{"id":"e37703ff-a88d-4962-907c-f95e14daef7a","arxiv_id":"2507.13796","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":7.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"For intraband absorption in a single Weyl node, semiclassical and quantum calculations of the circular photogalvanic effect give different currents, implying an unidentified semiclassical mechanism.","lead":"Physicists calculated the electric current produced by circularly polarized light in Weyl semimetals using two standard methods and found the methods disagree. The result means the usual semiclassical theory is missing a microscopic contribution to the photocurrent.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Quantum side of the comparison is not shown to be complete: Eq. (20) is an injection-term formula, and the paper never enumerates the order-E^2 diagrams (e.g., field-induced scattering / side-jump counterpart) that could cancel the claimed discrepancy.","rationale":"The paper's strongest claim is that the semiclassical and quantum-mechanical results for the intraband CPGE differ, implying a missing semiclassical mechanism. The load-bearing condition for that claim is that the quantum side is exhaustive. The reader's weakest assumption identified exactly this point: the quantum calculation is labeled complete without a diagrammatic enumeration. My read agrees and sharpens it: Eq. (20) is an injection-term formula, and the semiclassical calculation in Sec. II explicitly contains a side-jump contribution W^sj that is a field-dependent scattering term; the quantum calculation does not demonstrate how, or whether, this term is contained in Eq. (20). Appendix B rules out one specific field correction to the intraband scattering overlap but not the shift/phase contribution encoded in r_{k'k}. This is not a claim that the paper is wrong; it is a concrete unproven assumption on which the central cancellation rests. The paper otherwise gives detailed, parameter-free derivations and an explicit comparison for Gaussian disorder, so a conditional verdict with a demand to supply the missing completeness argument remains appropriate. I therefore do not move the reader's verdict.","tokens_in":12483,"tokens_out":26804,"duration_ms":341157,"concrete_test":"Compute the dc current at order |E|^2 by a direct Keldysh or Kubo calculation for the Weyl Hamiltonian (3) with delta-correlated disorder, keeping all self-energy and vertex diagrams at leading order in the disorder strength rather than assuming Eq. (20). Equivalently, add to Eq. (20) the shift/side-jump term e Σ W_in [f0(ε_k)-f0(ε_k')] R_{k'k}, with R_{k'k} the side-jump displacement used in Sec. II B, and evaluate γ for isotropic scattering. If the full result returns γ=-1, the discrepancy is an artifact of an incomplete quantum calculation; if it returns 0, the paper's conclusion survives.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim depends on treating Eq. (20) as the full quantum-mechanical CPGE. But Eq. (20) is an injection-type expression: it multiplies the Fermi-golden-rule intraband absorption rate by [v_k' τ(ε_k') - v_k τ(ε_k)]. It does not, by itself, include the quantum counterpart of the semiclassical side-jump, i.e., the E-linear modification of the scattering probability W^sj used in Sec. II B, nor a diagrammatic proof that no such term contributes at order E^2. Appendix B checks only the field-induced change of |⟨u_k'|u_k⟩|^2 and finds it zero; it does not check the phase/shift part of the scattering amplitude (the r_{k'k} term) or the corresponding diagrams with the photon vertex inserted in the impurity line. Therefore the cancellation γ_QM^(1)+γ_QM^(2)=0 is established only within the subset of processes contained in Eq. (20). If the missing diagrams contribute, the true γ_QM could equal γ_SC=-1, eliminating the claimed discrepancy.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper studies the intraband circular photogalvanic effect (CPGE) in a single Weyl node described by H = Cℏv0σ·k. In the semiclassical approach, the authors evaluate the Berry curvature dipole contribution (γ_BCD = -2/3), the side-jump contribution (γ_sj = -1/3), and note the vanishing of skew scattering, obtaining γ_SC = -1 for isotropic short-range scattering. In the quantum-mechanical approach, they use the injection-current formula of Eq. (20) with indirect optical transitions mediated by disorder, decomposing the transition amplitude into a conduction-band-mediated part M and a valence-band-mediated part δM. They find that the |δM|^2 contribution (γ_QM^(1) = 4/3, from Ref. [8]) is exactly cancelled by the M*δM interference term (γ_QM^(2) = -4/3, derived in Appendix