe2 phase diagram, the RIQAH prediction is a heuristic conjecture rather than a derived consequence. The application section is appropriately cautious, but the abstract should not present the RIQAH state as a direct output of the theory without clarifying that the transition mechanism itself is not developed.

minor comments (4)

[Eq. (9)] The phrase 'the only terms compatible with smooth disorder' should be qualified: smoothness alone allows valley-dependent diagonal potentials; the restricted form (9) follows only if the disorder is also valley-blind. This distinction should be stated explicitly to avoid the current overgeneralization.
[Fig. 4] The figure labels appear to place ρ_xy=−h/2e^2 next to the chiral topological superconducting phase; a superconductor should have ρ_xy=0. Resolve this labeling so that the σ_xy=−2 IQH phase and the superconducting phase are clearly distinguished.
[Abstract and application section] The terminology for the reentrant state is inconsistent: the abstract uses 'Reentrant Integer Quantum Hall state', the body uses 'Reentrant Integer Quantum Anomalous Hall (RIQAH)', and one instance reads 'Rentrant'. Standardize the terminology and the corresponding acronym.
[Dirty limit, disorder strength notation] The notation W_IJ and W_b is used both for the random fields in Eq. (8) and for their typical strength in the subsequent text. Introduce explicit disorder variances, e.g. ⟨W_IJ(r)W_IJ(0)⟩, to remove the ambiguity.

Circularity Check

1 steps flagged · score 3.0 of 10

Central disorder-induced transition derivation is self-contained; only the tMoTe2 anyon-assignment step is post hoc, turning observed asymmetry into a 'prediction'.

fitted input called prediction [Section 'Application to doped tMoTe2', paragraphs after Eq. (21)]
"At displacement field D=0 and ν=2/3, we propose that the anyon energetics of the Jain state has a particle-hole asymmetry, such that doping towards ν>2/3 induces a fluid of a_{2/3}, while doping towards ν<2/3 induces a fluid of a_{1/3}. ... Doping beyond the plateau, our theory predicts a topological superconductor at ν>ν2 and an RIQAH state at ν<ν1."

The relative anyon energetics (which parton band is closest to the chemical potential) is the input that decides whether a_{2/3} or a_{1/3} is doped. The paper chooses this input specifically so that ν>2/3 gives a_{2/3} (leading to SC) and ν<2/3 gives a_{1/3} (leading to RIQAH), matching the observed asymmetry of the tMoTe2 phase diagram. The subsequent 'prediction' of SC on one side and RIQAH on the other is therefore a restatement of the chosen input, not an independent consequence. No microscopic calculation of the anyon energetics is provided to fix this assignment; it is inferred from the same phenomenology it is used to explain.

full rationale

The core derivation chain—parton Lagrangian (following Ref. [14]), clean critical theory, the disorder Lagrangian Eq. (8), the smooth-disorder reduction to Eq. (9), the SU(3)-symmetric plateau transition, and the Ioffe-Larkin universal ρ_xx peak—is internally self-contained once the stated assumptions are granted. Ref. [14] supplies the clean-limit framework but is not used to bypass the new disorder analysis; the new conclusions follow from equations displayed in this paper. The main circularity found is in the application to tMoTe2: the particle-hole asymmetric anyon energetics is posited to match the observed SC/RIQAH asymmetry, then used to 'predict' the same asymmetry. The universal peak, direct transition, and AVG statements for a generic FQAH are not circular. The fragility of the smooth-disorder SU(3) reduction (valley-dependent strain or twist disorder can break it) is a correctness risk rather than a circularity, so it does not increase the score further.

