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The high-resistivity metal next to the 2/3 FQAH state in tMoTe2 is proposed to be a Z3 Orthogonal Metal of charge-1/3 fermions, not an ordinary dirty electron metal.

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2026-07-14 05:16 UTC pith:WAHJTMO2

load-bearing objection Clean, falsifiable proposal that the high-resistivity metal next to the 2/3 FQAH in tMoTe2 is a Z3 Orthogonal Metal of charge-1/3 fermions; constructions are solid, ground-state energetics remain open. the 2 major comments →

arxiv 2607.11484 v1 pith:WAHJTMO2 submitted 2026-07-13 cond-mat.str-el

Fractionalized metals from doped anyons: Application to tMoTe2

T. Senthil This is my paper
classification cond-mat.str-el
keywords Z3 Orthogonal Metalfractional quantum anomalous Halldoped anyonstwisted MoTe2non-Fermi liquidanyon superconductivitycharge fractionalization
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

When a fractional quantum anomalous Hall state is lightly doped, the added carriers are anyons. This paper argues that the resistive metal seen next to the 2/3 state in twisted MoTe2 is not a conventional dirty Fermi liquid of electrons, but a Z3 Orthogonal Metal: sharp charge-1/3 fermionic quasiparticles coupled to a discrete Z3 gauge field, with no well-defined electron quasiparticle at low energy. Two such U(3)-symmetric states are constructed for a dilute three-species anyon gas, and both naturally produce large electrical resistivities even when the fractionalized quasiparticles themselves are good metals, simply because conductivity is suppressed by the square of the fractional charge. Pairing those charge-1/3 fermions yields an ordinary charge-2e superconductor that is continuously connected to a BCS state. The proposal supplies a single fractionalized normal state that can explain the high residual resistivity, its doping dependence, and the subsequent superconductivity, and it points to concrete experimental signatures that would confirm fractionalized carriers.

Core claim

The high-resistivity metal observed adjacent to the σ_xy = 2e^{2}/3h FQAH state in tMoTe2 is a Z3 Orthogonal Metal: a non-Fermi liquid with sharp charge-1/3 fermionic quasiparticles coupled to a discrete Z3 gauge field but with no sharp electronic quasiparticle. For a dilute gas of three species of charge-1/3 anyons with π/3 statistics, two U(3)-symmetric realizations exist, distinguished by whether the gapless fermions transform as SU(3) triplets or singlets.

What carries the argument

The Z3 Orthogonal Metal (Z3OM): a metallic state whose low-energy theory consists of Fermi surfaces of charge-1/3 fermions coupled to a twisted Z3 gauge field. Electrical conductivity is thereby suppressed by the factor (1/3)^{2} even when the quasiparticles themselves form a good metal, and pairing of those fermions produces a conventional charge-2e superconductor.

Load-bearing premise

That the lightly doped 2/3 state is well described by a dilute, nearly ideal three-species anyon gas whose ground state is one of the two constructed Orthogonal Metals rather than a competing charge-ordered or crystalline phase.

What would settle it

Observe a fractional Josephson frequency 2eV/3h in a gate-defined SC–metal–SC junction, or 2e/3 shot noise at an SC–metal interface, or Landau-fan slopes nine times smaller than for ordinary electrons of the same density deviation from 2/3; any of these would confirm fractionalized carriers in the normal metal.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • Large residual resistivity can appear even when the fractionalized quasiparticles have a long mean free path, because conductivity scales with the square of the charge.
  • Pairing of the charge-1/3 fermions produces an ordinary charge-2e superconductor that is continuously connected to a BCS state yet arises from a fractionalized normal state.
  • In disordered samples the first superconductor is an Anomalous Vortex Glass with no finite-temperature BKT transition, matching the gradual onset seen experimentally.
  • Distinctive probes—fractional Josephson effect, 2e/3 shot noise, suppressed single-particle tunneling (G(V)∝V^{2}), enhanced Wiedemann–Franz ratio of 9L0, and modified quantum-oscillation slopes—can directly test for fractionalized carriers.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If confirmed, the same construction immediately generalizes to other FCI fillings and to N-species anyon fluids, offering a systematic route to fractionalized normal metals whose pairing yields conventional superconductors.
  • The competition between the Orthogonal Metal and the period-3 CDW metal already discussed for the same anyon fluid may organize the low-field versus high-field metallic regimes seen in the same devices.
  • A first-order transition between the Orthogonal Metal and a hole Fermi liquid near full filling would produce phase-separated puddles that naturally explain the high-resistivity metal that persists beyond the superconducting dome.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 4 minor