A), so γ_QM = 0 for isotropic scattering. For Gaussian-correlated disorder, they obtain γ_SC(α) and γ_QM(α) that remain different for all α = 2(k_F d)^2, with γ_QM ranging from 0 to -4/3 and γ_SC ranging only slightly around -1. The paper concludes that the established semiclassical mechanisms do not exhaust the intraband CPGE in Weyl semimetals.","tokens_in":12555,"tokens_out":21149,"duration_ms":242325,"significance":"If the quantum-mechanical calculation is complete, the result is significant: it would overturn the expectation, established in gapped gyrotropic systems, that Berry curvature dipole, side-jump, and skew-scattering mechanisms saturate the intraband CPGE, and it would point to a new microscopic contribution in gapless systems. The manuscript's strengths are its parameter-free analytic derivations, the explicit calculation of the interference contribution in Appendix A, and the extension to anisotropic Gaussian disorder, which yields a concrete prediction for the dependence of the CPGE constant on the dimensionless disorder range α. These are falsifiable statements that go beyond a re-derivation of known results. However, the significance is conditional: the claimed discrepancy is only meaningful if Eq. (20) truly captures the full quantum-mechanical response, and this is precisely the point that the manuscript leaves unproven.","major_comments":[{"comment":"The central claim of the paper rests on the assumption that Eq. (20) is the complete quantum-mechanical expression for the intraband CPGE current. This assumption is not demonstrated. Equation (20) is an injection-type formula: it multiplies the Fermi-golden-rule transition rate W_in by the difference [v_{k'}τ(ε_{k'}) - v_kτ(ε_k)]. It does not include the quantum counterpart of the semiclassical side-jump, i.e., the electric-field-induced correction to the scattering probability W^sj used in Sec. II.B, nor a shift/displacement contribution of the indirect optical transition. Appendix B investigates only one specific field-induced correction, the change in the spinor overlap |⟨u_{k'}|u_k⟩|^2, and shows that it vanishes; it does not examine the phase/shift part of the scattering amplitude (the r_{k'k} term in Eq. (11)) or diagrams in which the photon vertex is inserted in the impurity line. Consequently, the cancellation γ_QM^(1) + γ_QM^(2) = 0 in Eq. (25) is established only within the subset of processes contained in Eq. (20). A diagrammatic enumeration of all processes of order E^2 (one photon field and one disorder vertex) or a full quantum kinetic calculation that includes both injection and shift terms is needed to establish that no additional contribution modifies γ_QM. Without this, the discrepancy reported in Sec. V may be an artifact of an incomplete quantum calculation.","section":"Sec. III, Eq. (20), and Appendix B"}],"minor_comments":[{"comment":"There is a typo in the sentence following Eq. (21): 'thirs' should be 'third'.","section":"Sec. III, after Eq. (21)"},{"comment":"The phrase 'complete quantum-mechanical approach' overstates the scope of the calculation, which uses a specific injection-current formula; the authors should either qualify the claim or add the missing diagrammatic proof.","section":"Abstract and Sec. V"},{"comment":"The factor C and the direction κ in Eq. (1) are not carried through the later formulas; the text should state explicitly that the numerical values γ_SC and γ_QM are for C = +1 and for the current component along κ.","section":"Sec. II and Eqs. (24)-(25)"},{"comment":"The remark that the signs of the Berry curvatures in Eq. (6) of Ref. [1] should be reversed would be more useful if the corrected signs were displayed explicitly.","section":"Sec. II.A"},{"comment":"The angular averages leading to ⟨Φ cosθ_{k'}⟩ = ⟨Φ cosθ_k⟩ = -2/9 are stated without derivation; a short indication of the integration procedure would improve reproducibility.","section":"Appendix A, Eq. (A14)"},{"comment":"The upper and lower panels use different horizontal-axis limits (α up to 20 vs. α up to 10); a common range would make the comparison of γ_SC and γ_QM more direct.","section":"Fig. 2"}],"recommendation":"major_revision","confidential_remarks":"The paper is carefully written and the algebra is explicit, but the central claim depends on the exhaustiveness of the quantum-mechanical calculation, which is not established. The missing diagrammatic enumeration is a 'major revision' issue rather than a reason to reject, because the authors are well positioned to supply it. I would also encourage the editor to consider whether the abstract's claim of a 'complete quantum-mechanical approach' is too strong until the completeness question is resolved."