Assumptions & free parameters 3 free parameters · 9 assumptions · 0 invented entities

The paper introduces no new elementary particles or mediators. Its main input assumptions are the parton construction of the ν=2/3 Jain state, the dilute anyon fluid description, and the disorder symmetry assumptions. The anomalous vortex glass is a new phase, not a new entity, and it is argued with a classical model.

free parameters (3)

Effective mass m of d_I partons
Appears in the kinetic term and in the cyclotron gap ω_c(δ)∼δ/m; no value is fitted, and the qualitative conclusions do not depend on m.
Berry curvature Ω in Appendix C
Phenomenological parameter in the semiclassical anyon transport model used to infer mobile carrier density; it does not enter the central phase diagram claims.
Momentum relaxation time τ in Appendix C
Phenomenological scattering time in the Boltzmann transport model; only used for the proposed experimental measurement of carrier density.

assumptions (9)

domain assumption Parton decomposition c = f1 f2 f3 with emergent U(1) gauge fields a and b (Eq. 1).
The entire low-energy theory is built on this fractionalization scheme, standard for Jain states but not derived in this paper.
domain assumption Mean-field flux ansatz ⟨∇×a⟩/2π=-1/3 and ⟨∇×b⟩/2π=1/3 with Chern number assignment C1=-2, C2=C3=1 (Eq. 2 and following text).
This choice constructs the ν=2/3 lattice Jain state; the resulting effective Chern-Simons theory (Eq. 3) is the starting point for all doping analysis.
domain assumption Doped charges form a dilute, itinerant anyon fluid described by three species of d_I fermions with quadratic dispersion near band minima (Eq. 5 and Eq. 16).
The analysis assumes low dopant density and parabolic parton bands; the disorder physics is derived within this effective description.
domain assumption The relative energy gaps of a_{2/3} and a_{1/3} anyons determine which anyon is doped; the paper analyzes both branches separately.
This is an input from microscopics, not derived here; the application to tMoTe2 assumes f3 is nearest conduction band and f1 nearest valence band.
ad hoc to paper Smooth (long-wavelength) disorder preserves an emergent SU(3) symmetry among the d_I species, while short-wavelength disorder breaks it completely (Eq. 9 and following text).
The direct FQAH-SC transition for smooth disorder relies on this symmetry; the split into three transitions relies on complete symmetry breaking. The separation is a modeling choice about the disorder profile.
domain assumption The localized anyon glass is an insulator with quantized σ_xy=2e^2/3h, and gauge fluctuations convert the mean-field localized state into an anyon glass.
Needed to identify the plateau surrounding ν=2/3; localization of anyons at low density is assumed.
ad hoc to paper At the critical point, there is an SU(3)-symmetric plateau transition with a jump Δσ_xy^d=-3 in the d_I fermion Hall conductance.
The direct transition and universal resistance peak follow from this assumption, which is argued by analogy to known plateau transitions rather than derived.
ad hoc to paper Localized anyons near the superconducting transition become randomly pinned vortices with zero net vorticity, forming an anomalous vortex glass (Appendix B).
This is justified by a classical energy estimate and a gauge-glass model, not by a controlled many-body calculation; it is a central qualitative assumption.
standard math The Harris-Chayes bound ν̄≥1 and z=2 for the disordered superfluid-insulator transition are used to constrain the resistance peak width.
Standard results from the theory of disordered bosons are imported to make scaling predictions.

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Cite this review

Pith. "Pith review of Anyon delocalization transitions out of a disordered FQAH insulator." pith.science (2026). https://pith.science/paper/BFUIFNR6

@misc{pith2026250602128,
  author       = {Pith},
  title        = {Pith review of: Anyon delocalization transitions out of a disordered FQAH insulator},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/BFUIFNR6}},
  note         = {Machine review of arXiv:2506.02128}
}

abstract

Motivated by the experimental discovery of the fractional quantum anomalous Hall (FQAH) effect, we develop a theory of doping-induced transitions out of the $\nu = 2/3$ lattice Jain state in the presence of quenched disorder. We show that disorder strongly affects the evolution into the conducting phases described in our previous work. The delocalization of charge $2/3$ anyons leads to a chiral topological superconductor through a direct second order transition for a smooth random potential with long-wavelength modulations. The longitudinal resistance has a universal peak at the associated quantum critical point. Close to the transition, we show that the superconducting ground state is an ``Anomalous Vortex Glass (AVG)'' stabilized in the absence of an external magnetic field. For short-wavelength disorder, this transition generically splits into three distinct ones with intermediate insulating topological phases. If instead, the charge $1/3$ anyon delocalizes, then at low doping the result is a Reentrant Integer Quantum Hall state with $\rho_{xy} = h/e^2$. At higher doping this undergoes a second transition to a Fermi liquid metal. We show that this framework provides a plausible explanation for the complex phase diagram recently observed in twisted MoTe$_2$ near $\nu = 2/3$ and discuss future experiments that can test our theory in more detail.