Summary. The paper proposes that the high-resistivity metal adjacent to the σ_xy = 2e^{2}/3h FQAH state in twisted MoTe_{2} is a Z_{3} Orthogonal Metal: a non-Fermi liquid with sharp charge-1/3 fermionic quasiparticles coupled to a discrete Z_{3} gauge field but no sharp electronic quasiparticle. Starting from a dilute gas of three species of charge-1/3 anyons with π/3 statistics (motivated by projective lattice translation), it constructs two U(3)-symmetric Z_{3}OM mean-field states via parton/Chern–Simons methods (Eqs. 6–9, App. A), distinguished by whether the gapless fermions are SU(3) triplets or singlets. Transport formulas (Eqs. 10–13) show that large ho_xx arises from the squared fractional charge even when k_F l is large. Pair condensation of the charge-1/3 fermions is shown (App. B) to yield an ordinary charge-2e superconductor with h/2e flux quantization, smoothly connected to BCS. A suite of experimental signatures (fractional Josephson effect, 2e/3 shot noise, modified Landau fans, suppressed tunneling, enhanced Wiedemann–Franz ratio, anomalous vortex glass) is proposed.

Significance. If correct, the proposal reinterprets the resistive metal next to the 2/3 FQAH in tMoTe_{2} as a fractionalized non-Fermi liquid rather than a dirty electron metal, and supplies a concrete normal-state parent for the observed superconductivity. The constructions are standard, parameter-free once the ideal anyon Hamiltonian is accepted, and the pairing analysis cleanly recovers an ordinary 2e SC. The experimental signatures (especially fractional Josephson oscillations, 2e/3 shot noise, and Landau-fan slopes that distinguish the two Z_{3}OMs) are sharp and falsifiable. The work therefore supplies a useful theoretical framework and a clear experimental program even though ground-state selection is left open.

major comments (2)
  1. §I and §III explicitly state that determining whether either Z_{3}OM is the true ground state of the dilute anyon gas “requires an energetic calculation beyond the present work.” This is the load-bearing assumption for the application to tMoTe_{2}. The manuscript should strengthen the case by (i) a clearer comparison of the two Z_{3}OMs against the period-3 CDW metal of Ref. [13] and the Wigner-crystal/superconducting competitors of Refs. [26,28], and (ii) a more quantitative estimate of the density window in which the ideal-anyon (U(3)-symmetric) limit is expected to hold given the anyon size l_a ≈ 2–3 l_B. Without this, the claim remains a well-motivated proposal rather than a controlled prediction.
  2. §IV, Eqs. (11)–(13): the transport formulas contain two free parameters (elastic mean free path l of the charge-1/3 fermions and Berry field B_{0}). While the paper correctly notes that large ho_xx is possible for k_F l ≈ 16, the experimental residual resistivity peak height (~10 kΩ) and its doping dependence are not confronted even semi-quantitatively. A short discussion of the expected range of l (accounting for reduced charge scattering) and of whether B_{0} can be constrained by the measured Hall slope would make the comparison with Ref. [29] more persuasive.
minor comments (4)
  1. Notation for the two states (Z_{3}OM_t / Z_{3}OM_s and the ± superscripts for statistics) is introduced gradually; a short glossary or table early in §III would help the reader.
  2. Eq. (9) and the particle-hole conjugation for the doped 2/3 state are stated briefly; an explicit line showing how the filled Chern-band contribution produces the final CS terms would improve readability.
  3. Appendix C on N-species anyons is interesting but peripheral; consider moving the large-N remark to a footnote or the discussion if space is limited.
  4. A few typos: “intM oT e 2” spacing, “Aharanov-Casher”, and occasional missing spaces around δ u.