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague,\n\nThe headline: this paper claims to have found a genuine discrepancy between semiclassical and fully quantum-mechanical calculations of the intraband circular photogalvanic effect in a minimal Weyl node. For isotropic short-range disorder, semiclassical gives γ_SC = -1 (Berry curvature dipole -2/3 plus side-jump -1/3, skew scattering zero), while the quantum-mechanical result is γ_QM = 0, because a previously ignored interference term γ_QM^(2) = -4/3 exactly cancels the known |δM|^2 contribution +4/3. They further show the discrepancy persists for Gaussian-correlated disorder of any correlation length. If true, this says the standard semiclassical mechanisms do not exhaust intraband CPGE in gapless systems, which is a meaningful result for the photogalvanic subfield.\n\nThe paper does several things well. The algebra in Sections II and III and Appendices A and C is explicit and checkable. The correction to the earlier semiclassical value γ_SC = 0 from Ref. [13], traced to a missing term in the side-jump distribution function, is plausible and clearly explained. The Gaussian-disorder extension is a new calculation. The writing is clear and the model is minimal, so the logic is easy to follow.\n\nThe soft spot is the quantum-mechanical side. The current formula used, Eq. (20), is an injection-type expression: it multiplies the Fermi-golden-rule absorption rate by [v' τ' - v τ]. It does not by itself include the quantum counterpart of the semiclassical side-jump, which in the Boltzmann language is a field-induced correction to the scattering probability W^sj. The paper never enumerates the full set of order-E^2 diagrams. Appendix B rules out one candidate, the field-induced change of the spinor overlap |⟨u_k'|u_k⟩|^2, but it does not check the phase/shift part of the scattering amplitude (the r_{k'k} term) or diagrams with the photon vertex inserted in the impurity line. If such terms contribute, they could cancel the -4/3 interference term and bring γ_QM to -1, eliminating the discrepancy. This is not a small footnote; it is the load-bearing assumption of the paper's central claim.\n\nThere is also a minor typo: Eq. (A10) seems to contain an extra impurity density n_i on the right-hand side, inconsistent with the definitions of M and δM.\n\nWho is this for? Specialists in photogalvanic effects, nonlinear transport, and Weyl semimetal theory. It deserves a serious referee: the claim is important enough and the calculation detailed enough that the completeness issue should be settled rather than the paper desk-rejected. My recommendation: send it to peer review with a request that the authors either provide a diagrammatic enumeration of all second-order photon-plus-disorder processes or explicitly justify why Eq. (20) captures the full current. Once that gap is closed, the result will either be a solid correction or an instructive cancellation.\n\nOn balance, I would not cite it in my own work until that completeness issue is resolved.","headline":"Claims a new semiclassical/quantum discrepancy in intraband CPGE, but the quantum side is missing a diagrammatic completeness proof.","tokens_in":13259,"tokens_out":5877,"would_cite":false,"duration_ms":69941,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"Two standard calculations of the circular photogalvanic effect in Weyl semimetals disagree, showing that the known semiclassical mechanisms — Berry curvature dipole, side jumps, and skew scattering — do not exhaust the intraband…","keywords":["circular photogalvanic effect","Weyl semimetals","Berry curvature dipole","side jump","skew scattering","intraband optical transitions","disorder scattering","semiclassical versus quantum theory"],"falsifier":"Enumerate all Feynman diagrams for the second-order photon-plus-disorder response of a single Weyl node and check whether any amplitude beyond $M_{\\mathbf{k}'\\mathbf{k}}$ and $\\delta M_{\\mathbf{k}'\\mathbf{k}}$ contributes to the intraband CPGE; alternatively, run a numerically exact Kubo-formula calculation of the intraband CPGE with short-range and Gaussian disorder to see whether $\\gamma$ is $0$ or $-1$ and how it varies with $\\alpha$. A clean experimental measurement in a material with one dominant Weyl node would also discriminate, but the decisive check is the theoretical enumeration.","tokens_in":12131,"feed_emoji":"⚡","tokens_out":8060,"duration_ms":79211,"temperature":0.7,"pith_summary":"This paper asks whether the standard semiclassical theory of the circular photogalvanic effect, which accounts for the Berry curvature dipole, side jumps, and skew scattering, gives