Figures

Figures reproduced from arXiv: 2506.02128 by the authors.

**Figure 2.** FIG. 2. Onset of [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 4.** FIG. 4. With short-wavelength disorder, the FQAH-SC evolu [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗

Figures from the paper (4 more)

**Figure 3.** Figure 3: FIG. 3. Evolution of [PITH_FULL_IMAGE:figures/full_fig_p005_3.png]

**Figure 5.** Figure 5: FIG. 5. Evolution of [PITH_FULL_IMAGE:figures/full_fig_p006_5.png]

**Figure 6.** Figure 6: FIG. 6. Schematic phase diagram showing the 2 [PITH_FULL_IMAGE:figures/full_fig_p006_6.png]

**Figure 7.** Figure 7: FIG. 7. Phase diagram of the doped bosonic Jain state in the dirty limit with short-wavelength disorder. Note that the four [PITH_FULL_IMAGE:figures/full_fig_p012_7.png]

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Forward citations

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Reference graph

Works this paper leans on

59 extracted references · 29 canonical work pages · cited by 9 Pith papers

[1]

H. Park, J. Cai, E. Anderson, Y. Zhang, J. Zhu, X. Liu, C. Wang, W. Holtzmann, C. Hu, Z. Liu, T. Taniguchi, K. Watanabe, J.-H. Chu, T. Cao, L. Fu, W. Yao, C.- Z. Chang, D. Cobden, D. Xiao, and X. Xu, Observa- tion of fractionally quantized anomalous Hall effect, Na- ture (London)622, 74 (2023), arXiv:2308.02657 [cond- mat.mes-hall]

arXiv 2023
[2]

Y. Zeng, Z. Xia, K. Kang, J. Zhu, P. Kn¨ uppel, C. Vaswani, K. Watanabe, T. Taniguchi, K. F. Mak, and J. Shan, Integer and fractional Chern insulators in twisted bilayer MoTe2, arXiv e-prints , arXiv:2305.00973 (2023), arXiv:2305.00973 [cond-mat.mes-hall]

arXiv 2023
[3]

J. Cai, E. Anderson, C. Wang, X. Zhang, X. Liu, W. Holtzmann, Y. Zhang, F. Fan, T. Taniguchi, K. Watanabe, Y. Ran, T. Cao, L. Fu, D. Xiao, W. Yao, and X. Xu, Signatures of fractional quantum anomalous Hall states in twisted MoTe 2, Nature (London)622, 63 (2023), arXiv:2304.08470 [cond-mat.mes-hall]

arXiv 2023
[4]

F. Xu, Z. Sun, T. Jia, C. Liu, C. Xu, C. Li, Y. Gu, K. Watanabe, T. Taniguchi, B. Tong, J. Jia, Z. Shi, S. Jiang, Y. Zhang, X. Liu, and T. Li, Observation of Integer and Fractional Quantum Anomalous Hall Effects in Twisted Bilayer MoTe2, Physical Review X13, 031037 (2023), arXiv:2308.06177 [cond-mat.mes-hall]

arXiv 2023
[5]

Z. Lu, T. Han, Y. Yao, A. P. Reddy, J. Yang, J. Seo, K. Watanabe, T. Taniguchi, L. Fu, and L. Ju, Fractional quantum anomalous Hall effect in multilayer graphene, Nature (London)626, 759 (2024), arXiv:2309.17436 [cond-mat.mes-hall]

arXiv 2024
[6]

Z. Lu, T. Han, Y. Yao, Z. Hadjri, J. Yang, J. Seo, L. Shi, S. Ye, K. Watanabe, T. Taniguchi, and L. Ju, Ex- tended quantum anomalous Hall states in graphene/hBN moir´ e superlattices, Nature (London)637, 1090 (2025), arXiv:2408.10203 [cond-mat.mes-hall]

arXiv 2025
[7]

