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REVIEW 2 major objections 5 minor 99 references

Broken inversion symmetry lets lattice composite Fermi liquids show non-analytic optical resistivity and finite-q Hall responses that continuum quantum-Hall CFLs hide.

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2026-07-31 02:09 UTC pith:VUB2Y2OB

load-bearing objection Solid theory paper: inversion breaking really does unlock a non-analytic optical resistivity in lattice CFLs that continuum HLR forbids, with clean SAW predictions for the moiré experiments. the 2 major comments →

arxiv 2607.28613 v1 pith:VUB2Y2OB submitted 2026-07-30 cond-mat.str-el cond-mat.mes-hallcond-mat.stat-mech

Lattice composite Fermi liquid with broken inversion symmetry

Pavel A. Nosov , Zhengyan Darius Shi This is my paper
classification cond-mat.str-el cond-mat.mes-hallcond-mat.stat-mech
keywords composite Fermi liquidinversion symmetry breakingoptical resistivityChern bandgauge fluctuationssurface acoustic wavesUmklapp scatteringtwisted MoTe2
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.

Composite Fermi liquids form when electrons at half filling bind two flux quanta and make a compressible metal of composite fermions. In the usual Landau-level setting, symmetries force the homogeneous optical resistivity to stay analytic. This paper argues that realistic half-filled Chern bands break inversion (for example by trigonal warping down to C3), so those constraints lift. Gauge-mediated small-momentum scattering between non-antipodal patches on the composite Fermi surface then produces a dissipative optical resistivity that scales as a fractional power of frequency, |ω|^{4/z} (explicitly |ω|^{4/3} for gate-screened interactions). At finite wave vector the same symmetry reduction yields nonreciprocal transport and a non-analytic |q| piece in the Hall conductivity, both readable in surface-acoustic-wave velocity shift and attenuation. A separate channel—gauge-enhanced 2k_F scattering feeding Umklapp—can also make the DC resistivity non-analytic in temperature. The claimed signatures are absent in continuum quantum-Hall composite Fermi liquids and are proposed as direct tests in twisted MoTe2 and rhombohedral graphene, where zero-field composite Fermi liquids have already been reported.

Core claim

In a lattice composite Fermi liquid with broken inversion, gauge-field fluctuations generate a non-analytic homogeneous optical resistivity Re ρ^{xx}(ω) ∼ C(z) λ² |ω|^{4/z} (for gate-screened Coulomb, z=3, Re ρ^{xx} ∼ |ω|^{4/3}), forbidden for convex inversion-symmetric Fermi surfaces and by magnetic Galilean invariance in the continuum Landau-level setting. At finite q, inversion breaking also produces nonreciprocal transport and a non-analytic ∼|q| dependence of the Hall conductivity, and 2k_F-enhanced Umklapp can yield non-analytic DC resistivity.

What carries the argument

Ioffe–Larkin composition of composite-fermion and Chern–Simons responses, combined with large-N gauge fluctuations: on-shell small-q scattering between non-antipodal tangential Fermi-surface patches produces a nonzero net velocity change once inversion is broken, yielding the singular incoherent conductivity that inverts into Re ρ^{xx} ∼ |ω|^{4/z}.

Load-bearing premise

The singular DC resistivity claim rests on extrapolating a large-N 2k_F vertex exponent to the physical case; if that exponent is too small, ordinary T-squared Umklapp wins and the non-analytic temperature law disappears.

What would settle it

Measure the low-frequency optical resistivity of an inversion-asymmetric lattice CFL (for example in twisted MoTe2) in the window T ≪ ω ≪ E_F: a clear |ω|^{4/3} (or more generally |ω|^{4/z}) dissipative part that vanishes when inversion is restored would confirm the central optical claim; surface-acoustic-wave anisotropy linear in the warping parameter would confirm the finite-q Hall piece.

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

If this is right

  • Microwave/THz spectroscopy of twisted MoTe2 or rhombohedral graphene CFLs should show Re ρ^{xx}(ω) ∼ |ω|^{4/z} when inversion is broken and T ≪ ω ≪ E_F.
  • Surface-acoustic-wave velocity shift and attenuation become direction-dependent at linear order in the warping parameter, allowing a map of the odd-in-q Hall correction.
  • Comparing optical |ω|^{4/z} with DC temperature scaling can extract both the gauge dynamical exponent z and the 2k_F vertex exponent.
  • The same inversion-breaking mechanism implies singular optical conductivity in a broader class of 2+1D non-Fermi liquids at q=0 order-parameter criticality.
  • Strong enough warping can drive a gauge-flux Lifshitz point and possible spontaneous flux-density order.