Circularity Check

1 steps flagged

Minor self-citation of the author's prior Z3OM construction; the parton Lagrangians, transport formulas, and pairing analysis are independently derived and do not reduce by construction to fitted inputs or uniqueness claims.

specific steps
  1. self citation load bearing [Sec. I (paragraph introducing Z3OM) and Sec. III]
    "In a recent study on the physics of a fluid of mobile charge 1/3 anyons, the author, together with Z.D. Shi, described[28] the possibility of a non-fermi liquid metal that emerges at low density. This metal has a Fermi surface of sharply defined charge 1/3 fermions coupled to a discrete Z3 gauge field. ... We denoted this state a Z3 Orthogonal Metal (Z3OM). ... Precisely this state was obtained in Ref. [28] through a different (Jain) composite fermion representation of the 1/3 anyons."

    The identification of the experimental metal with a Z3OM, and the claim that such a state is natural for the dilute anyon gas, rest on the state and its low-density analysis first introduced in the author's overlapping prior work [28]. While the present paper re-derives the Lagrangians, the nomenclature, the assertion of stability at low density, and the framing as the parent normal state are imported rather than independently established by new energetics (explicitly deferred).

full rationale

The paper's central claim is an explicit proposal (not a forced derivation) that the high-resistivity metal near the 2/3 FQAH is one of two Z3 Orthogonal Metals. The two states are constructed from the ideal anyon Hamiltonian via standard parton decompositions (Eqs. 6–9 and App. A), yielding parameter-free effective Lagrangians once the dilute U(3)-symmetric anyon gas is accepted. Resistivity expressions (Eqs. 11–13) contain free parameters l and B0 that are left untuned; the text states that quantitative fits are not attempted. Pairing to a charge-2e SC is shown by a self-contained Chern–Simons calculation (App. B). The only mild circularity is reliance on the author's prior introduction of the Z3OM concept and its low-density stability arguments; those citations supply context and nomenclature but are not uniqueness theorems that forbid alternatives, and the present constructions stand alone. No self-definitional loops, fitted-as-prediction steps, or ansatz smuggling appear. Score 2 reflects ordinary self-citation that is not load-bearing for the new transport or experimental-signature claims.

Axiom & Free-Parameter Ledger

2 free parameters · 4 axioms · 1 invented entities

The central claim rests on the standard anyon/Chern–Simons framework plus the modeling assumption that the lightly doped 2/3 FQAH realizes a dilute three-species anyon gas with approximate U(3) symmetry whose ground state is one of the two constructed Orthogonal Metals. No free parameters are fitted to data; mean free path and Berry curvature remain free. The Orthogonal Metal itself is an invented entity with independent theoretical pedigree but no prior experimental confirmation in this platform.