H. L. Stormer, D. C. Tsui, and A. C. Gossard, The frac- tional quantum hall effect, Rev. Mod. Phys.71, S298 (1999)

1999
[8]

J. M. Leinaas and J. Myrheim, On the theory of identical particles, Nuovo Cim. B37, 1 (1977). 9

work page 1977

Show all 59 references

[9]

Wilczek, Magnetic flux, angular momentum, and statistics, Phys

F. Wilczek, Magnetic flux, angular momentum, and statistics, Phys. Rev. Lett.48, 1144 (1982)

1982
[10]

Wilczek, Quantum mechanics of fractional-spin parti- cles, Phys

F. Wilczek, Quantum mechanics of fractional-spin parti- cles, Phys. Rev. Lett.49, 957 (1982)

1982
[11]

R. B. Laughlin, Anomalous quantum hall effect: An in- compressible quantum fluid with fractionally charged ex- citations, Phys. Rev. Lett.50, 1395 (1983)

1983
[12]

B. I. Halperin, Statistics of quasiparticles and the hierar- chy of fractional quantized hall states, Phys. Rev. Lett. 52, 1583 (1984)

1984
[13]

Huckestein, Scaling theory of the integer quantum hall effect, Rev

B. Huckestein, Scaling theory of the integer quantum hall effect, Rev. Mod. Phys.67, 357 (1995)

1995
[14]

Darius Shi and T

Z. Darius Shi and T. Senthil, Doping a fractional quantum anomalous Hall insulator, arXiv e-prints , arXiv:2409.20567 (2024), arXiv:2409.20567 [cond- mat.str-el]

2024
[15]

M. Kim, A. Timmel, L. Ju, and X.-G. Wen, Topological chiral superconductivity (2024), arXiv:2409.18067 [cond- mat.str-el]

2024 arXiv
[16]

Darius Shi, C

Z. Darius Shi, C. Zhang, and T. Senthil, Doping lat- tice non-abelian quantum Hall states, arXiv e-prints , arXiv:2505.02893 (2025), arXiv:2505.02893 [cond- mat.str-el]

2025 arXiv
[17]

R. B. Laughlin, Superconducting ground state of non- interacting particles obeying fractional statistics, Phys. Rev. Lett.60, 2677 (1988)

1988
[18]

A. L. Fetter, C. B. Hanna, and R. B. Laughlin, Random- phase approximation in the fractional-statistics gas, Phys. Rev. B39, 9679 (1989)

1989
[19]

Y.-H. Chen, F. Wilczek, E. Witten, and B. I. Halperin, On Anyon Superconductivity, International Journal of Modern Physics A4, 3983 (1989)

1989
[20]

Lee and M

D.-H. Lee and M. P. A. Fisher, Anyon superconductivity and the fractional quantum hall effect, Phys. Rev. Lett. 63, 903 (1989)

1989
[21]

Divic, V

S. Divic, V. Cr´ epel, T. Soejima, X.-Y. Song, A. Mil- lis, M. P. Zaletel, and A. Vishwanath, Anyon Supercon- ductivity from Topological Criticality in a Hofstadter- Hubbard Model, arXiv e-prints , arXiv:2410.18175 (2024), arXiv:2410.18175 [cond-mat.str-el]

2024 arXiv
[22]

F. Xu, Z. Sun, J. Li, C. Zheng, C. Xu, J. Gao, T. Jia, K. Watanabe, T. Taniguchi, B. Tong, L. Lu, J. Jia, Z. Shi, S. Jiang, Y. Zhang, Y. Zhang, S. Lei, X. Liu, and T. Li, Signatures of unconventional superconduc- tivity near reentrant and fractional quantum anomalous Hall insu...