Where Pith is reading between the lines

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

  • If annular or multi-pocket composite Fermi surfaces appear in the same moiré platforms, inter-pocket small-q scattering could produce the same |ω|^{4/z} optical law even without inversion breaking.
  • Phase- and orientation-resolved magnetometry would be needed to see the leading non-dissipative Im σ_LT and Im σ_TT pieces that ordinary directional averages wash out.
  • Pairing instabilities on an inversion-asymmetric composite Fermi surface should leave gapless Bogoliubov pockets whose transport inherits the same singular gauge corrections.

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 / 5 minor

Summary. The paper analyzes transport in lattice composite Fermi liquids (CFLs) realized in half-filled Chern bands with C3 symmetry but broken inversion, motivated by twisted MoTe2 and rhombohedral graphene. Using a parton/RPA effective theory and a large-N expansion beyond RPA, it argues that inversion breaking lifts kinematic cancellations that protect continuum and inversion-symmetric CFLs, yielding a non-analytic homogeneous optical resistivity Re ρ^{xx}(ω) ∼ C(z) λ² |ω|^{4/z} (explicitly ∼ |ω|^{4/3} for screened Coulomb, z=3). At finite q it finds angle-dependent |q| corrections to the Hall and longitudinal conductivities relevant for surface acoustic waves, and it discusses a separate 2k_F-enhanced Umklapp channel that can produce non-analytic DC resistivity ∼ T^{4/z} if the 2k_F exponent σ is large enough. Experimental probes (microwave/THz optics, SAW) and open directions (Berry curvature, pairing, flux Lifshitz) are outlined.

Significance. If correct, the work identifies concrete, symmetry-protected transport signatures that distinguish lattice/zero-field CFLs from continuum Landau-level CFLs and that are directly relevant to ongoing moiré experiments. The optical result is the strongest contribution: the kinematic argument (non-antipodal tangential patches, Fig. 3, Eqs. 49–51) is clean, the large-N organization with explicit cancellation of diamagnetic diagrams as subleading (App. B) is careful, and a closed-form z=3 coefficient for weak trigonal warping is given. Finite-q RPA predictions for SAW velocity shift and attenuation (Sec. V B) are falsifiable with near-term probes. The paper is appropriately cautious that the DC exponent relies on a large-N extrapolation of σ. Overall this is a solid, timely contribution to composite-fermion and non-Fermi-liquid transport theory.

major comments (2)
  1. [Sec. III B, Eqs. (64)–(66); abstract; Sec. V A] Sec. III B, Eqs. (64)–(66): The singular DC claim Γ_U(T)∼T^{4/z} rests on extrapolating σ=1/(2N)→1/2 at N=1. The manuscript correctly notes that standard large-N is uncontrolled in the deep IR even at N=∞ (after Eq. 65; Lee 2009, Metlitski–Sachdev). If σ falls below 2/z−1/2, ordinary T² Umklapp wins. Please state more sharply in the abstract and Sec. V A that the DC power is conditional on σ, and separate it more clearly from the optical result, which does not rely on this extrapolation.
  2. [Sec. III A; Appendix B; Sec. V A] Sec. III A / App. B: The optical scaling is obtained within large-N with free-fermion bubbles, known to break down for ω≪E_F N^{−3}. The existence of an inversion-odd non-analytic piece once a Landau-damped gauge propagator is assumed is robust and consistent with other controlled expansions cited, but the O(1) prefactor (0.963…) and the width of the scaling window at physical N=1 are not guaranteed. A short paragraph quantifying the expected asymptotic window (relative to E_F∼30 K quoted in Sec. V A) and stating that C(z) is scheme-dependent at N=1 would strengthen the experimental claim without changing the central result.
minor comments (5)
  1. [Eq. (2); Eq. (55)] Eq. (2) vs Eq. (55): the numerical factor is written as 1.926 π²/μ^{4/3}… in (2) and as 1.926 λ² π²/μ^{4/3}… after (55); ensure λ² is consistently displayed in the abstract/Eq. (2) form used in the introduction.
  2. [Appendix A; Sec. II B] Fig. 4 is referenced in App. A for f1 and f̃2 angular dependence but is not described in the main-text figure list early on; a brief main-text pointer when fα are introduced would help.
  3. [Sec. V C] Sec. V C mentions Berry curvature as an open additive correction. A one-sentence statement that the present optical singularity is derived without Berry curvature (and is not claimed to cancel it) would preempt a common referee concern.
  4. [Section headers; Sec. IV] Typos/notation: “LA TTICE”, “TRANSPOR T”, “W A VE” in section headers; “Seff” vs S_eff consistency; ℏ=e²=1 units stated late in Sec. IV—state once at first conductivity formula.
  5. [Sec. V B] References to SAW and microwave/THz techniques are good; adding a short note on whether existing SAW setups on graphene/TMD heterostructures already reach the v_s q ≪ v_F q window assumed in Sec. IV would aid experimental readers.