the same intraband photocurrent as a full quantum-mechanical calculation in a Weyl semimetal. For the simplest single Weyl node with isotropic short-range disorder, the answer is no: the semiclassical constant is $\\gamma = -1$ while the quantum value is $\\gamma = 0$. The authors extend the comparison to Gaussian-correlated disorder of arbitrary spatial range and find that the two approaches still disagree at every correlation length. They conclude that an additional microscopic mechanism, beyond the known semiclassical corrections, is required to describe intraband CPGE in gapless systems. The discrepancy matters because the same semiclassical machinery is known to be complete in gapped gyrotropic materials, so the failure appears precisely where the spectrum is gapless.","feed_headline":"Two standard calculations disagree on Weyl photocurrent","feed_subtitle":"Semiclassical theory gives gamma = -1, quantum gives gamma = 0; the gap persists at all disorder ranges.","key_machinery":"The load-bearing object is the dimensionless CPGE constant $\\gamma$ defined by $\\mathbf{j} = \\gamma \\, e^3/(h^2\\omega) \\, \\boldsymbol{\\kappa} |\\mathbf{E}|^2$, which both approaches are supposed to compute. Semiclassically, $\\gamma$ is the sum of the Berry curvature dipole contribution $\\gamma_{\\rm BCD} = -2/3$ and the side-jump contribution $\\gamma_{\\rm sj} = -1/3$, with skew scattering vanishing by the model's rotational symmetry. Quantum-mechanically, $\\gamma$ comes from the indirect optical transition matrix element $M_{\\mathbf{k}'\\mathbf{k}}$ for conduction-band intermediate states plus $\\delta M_{\\mathbf{k}'\\mathbf{k}}$ for virtual transitions through the valence band, inserted into the current formula of Eq. (20); the $|\\delta M|^2$ term gives $+4/3$ and the interference term gives $-4/3$, cancelling exactly at isotropic scattering. The anisotropic-scattering extension carries the argument to arbitrary disorder range by replacing $n_i|U_0|^2$ with the disorder correlator $K(|\\mathbf{k}' - \\mathbf{k}|)$, producing the non-crossing curves plotted in Fig. 2.","core_discovery":"The central claim is that, in the intraband frequency range $\\hbar/\\tau \\ll \\hbar\\omega \\ll \\varepsilon_F$, the complete quantum-mechanical calculation of the CPGE in a single Weyl node does not coincide with the semiclassical calculation. For isotropic short-range scattering, $\\gamma_{\\rm SC} = \\gamma_{\\rm BCD} + \\gamma_{\\rm sj} = -2/3 - 1/3 = -1$, while the quantum-mechanical result is $\\gamma_{\\rm QM} = \\gamma^{(1)}_{\\rm QM} + \\gamma^{(2)}_{\\rm QM} = 4/3 - 4/3 = 0$. With a Gaussian disorder correlator the two curves $\\gamma_{\\rm SC}(\\alpha)$ and $\\gamma_{\\rm QM}(\\alpha)$, with $\\alpha = 2(k_F d)^2$, never cross for any $\\alpha > 0$: $\\gamma_{\\rm QM}$ vanishes only at $\\alpha = 0$ and tends to $-4/3$ at large $\\alpha$, while $\\gamma_{\\rm SC}$ has $|\\gamma_{\\rm SC}| = 1$ at both limits with a nonmonotonic interpolation. The paper argues that this persistent discrepancy indicates an extra contribution to intraband CPGE in gapless systems, on top of the Berry curvature dipole, side jumps, and skew scattering.","pith_inferences":["If the quantum result is exact, intraband helicity photocurrent in a clean single Weyl node may vanish completely at isotropic disorder, which would redirect experimental searches toward finite-range disorder or multi-node effects.","A diagrammatic enumeration of all second-order photon-plus-disorder processes would settle the discrepancy directly; if an additional amplitude exists, it would likely be a field-dependent correction to scattering beyond the overlap correction ruled out in Appendix B.","The same tension may appear in other gapless systems such as Dirac semimetals and graphene, where interband virtual transitions are kinematically available at small photon energy.","A numerically exact Kubo-formula calculation of the intraband CPGE in the single-node model, as a function of disorder strength and correlation length, would reveal which side of the discrepancy survives beyond the approximations used here."],"forward_implications":["In a single ideal Weyl node with isotropic short-range scattering, the intraband CPGE constant is exactly zero quantum-mechanically, so the known mechanisms produce no helicity-dependent current in that limit.","For Gaussian-correlated disorder, $\\gamma_{\\rm QM}$ is finite for every correlation length and ranges from 0 to $-4/3$, while $\\gamma_{\\rm SC}$ is nonmonotonic and never matches it.","The equivalence between semiclassical and quantum approaches that holds in gapped gyrotropic materials does not extend to gapless Weyl