free parameters (2)
  • elastic mean free path l of charge-1/3 fermions
    Enters the longitudinal conductivity σ_xx = (e^{2}/18h) k_F l; left undetermined and not fitted to the experimental resistivity peak.
  • Berry magnetic field B0 at the d-band bottom
    Appears in the Hall conductivity correction 6π B0 δρ; stated to be unknown from microscopic details and not fitted.
axioms (4)
  • domain assumption Microscopic lattice translation acts projectively on the anyons of the 2/3 state, producing three dispersion minima and hence three species of charge-1/3 anyons.
    Invoked in §II; standard for FCI/FQAH anyons but essential for the U(3) structure.
  • domain assumption At sufficiently low density (n l_a^{2} ≪ 1) the ideal anyon model (H_int = 0) with exact U(3) symmetry captures the leading physics.
    Stated in §II; justifies the constructions but is acknowledged to break down once anyons overlap.
  • standard math Parton decompositions Φ_I = Ψ_I d (or f_I = Φ̂_I d) together with integer quantum Hall fillings of the gapped partons yield the low-energy Z3 gauge theories of Eqs. 7–9.
    Standard Chern–Simons/parton technology used throughout §III and Appendices A–B.
  • ad hoc to paper Either of the two Z3OM states is a candidate ground state of the ideal anyon gas; true ground-state selection requires energetics beyond the present work.
    Explicitly stated in §I and §III; the experimental identification rests on this unproven selection.
invented entities (1)
  • Z3 Orthogonal Metal (Z3OM_t and Z3OM_s) no independent evidence
    purpose: Provide a non-Fermi-liquid metallic phase of charge-1/3 fermions that can explain the high residual resistivity adjacent to the 2/3 FQAH and serve as the parent of the observed superconductor.
    Constructed via parton mean-field; the concept of Orthogonal Metal is older, but the concrete Z3 realizations for π/3 anyons and their application to tMoTe2 are new. Independent experimental evidence is precisely what the paper proposes to seek.

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read the original abstract

A fluid of mobile anyons may arise naturally when a Fractional Quantum Anomalous Hall (FQAH) state is doped. Motivated by recent experiments on twisted $MoTe_2$, we study metallic phases obtained by doping the $\sigma_{xy} = 2e^2/3h$ state. We propose that the high-resistivity metal observed adjacent to this FQAH state is a $Z_3$ Orthogonal Metal: a non-Fermi liquid with sharp charge $1/3$ fermionic quasiparticles coupled to a discrete $Z_3$ gauge field but with no sharp electronic quasiparticle. For a dilute gas of three species of charge-$1/3$ anyons with $\pi/3$ statistics, we construct two $U(3)$ symmetric $Z_3$ Orthogonal Metals, distinguished by whether the gapless fermions transform as $SU(3)$ triplets or singlets. We show that these states naturally yield large electrical resistivities even when the fractionalized quasiparticles are in a good metallic regime. Pairing of the charge-$1/3$ fermions produces an ordinary charge-$2e$ superconductor, smoothly connected to a BCS state but obtained through an intrinsically fractionalized normal state. We discuss experimental signatures of the idea that the normal metallic state in the lightly doped $2/3$ state may have fractionalized charge carriers.

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Forward citations

Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Charge-6e superconductivity from doping SU(3) spin liquids

    cond-mat.str-el 2026-07 conditional novelty 7.0

    Doping SU(3) spin liquids can yield charge-6e superconductors, including a non-Abelian chiral version with h/(6e) vortices.

  2. Single-component twisted $\mathbb{Z}_3$ orthogonal metal in an $e/3$-anyon fluid

    cond-mat.str-el 2026-07 conditional novelty 7.0

    Doping the nu=1/3 fractional Chern insulator can produce a twisted Z_3 orthogonal metal — a single hidden Fermi surface of emergent e/3 fermions — whose pairing yields superconductors with arbitrary chiral central cha...

  3. Coloring in anyon superconductivity

    cond-mat.str-el 2026-07 conditional novelty 6.0

    Doping the ν=2/3 FQAH state produces a unifying 'quark metal' of charge-e/3 fermions whose superconducting and ferromagnetic instabilities reproduce and extend the known zoo of anyon-driven superconductors.

  4. Color superconductors and holon metals from doping a Fractional Chern insulator

    cond-mat.str-el 2026-07 conditional novelty 6.0

    Doping a C=1/3 fractional Chern insulator can produce charge-2e superconductors and holon metals described by a nine-pocket SU(3) parton theory.

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