Circularity Check

1 steps flagged

No significant circularity: optical and finite-q results are computed from a stated parton/RPA/large-N action; self-citations supply methods, not the target scaling by construction.

specific steps
  1. self citation load bearing [Sec. III A (large-N setup); citations to Refs. [25, 28] and App. B organization]
    "Towards that end, we follow the approach of Refs. [44, 45, 65] and consider a deformation of the original model with N flavors of CFs... Although this expansion scheme ceases to be controlled in the ultimate low energy limit ω≪E_F N^{-3} [47, 48], the frequency-scaling of σ^{ij}_{CF} extracted from this expansion agrees with more sophisticated controlled expansions as shown in Refs. [26, 28, 29, 49]."

    Minor only: diagram organization and the claim that large-N frequency scaling matches other expansions lean on overlapping-author transport papers. Those citations justify the calculational scheme, not the numerical value or existence of the inversion-odd ω^{4/z} piece, which is recomputed from the CFL action in App. B. Not load-bearing for the central claim.

full rationale

The headline claim Re ρ^{xx}(ω)∼C(z)λ²|ω|^{4/z} is obtained by explicit large-N evaluation of paramagnetic SE/MT/AL diagrams for an inversion-asymmetric CF dispersion coupled to a Landau-damped gauge field (Sec. III A, App. B), with the kinematic lifting of antipodal Δv cancellation stated and used as an intermediate step (Fig. 3, Eqs. 49–52), not as a definition of the resistivity. Prefactors (e.g. 0.963, C(3)) are numerical integrals over the gauge propagator and angular form factors, not fits to data. Finite-q Hall/SAW signatures follow from RPA response functions of the same effective action (Sec. II B, IV). The secondary DC Umklapp scaling imports σ from large-N (Eqs. 64–66) with the paper’s own IR-control caveat; that is an uncontrolled extrapolation, not a circular reduction of a prediction to a fitted input. Self-citations (prior CBFL work; Shi et al. transport expansions) provide methodology and related constraints; the target CFL optical law is newly computed here and does not reduce by construction to those citations. No self-definitional loop, fitted-input-as-prediction, or uniqueness theorem that forces the result from the authors’ prior claims alone.

Axiom & Free-Parameter Ledger

5 free parameters · 7 axioms · 1 invented entities

Load-bearing content is an effective parton CFL action plus controlled (RPA / large-N) response calculations. No experimental fits. Free parameters are microscopic EFT inputs (mass, warping, interaction, dynamical exponent). Axioms are standard gauge/parton and Fermi-surface assumptions plus the large-N deformation. Invented entities are none beyond the standard composite-fermion / gauge construction already in the literature; CBFL is mentioned only as prior/future context.

