{"id":"5c4b5fba-bbca-4373-becc-8bd5d4697a7b","arxiv_id":"2411.08102","paper_version":2,"verdict":"ACCEPT","confidence":"HIGH","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":2,"one_line_summary":"A small magnetic field suppresses tomographic electron transport at a field scale set by the odd-parity mean free path, much below the scale for hydrodynamic suppression.","lead":"This paper predicts that a small magnetic field shuts off the 'tomographic' electron transport regime in clean two-dimensional metals, where even and odd Fermi-surface distortions relax at very different rates. The effect can be used as an experimental knob to measure the long odd-mode mean free path.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The weakest point is the assumed B-independence of the odd-parity collision rates (Eq. 3); it is standard semiclassical input, but a microscopic check would confirm that the suppression scale (8) is not shifted.","rationale":"The reader correctly identifies the B-independence of the collision rates as the weakest input of the model. I reach the same conclusion after checking the derivation: Eq. (8) follows from the competition between mω_c and γ′m^4 in the tight-binding representation (4), so any B-dependence of γ_m would directly shift the predicted suppression field. However, this is not an internal inconsistency of the paper: within the stated semiclassical Fermi-liquid framework, the Boltzmann collision integral is independent of B, and the paper is explicit about the assumption. The physical scales also make large corrections unlikely in the intended regime: the suppression field is always below the even-parity scale γ, and for the Fermi-liquid scalings γ ∼ T^2/T_F and γ′ ∼ T^4/T_F^3, the maximum ω_c^supp satisfies ω_c^supp/T ∼ (T/T_F)^{3/2} ≪ 1. Thus Landau-quantization or field-dependent screening corrections to γ_m are expected to be subleading rather than to destroy the effect. The paper’s internal evidence is strong: the zero-field tomographic scaling is reproduced by exact numerics, a variational lower bound, and a derivative/Hilbert expansion, and the finite-B crossover is checked numerically in Figs. 2–4. The one unresolved element is a microscopic estimate of γ_m(B), which would make the proposed experimental protocol fully quantitative. Since the concern is a standard-model input rather than a demonstrated flaw, the verdict does not change.","tokens_in":27439,"tokens_out":10869,"duration_ms":124388,"concrete_test":"Compute the odd-parity eigenvalues γ_m(B) of the linearized electron-electron collision integral for a circular 2D Fermi surface at T ≪ T_F, using a finite-B microscopic approach (Fermi golden rule with Landau-level density of states, or a linearized quantum Boltzmann equation with Landau-quantized propagators). Evaluate m = 3 and m = 5 for ω_c from 0 up to γ′(kξ)_max with γ′/γ = 10^−4, and compare |γ_m(B) − γ_m(0)|/γ_m(0) at the field predicted by Eq. (8). If the relative change is O(1), the suppression scale must be corrected and the proposed extraction of γ′ revised; if it remains below ~20%, the central claim is quantitatively confirmed.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central prediction, ω_c^supp ≃ γ′(kξ) ≪ γ, is obtained by balancing the Lorentz streaming term mω_c against the odd-parity damping γ_m^odd ≈ γ′m^4 with m̄ ∼ (kξ)^{1/3} in the tight-binding equation (4). This comparison is meaningful only if the eigenvalues γ_m of the linearized collision integral are unaffected by B. The paper states this explicitly: “We follow Fermi liquid conventions and do not assume a strong dependence of the relaxation rates on the magnetic field” (Sec. I, near Eq. (3)), and it is implemented by adding B only through the term imω_c in Eqs. (4) and (B5). Within semiclassical Boltzmann theory this is exact: collisions are local, and the Lorentz force acts only between collisions, so the collision integral I[δf] is B-independent. The open question is therefore not internal consistency but the size of quantum corrections. In the relevant window, ω_c^supp/T ≤ (T/T_F)^{3/2} ≪ 1 when γ ∼ T^2/T_F and γ′ ∼ T^4/T_F^3, so Landau-quantization corrections to γ_m are expected to be suppressed by powers of ω_c/T, typically giving a shift of the suppression field by at most an O(1) prefactor rather than erasing the effect. Still, because the proposed experimental protocol extracts γ′ from the location of the suppression, an independent microscopic computation of γ_m(B) is the one check worth running.