2025 arXiv
[23]

Willett, J

R. Willett, J. P. Eisenstein, H. L. Stormer, A. C. Gossard, and D. C. Tsui, Observation of an even-denominator quantum number in the fractional quantum Hall effect, Phys. Rev. Lett.59, 1776 (1987)

1987
[24]

Q. Xu, G. Ji, Y. Wang, H. Quang Trung, and B. Yang, Dynamics of Clusters of Anyons in Fractional Quantum Hall Fluids, arXiv e-prints , arXiv:2505.20257 (2025), arXiv:2505.20257 [cond-mat.str-el]

2025
[25]

Gattu and J

M. Gattu and J. K. Jain, Molecular anyons in fractional quantum hall effect (2025), arXiv:2505.22782 [cond- mat.str-el]

2025
[26]

M. P. A. Fisher, Vortex-glass superconductivity: A pos- sible new phase in bulk high-t c oxides, Phys. Rev. Lett. 62, 1415 (1989)

1989
[27]

D. S. Fisher, M. P. A. Fisher, and D. A. Huse, Thermal fluctuations, quenched disorder, phase transitions, and transport in type-ii superconductors, Phys. Rev. B43, 130 (1991)

1991
[28]

Senthil and M

T. Senthil and M. P. A. Fisher, Z 2 gauge theory of electron fractionalization in strongly correlated systems, Phys. Rev. B62, 7850 (2000), arXiv:cond-mat/9910224 [cond-mat.str-el]

2000 arXiv
[29]

Senthil and M

T. Senthil and M. P. A. Fisher, Fractionalization in the Cuprates: Detecting the Topological Order, Phys. Rev. Lett.86, 292 (2001), arXiv:cond-mat/0006481 [cond- mat.supr-con]

2001 arXiv
[30]

M. P. A. Fisher, P. B. Weichman, G. Grinstein, and D. S. Fisher, Boson localization and the superfluid-insulator transition, Phys. Rev. B40, 546 (1989)

1989
[31]

M. P. A. Fisher, T. A. Tokuyasu, and A. P. Young, Vor- tex variable-range-hopping resistivity in superconducting films, Phys. Rev. Lett.66, 2931 (1991)

1991
[32]

M.-C. Cha, M. P. A. Fisher, S. M. Girvin, M. Wallin, and A. P. Young, Universal conductivity of two-dimensional films at the superconductor-insulator transition, Phys. Rev. B44, 6883 (1991)

1991
[33]

Damle and S

K. Damle and S. Sachdev, Nonzero-temperature trans- port near quantum critical points, Phys. Rev. B56, 8714 (1997), arXiv:cond-mat/9705206 [cond-mat.str-el]

1997 arXiv
[34]

Sachdev, Nonzero-temperature transport near frac- tional quantum Hall critical points, Phys

S. Sachdev, Nonzero-temperature transport near frac- tional quantum Hall critical points, Phys. Rev. B57, 7157 (1998), arXiv:cond-mat/9709243 [cond-mat.mes- hall]

1998 arXiv
[35]

M. P. A. Fisher, G. Grinstein, and S. M. Girvin, Presence of quantum diffusion in two dimensions: Universal resis- tance at the superconductor-insulator transition, Phys. Rev. Lett.64, 587 (1990)

1990
[36]

A. B. Harris, Effect of random defects on the critical behaviour of ising models, Journal of Physics C: Solid State Physics7, 1671 (1974)

1974
[37]

J. T. Chayes, L. Chayes, D. S. Fisher, and T. Spencer, Finite-size scaling and correlation lengths for disordered systems, Phys. Rev. Lett.57, 2999 (1986)

1986
[38]

Song, Y.-H

X.-Y. Song, Y.-H. Zhang, and T. Senthil, Phase tran- sitions out of quantum Hall states in moir´ e materi- als, Phys. Rev. B109, 085143 (2024), arXiv:2308.10903 [cond-mat.str-el]

2024 arXiv
[39]

C. L. Kane, M. P. A. Fisher, and J. Polchinski, Ran- domness at the edge: Theory of quantum Hall trans- port at fillingν=2/3, Phys. Rev. Lett.72, 4129 (1994), arXiv:cond-mat/9402108 [cond-mat]

1994 arXiv
[40]

C. L. Kane and M. P. A. Fisher, Impurity scattering and transport of fractional quantum Hall edge states, Phys. Rev. B51, 13449 (1995), arXiv:cond-mat/9409028 [cond- mat]

1995 arXiv
[41]