nodes.","A missing microscopic contribution must be added to the quasiclassical description of CPGE in gapless systems, since the Berry curvature dipole, side jumps, and skew scattering together cannot reproduce the quantum result.","The side-jump term in an earlier Weyl-semimetal calculation omitted a piece; restoring it changes the isotropic semiclassical value from 0 to $-1$."],"supporting_citations":[{"why":"Supplies the quantum-mechanical CPGE calculation for Weyl semimetals, including the valence-band virtual amplitude $\\delta M_{\\mathbf{k}'\\mathbf{k}}$ and the $|\\delta M|^2$ contribution $\\gamma^{(1)}_{\\rm QM} = 4/3$.","marker":"[8]"},{"why":"Provides the semiclassical theory of CPGE in gyrotropic systems and the established equivalence of semiclassical and quantum approaches in gapped systems that this paper tests.","marker":"[9]"},{"why":"Gives the skew-scattering and side-jump results for Weyl semimetals that this paper builds on and corrects by adding a missing term in the side-jump contribution.","marker":"[13]"},{"why":"Supplies the side-jump corrections to the kinetic equation used for the semiclassical distribution function.","marker":"[12]"},{"why":"Yield the Berry curvature dipole value $\\gamma_{\\rm BCD} = -2/3$ used in the semiclassical sum.","marker":"[15, 16]"},{"why":"Provides the side-jump displacement formula used in Eq. (11) for the semiclassical calculation.","marker":"[17]"},{"why":"Identifies the interband-coherence effect as a candidate semiclassical mechanism, checked and found absent in Weyl semimetals in Appendix B.","marker":"[19]"}],"fun_headline_variants":["Weyl photocurrent: semiclassical vs quantum mismatch persists","Semiclassical and quantum CPGE diverge in Weyl semimetals","Intraband CPGE in Weyls: known mechanisms come up short","Quantum calculation exposes gap in semiclassical photocurrent theory"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The quantum-mechanical side is assumed complete: the paper treats the indirect-transition amplitude $M_{\\mathbf{k}'\\mathbf{k}}$ plus $\\delta M_{\\mathbf{k}'\\mathbf{k}}$, together with the current formula of Eq. (20), as containing every second-order photon-plus-disorder process, without a diagrammatic proof that no other amplitude of the same order contributes.","fun_headline_variants_meta":{"raw":{"variants":["Weyl photocurrent: semiclassical vs quantum mismatch persists","Semiclassical and quantum CPGE diverge in Weyl semimetals","Intraband CPGE in Weyls: known mechanisms come up short","Quantum calculation exposes gap in semiclassical photocurrent theory"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000213,"raw_usage":{"total_tokens":1420,"prompt_tokens":944,"completion_tokens":476,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":560,"completion_tokens_details":{"reasoning_tokens":396}},"tokens_in":560,"tokens_out":476,"duration_ms":4993,"temperature":1.0,"reasoning_tokens":396,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-06T16:17:12.355672+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Enumerate all Feynman diagrams for the second-order photon-plus-disorder response of a single Weyl node and check whether any amplitude beyond $M_{\\mathbf{k}'\\mathbf{k}}$ and $\\delta M_{\\mathbf{k}'\\mathbf{k}}$ contributes to the intraband CPGE; alternatively, run a numerically exact Kubo-formula calculation of the intraband CPGE with short-range and Gaussian disorder to see whether $\\gamma$ is $0$ or $-1$ and how it varies with $\\alpha$. A clean experimental measurement in a material with one dominant Weyl node would also discriminate, but the decisive check is the theoretical enumeration.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the quantum-mechanical CPGE calculation for Weyl semimetals, including the valence-band virtual amplitude $\\delta M_{\\mathbf{k}'\\mathbf{k}}$ and the $|\\delta M|^2$ contribution $\\gamma^{(1)}_{\\rm QM} = 4/3$."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Gives the skew-scattering and side-jump results for Weyl semimetals that this paper builds on and corrects by adding a missing term in the side-jump contribution."},{"cited_title":"de Juan, A","cited_arxiv_id":null,"evidence_quote":"Supplies the side-jump corrections to the kinetic equation used for the semiclassical distribution function."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the side-jump displacement formula used in Eq. (11) for the semiclassical calculation."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Identifies the interband-coherence effect as a candidate semiclassical mechanism, checked and found absent in Weyl semimetals in Appendix B."}],"review_version":1}