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper studies a minimal kinetic model of a two-dimensional Fermi liquid with parity-dependent collisional relaxation (the tomographic regime), in which even-parity Fermi-surface deformations relax at a rate γ and odd-parity deformations relax at the much smaller rate γ′m^4. A magnetic field is introduced through the Lorentz streaming term in the Boltzmann equation, and the static transverse conductivity σ_T(k,B) is computed by four complementary methods: exact numerical solution of the resulting tight-binding equation via continued fractions, a derivative expansion at long wavelengths cross-checked by a Hilbert expansion, and variational lower bounds. The central result is that the intermediate tomographic scaling window k^2σ_T ∼ (kξ)^{1/3} is suppressed at a small cyclotron frequency ω_c^supp ∼ γ′(kξ) ≪ γ, far below the field scale that suppresses hydrodynamic transport. The authors propose this as an in-situ experimental probe of tomographic transport, for example through the magnetoresistance of a Corbino device.","tokens_in":27746,"tokens_out":20019,"duration_ms":202840,"significance":"If correct, the result is significant: it offers a magnetic-field-based protocol for identifying the tomographic regime without requiring multiple samples or temperature sweeps. The central prediction is expressed directly in terms of the model's damping rates, and it is supported by three independent calculations: exact continued-fraction solutions, a derivative expansion that is independently reproduced by a Hilbert expansion, and variational bounds that match the numerical conductivity within 9.6–20.2%. The paper also makes a concrete, falsifiable prediction for the magnetoresistance factor α(B) in a Corbino geometry, including a resistance minimum at intermediate fields whose location is controlled by γ′. The main assumption, that the collision rates γ_m are independent of B, is standard semiclassical input and is explicitly stated in the manuscript. The remaining issues are local presentation and proof-detail problems rather than errors in the central suppression mechanism.","major_comments":[{"comment":"The statement that suppression occurs when the cyclotron radius is comparable to the ballistic mean free path of the dominant odd-parity mode is inconsistent with the derivation leading to Eq. (8). The balance γ′\\bar m^4 ≃ ω_c \\bar m with \\bar m ∼ (kξ)^{1/3} gives ω_c^supp ≃ γ′(kξ). The ratio of the cyclotron radius to the mean free path of that mode is r_c/l_{\\bar m} = \\bar m, not 1; for γ′/γ = 10^{-4} and kξ = 100 it is about 4.6, and it grows as (kξ)^{1/3}. Please correct the geometric interpretation in the abstract and in the caption of Fig. 3, e.g., by stating that suppression occurs when the cyclotron frequency matches the dominant odd-mode damping rate divided by its angular momentum, or equivalently when r_c ≈ \\bar m l_{\\bar m}.","section":"Abstract and Sec. II C"},{"comment":"The variational lower bound (23) is derived from a Cauchy-Schwarz inequality applied to the 'nonnegative norm' ⟨f|G^{-1}|f⟩. However, G^{-1} defined in Eq. (21) contains the anti-Hermitian streaming terms i k·v(θ) + ω_c ∂/∂θ, so this quadratic form is complex for a general trial function and is not a norm. The proof as written therefore does not establish a rigorous bound for arbitrary h̃. The bound may be valid for the specific parity-symmetric trial functions used, because their streaming expectation vanishes, but the general claim and the word 'rigorous' need to be justified, for example by restricting the argument to the relevant subspace or by using only the Hermitian part of G^{-1}. This does not affect the central suppression result, which is confirmed by the exact continued-fraction solution, but the mathematical status of Eq. (26) is overstated.","section":"Sec. III B and Appendix C"},{"comment":"The statement that the magnetic field 'breaks time-reversal invariance, which is a prerequisite for the odd-even parity effect in the collisional relaxation' is not what the calculation implements. In the model, the relaxation rates γ_m in Eq. (3) are independent of B, and the odd-even structure of the collision integral is preserved at all fields; the suppression arises from the parity-mixing Lorentz streaming term −i m ω_c in Eq. (4). Please rephrase to avoid implying that B modifies the collision rates