C. L. Kane and M. P. A. Fisher, Contacts and edge-state equilibration in the fractional quantum Hall effect, Phys. Rev. B52, 17393 (1995), arXiv:cond-mat/9506116 [cond- mat]

1995 arXiv
[42]

C. de C. Chamon and E. Fradkin, Distinct universal con- ductances in tunneling to quantum hall states: The role of contacts, Phys. Rev. B56, 2012 (1997)

1997
[43]

Young, Private communication (2024)

A. Young, Private communication (2024)

2024
[44]

Park, Private communication (2025)

H. Park, Private communication (2025)

2025
[45]

Gon¸ calves, J

M. Gon¸ calves, J. F. Mendez-Valderrama, J. Herzog- Arbeitman, J. Yu, X. Xu, D. Xiao, B. A. Bernevig, and N. Regnault, Spinless and spinful charge exci- tations in moir´ e Fractional Chern Insulators, arXiv e-prints , arXiv:2506.05330 (2025), arXiv:2506.05330 [cond-mat.str-el]. 10

2025 arXiv
[46]

J. K. Jain, Composite-fermion approach for the fractional quantum hall effect, Phys. Rev. Lett.63, 199 (1989)

1989
[47]

Goldman, A

H. Goldman, A. P. Reddy, N. Paul, and L. Fu, Zero- Field Composite Fermi Liquid in Twisted Semicon- ductor Bilayers, Phys. Rev. Lett.131, 136501 (2023), arXiv:2306.02513 [cond-mat.mes-hall]

2023 arXiv
[48]

J. Dong, J. Wang, P. J. Ledwith, A. Vishwanath, and D. E. Parker, Composite Fermi Liquid at Zero Magnetic Field in Twisted MoTe 2, Phys. Rev. Lett.131, 136502 (2023), arXiv:2306.01719 [cond-mat.str-el]

2023 arXiv
[49]

Saminadayar, D

L. Saminadayar, D. C. Glattli, Y. Jin, and B. Etienne, Observation of the e/3 Fractionally Charged Laugh- lin Quasiparticle, Phys. Rev. Lett.79, 2526 (1997), arXiv:cond-mat/9706307 [cond-mat]

1997 arXiv
[50]

de-Picciotto, M

R. de-Picciotto, M. Reznikov, M. Heiblum, V. Uman- sky, G. Bunin, and D. Mahalu, Direct observation of a fractional charge, Physica B Condensed Matter249, 395 (1998), arXiv:cond-mat/9707289 [cond-mat.mes-hall]

1998 arXiv
[51]

Martin, S

J. Martin, S. Ilani, B. Verdene, J. Smet, V. Umansky, D. Mahalu, D. Schuh, G. Abstreiter, and A. Yacoby, Lo- calization of Fractionally Charged Quasi-Particles, Sci- ence305, 980 (2004)

2004
[52]

Song and T

X.-Y. Song and T. Senthil, Density wave halo around anyons in fractional quantum anomalous hall states, Phys. Rev. B110, 085120 (2024)

2024
[53]

Senthil and M

T. Senthil and M. P. Fisher, Fractionalization, topolog- ical order, and cuprate superconductivity, Phys. Rev. B63, 134521 (2001), arXiv:cond-mat/0008082 [cond- mat.supr-con]

2001 arXiv
[54]

D. Bonn, J. C. Wynn, B. W. Gardner, Y.-J. Lin, R. Liang, W. Hardy, J. Kirtley, and K. Moler, A limit on spin–charge separation in high-t c superconductors from the absence of a vortex-memory effect, Nature414, 887 (2001)

2001
[55]

P. A. Nosov, Z. Han, and E. Khalaf, Anyon super- conductivity and plateau transitions in doped frac- tional quantum anomalous Hall insulators, arXiv e-prints , arXiv:2506.02108 (2025), arXiv:2506.02108 [cond- mat.str-el]

2025 arXiv
[56]

Y.-H. Zhang, Holon metal, charge-density-wave and chi- ral superconductor from doping fractional Chern in- sulator and SU(3) 1 chiral spin liquid, arXiv e-prints , arXiv:2506.00110 (2025), arXiv:2506.00110 [cond- mat.str-el]