free parameters (5)
  • trigonal warping λ = λ ≪ 1 (symbolic)
    Strength of C3-symmetric inversion-breaking deformation of the CF dispersion; expanded to O(λ²). Not fitted; treated as small free microscopic input.
  • CF effective mass m and chemical potential μ
    Enter Drude weight and prefactors of singular resistivity; inherited from EFT, not microscopically computed from MoTe₂.
  • interaction v(q) / dynamical exponent z = z=2 or 3
    z=3 for short-range/gate-screened, z=2 for Coulomb; V0 combination appears in denominators of C(z). Choice sets the power 4/z.
  • large-N flavor number N (extrapolated to 1) = N→1
    Organizes diagram expansion for optical and 2k_F exponents; physical results quoted after N→1.
  • Umklapp coupling V_G and reciprocal lattice vectors G
    Overall scale A of DC resistivity is non-universal; kinematics assume FS large enough that 2k_F processes hit Umklapp.
axioms (7)
  • domain assumption Parton decomposition c=f Φ with bosonic Laughlin U(1)_2 mean-field for Φ and Fermi liquid for f yields the lattice CFL effective action (Eqs. 6–10).
    Standard construction following Barkeshli–McGreevy and moiré CFL numerics; stability under gauge fluctuations assumed, not proved from microscopic MoTe₂ Hamiltonian.
  • domain assumption Ioffe–Larkin composition ρ = ρ_CF + (2h/e²) ε at q=0 (and finite-q analogue) relates physical resistivity to CF response.
    Used throughout Secs. III–IV; standard for flux-attached CFLs.
  • domain assumption Leading singular optical conductivity is captured by O(1/N) paramagnetic diagrams; diamagnetic-vertex diagrams are IR-subleading (App. B scaling).
    Justified by power counting with dynamical exponent z; central to claiming ω^{(4−z)/z} in Π_CF.
  • standard math For convex inversion-symmetric FS, on-shell small-q scattering gives Δv=0 so QBE/optical singular piece vanishes; broken inversion lifts this.
    Kinematic identity used in Sec. III A and Fig. 3; aligns with prior anomaly/memory-matrix constraints cited.
  • domain assumption 2k_F density susceptibility scales as ω^{2/z − 2σ} with σ ≈ 1/(2N) from large-N (Altshuler–Ioffe–Millis / Polchinski-type analysis).
    Imported for DC Umklapp (Sec. III B); authors note IR control issues of large-N.
  • ad hoc to paper Clean limit: disorder neglected; DC relaxation solely from Umklapp.
    Stated at opening of Sec. III; real devices have disorder that may mask power laws.
  • ad hoc to paper Weakly trigonally warped dispersion ξ(k)=k²/2m (1+λ cos 3θ_k)−μ is representative of generic C3-without-inversion CF surfaces.
    Used for explicit coefficients; qualitative claims asserted to hold for generic inversion-asymmetric convex FS.
invented entities (1)
  • None beyond standard lattice composite fermion + dynamical U(1) gauge field independent evidence
    purpose: The paper applies existing CF/parton degrees of freedom; it does not postulate a new particle or force.
    Composite fermions, Chern–Simons gauge field, and RPA/large-N are prior literature. CBFL is cited as related prior work, not required for the normal-state transport claims.

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read the original abstract

We study transport in lattice composite Fermi liquids realized in half-filled Chern bands with broken inversion symmetry. We show that reduced crystalline symmetry exposes intrinsic singular dynamical responses of composite fermions that are otherwise hidden in the conventional Landau-level setting. At zero wave vector, inversion breaking allows gauge-field fluctuations to generate a non-analytic longitudinal optical resistivity, with $\operatorname{Re}\rho^{xx}(\omega)\sim |\omega|^{4/3}$ for gate-screened Coulomb interactions. At finite wave vector $\mathbf{q}$, inversion breaking leads to nonreciprocal transport and a non-analytic $\sim |\mathbf{q}|$ dependence of the Hall conductivity, both of which can be probed through surface acoustic wave propagation. We also discuss a distinct mechanism for singular DC transport in lattice composite Fermi liquids: renormalization of $2k_F$ scattering at the composite Fermi surface enhances Umklapp relaxation and can lead to a non-analytic temperature dependence of the resistivity. Taken together, our results identify transport signatures of lattice composite Fermi liquids that are absent in their continuum quantum Hall counterparts and can be directly tested in ongoing experiments on twisted MoTe$_2$ and rhombohedral graphene, where evidence for zero-field composite Fermi liquids has recently been reported.

Figures

Figures reproduced from arXiv: 2607.28613 by Pavel A. Nosov, Zhengyan Darius Shi.

Figure 1
Figure 1. Figure 1: FIG. 1. Paramagnetic (left) and diamagnetic (right) vertices for the lattice CFL with arbitrary CF dispersion [PITH_FULL_IMAGE:figures/full_fig_p009_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. The set of paramagnetic diagrams contributing to [PITH_FULL_IMAGE:figures/full_fig_p010_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. On-shell scattering kinematics controlling optical and DC transport. (a) For a convex inversion-symmetric Fermi [PITH_FULL_IMAGE:figures/full_fig_p012_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Angular dependence of [PITH_FULL_IMAGE:figures/full_fig_p024_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. At leading order in the 1 [PITH_FULL_IMAGE:figures/full_fig_p026_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. The set of diagrams contributing to the gauge field self energy at [PITH_FULL_IMAGE:figures/full_fig_p029_6.png] view at source ↗

discussion (0)

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Reference graph

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