themselves.","section":"Abstract and Sec. I"}],"minor_comments":[{"comment":"The B-independence of γ_m is load-bearing but standard, and the paper states it explicitly. Since the proposed protocol extracts γ′ from the suppression field, a brief remark that quantum corrections to γ_m(B) are suppressed by powers of ω_c/T (in the relevant window ω_c^supp/T ≲ (T/T_F)^{3/2}) would strengthen the experimental discussion.","section":"Sec. I near Eq. (3)"},{"comment":"In Eq. (9), the notation γ_2 and γ_3 is used before these quantities are defined; please define them at first use and check the typesetting of the denominators, which is difficult to parse in the current version.","section":"Sec. II A, Eq. (9)"},{"comment":"The impurity scattering rate γ_i is set to 10^{-7}γ in Fig. 1 and Fig. 6 but is omitted in the analytic results of Secs. III B and III C; a sentence clarifying the role of impurities in the phase diagram and in the Stokes-Ohm modeling would improve readability.","section":"Fig. 1 and Sec. IV"}],"recommendation":"minor_revision","confidential_remarks":"This is a solid manuscript whose central claim is well supported by independent calculations. The main issues are a wrong geometric interpretation in the abstract (an extra factor of the dominant angular momentum m̄), an overclaimed variational proof, and a framing issue about time-reversal symmetry. These are local and fixable, so I recommend minor revision. The paper is a good fit for cond-mat.mes-hall."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The paper has one genuinely new result: in a minimal kinetic model of tomographic electrons, a magnetic field kills the intermediate tomographic scaling window at a surprisingly small cyclotron frequency, ω_c^supp ~ γ′(kξ) ≪ γ. That suppression scale is derived by balancing the Lorentz streaming term against the m^4 odd-mode damping, and it is confirmed by three independent calculations: exact continued-fraction numerics, a derivative expansion, and a Hilbert expansion. The variational lower bounds are a nice touch, giving rigorous anchors that match the full solution to within 10–20%. The Fermi-surface pictures in Fig. 4 make the mechanism concrete. I think the central claim holds up within the stated model.\n\nThe weakest assumption, flagged explicitly by the authors (Sec. I, near Eq. 3), is that the relaxation rates γ_m do not depend on the magnetic field. Within semiclassical Boltzmann theory this is exact — collisions are local and the Lorentz force acts only between collisions — so the concern is not internal consistency but quantum corrections. Landau quantization or field-dependent screening could shift the suppression scale by an O(1) prefactor, but since the relevant fields satisfy ω_c^supp/T ≪ 1, the effect is not obviously erased. The paper's own statement that it follows Fermi liquid conventions is honest about this limit. The self-citation of the odd-even effect is appropriate: those earlier results are the input here, and the B-field dependence is an independent calculation. The connection to the Zeng et al. experiment is speculative but clearly marked as an outlook, not a definitive explanation.\n\nWhat the paper does not do is derive γ_m(B) from a microscopic theory. That is the one check worth running if the proposed protocol is used to extract γ′. But that is a natural follow-up, not a defect of this calculation. The paper is well suited for a serious referee: the math is transparent, the approximations are stated, and the observable prediction is falsifiable. I would accept it with minor revision, mainly asking for a slightly more detailed discussion of the quantum-correction caveat and a clearer statement that the variational bounds are rigorous lower bounds rather than exact results. For anyone working on hydrodynamic or tomographic transport, this is a useful and citable contribution.","headline":"A clean, internally consistent calculation showing that a small magnetic field suppresses tomographic transport at a scale set by the odd-parity mean free path; the main caveat is the assumed B-independence of collision rates, which is standard semiclassical input and not a loading flaw.","tokens_in":28284,"tokens_out":1245,"would_cite":true,"duration_ms":15525,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":null,"created_at":"2026-08-12T21:57:36.987663+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":null,"supporting_citations":[],"review_version":1}