2025
[57]

Pichler, C

F. Pichler, C. Kuhlenkamp, M. Knap, and A. Vish- wanath, Microscopic mechanism of anyon superconduc- tivity emerging from fractional chern insulators (2025), arXiv:2506.08000 [cond-mat.str-el]

2025
[58]

Cheng, S

M. Cheng, S. Musser, A. Raz, N. Seiberg, and T. Senthil, Ordering the topological order in the fractional quan- tum Hall effect, arXiv e-prints , arXiv:2505.14767 (2025), arXiv:2505.14767 [cond-mat.str-el]. 11 Appendix A: Connection between the transitions out of bosonic/fermi...

2025
[59]

gauge glass

for a recent study of superconductivity and topological quantum criticality in an electronic Hofstadter-Hubbard model that can be given a similar interpretation. The fermionic 2/3 Jain state has Hall conductivityσ f xy = 2e 2/3hand a chiral central chargec f − = 0. The 3 disti...

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.

[1] [1]

H. Park, J. Cai, E. Anderson, Y. Zhang, J. Zhu, X. Liu, C. Wang, W. Holtzmann, C. Hu, Z. Liu, T. Taniguchi, K. Watanabe, J.-H. Chu, T. Cao, L. Fu, W. Yao, C.- Z. Chang, D. Cobden, D. Xiao, and X. Xu, Observa- tion of fractionally quantized anomalous Hall effect, Na- ture (London)622, 74 (2023), arXiv:2308.02657 [cond- mat.mes-hall]

arXiv 2023

[2] [2]

Y. Zeng, Z. Xia, K. Kang, J. Zhu, P. Kn¨ uppel, C. Vaswani, K. Watanabe, T. Taniguchi, K. F. Mak, and J. Shan, Integer and fractional Chern insulators in twisted bilayer MoTe2, arXiv e-prints , arXiv:2305.00973 (2023), arXiv:2305.00973 [cond-mat.mes-hall]

arXiv 2023

[3] [3]

J. Cai, E. Anderson, C. Wang, X. Zhang, X. Liu, W. Holtzmann, Y. Zhang, F. Fan, T. Taniguchi, K. Watanabe, Y. Ran, T. Cao, L. Fu, D. Xiao, W. Yao, and X. Xu, Signatures of fractional quantum anomalous Hall states in twisted MoTe 2, Nature (London)622, 63 (2023), arXiv:2304.08470 [cond-mat.mes-hall]

arXiv 2023

[4] [4]

F. Xu, Z. Sun, T. Jia, C. Liu, C. Xu, C. Li, Y. Gu, K. Watanabe, T. Taniguchi, B. Tong, J. Jia, Z. Shi, S. Jiang, Y. Zhang, X. Liu, and T. Li, Observation of Integer and Fractional Quantum Anomalous Hall Effects in Twisted Bilayer MoTe2, Physical Review X13, 031037 (2023), arXiv:2308.06177 [cond-mat.mes-hall]

arXiv 2023

[5] [5]

Z. Lu, T. Han, Y. Yao, A. P. Reddy, J. Yang, J. Seo, K. Watanabe, T. Taniguchi, L. Fu, and L. Ju, Fractional quantum anomalous Hall effect in multilayer graphene, Nature (London)626, 759 (2024), arXiv:2309.17436 [cond-mat.mes-hall]

arXiv 2024

[6] [6]

Z. Lu, T. Han, Y. Yao, Z. Hadjri, J. Yang, J. Seo, L. Shi, S. Ye, K. Watanabe, T. Taniguchi, and L. Ju, Ex- tended quantum anomalous Hall states in graphene/hBN moir´ e superlattices, Nature (London)637, 1090 (2025), arXiv:2408.10203 [cond-mat.mes-hall]

arXiv 2025

[7] [7]

H. L. Stormer, D. C. Tsui, and A. C. Gossard, The frac- tional quantum hall effect, Rev. Mod. Phys.71, S298 (1999)

1999

[8] [8]

J. M. Leinaas and J. Myrheim, On the theory of identical particles, Nuovo Cim. B37, 1 (1977). 9

work page 1977