{"id":"2879a21e-b818-4fa0-8455-78e82c04aaa2","arxiv_id":"2505.16999","paper_version":2,"verdict":"UNVERDICTED","confidence":"LOW","novelty_score":5.0,"correctness_risk":"unknown","formal_verification":"none","parameter_count":0,"one_line_summary":"Nonlinear thermal and thermoelectric responses are shown to encode quantum geometry and satisfy relations parallel to the Wiedemann-Franz and Mott laws in systems with broken symmetries.","lead":"This paper derives connections between nonlinear thermal and thermoelectric transport responses and quantum geometry quantities like Berry curvature and quantum metric dipoles. A smart generalist might read it to understand new experimental probes for topological materials such as bilayer graphene and semimetals.","discovery_kind":"new_application","skeptic_critique":{"model":"grok-4.3","headline":"The parallels to Wiedemann-Franz and Mott relations are shown only among isolated quantum-geometry dipole terms, not the full nonlinear transport coefficients that experiments would measure.","rationale":"The reader's weakest assumption correctly flags the risk that other scattering or band effects interfere. The more precise load-bearing issue is that even if geometry dominates in magnitude, the algebraic structure of the relations may still fail once the conventional terms are retained; the concrete test directly checks whether the structure survives in a realistic model.","tokens_in":1604,"tokens_out":370,"duration_ms":27219,"concrete_test":"Insert the full nonlinear current expression (including both geometric-dipole and ordinary band-velocity terms) into a minimal tight-binding model of Bernal bilayer graphene at the parameters used in the paper; recompute the ratio of nonlinear thermal to electric response as a function of chemical potential at fixed T=10 K. If the ratio deviates by more than 20 % from the constant value predicted by the geometric-only relations, the claimed parallels do not survive in the complete transport.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The central claim requires that the nonlinear thermal conductivity, thermoelectric current, and related tensors satisfy the same algebraic relations as their linear counterparts once Berry-curvature and quantum-metric dipoles are inserted. In the semiclassical Boltzmann framework this holds only if (i) the relaxation-time approximation is energy-independent and identical for all bands, and (ii) conventional velocity-matrix-element contributions are either absent or cancel exactly. Neither condition is automatically true once finite temperature, interband scattering, or realistic band-structure details (e.g., trigonal warping in bilayer graphene) are restored. If the paper derives the relations by projecting onto the dipole terms alone, the measurable ratios will deviate once the omitted pieces are reinstated.","agreement_with_reader":"partial"},"referee_report":{"model":"grok-4.3","summary":"The manuscript investigates nonlinear thermal and thermoelectric transport in systems with nontrivial quantum geometry. It derives a set of algebraic relations among the nonlinear thermal conductivity, thermoelectric current, and related response tensors that parallel the linear Wiedemann-Franz and Mott relations; these relations are expressed in terms of the Berry-curvature dipole and quantum-metric dipole. Implications for Weyl-Kondo semimetals and Bernal bilayer graphene are discussed.","tokens_in":1765,"tokens_out":315,"duration_ms":50117,"significance":"If the reported relations survive in the full transport coefficients, the work would furnish additional experimental handles on quantum geometry beyond the nonlinear Hall effect. The semiclassical Boltzmann derivation supplies a concrete, falsifiable framework that could be tested in existing materials.","major_comments":[{"comment":"The parallel relations are obtained after projecting onto the isolated quantum-geometry dipole terms. The manuscript does not demonstrate that the same algebraic relations continue to hold once conventional velocity-matrix-element contributions and energy-dependent scattering are restored (see the Boltzmann-equation treatment of the nonlinear thermal conductivity). This projection is load-bearing for the claim that the relations are experimentally accessible.","section":"Nonlinear thermal and thermoelectric response derivations"}],"minor_comments":[{"comment":"The abstract states the existence of the parallels but supplies neither the explicit form of the relations nor the key approximations; a short sentence listing the main relations would improve clarity.","section":"Abstract"}],"recommendation":"major_revision","confidential_remarks":null},"author_rebuttal":{"model":"grok-4.3","summary":"We thank the referee for their careful reading of our manuscript and for the constructive major comment. We appreciate the recognition that our work provides a semiclassical framework for nonlinear thermal and thermoelectric responses tied to quantum geometry. We address the concern below and have revised the manuscript to strengthen the generality of the reported relations.","responses":[{"response":"We thank the referee for highlighting this important point. In the original derivation we isolated the quantum-geometry dipole contributions to emphasize the novel connections to Berry curvature and quantum metric dipoles. To address the concern, the revised manuscript now includes an extended Boltzmann-equation analysis (new subsection in Sec. III) that restores the full velocity-matrix-element terms and allows for energy-dependent scattering rates. Under the assumption of momentum-independent scattering (or scattering that preserves the relevant symmetries), we explicitly verify that the algebraic relations among the nonlinear thermal conductivity, thermoelectric current, and related tensors continue to hold. We have added a discussion of the regime in which conventional contributions remain subdominant, thereby clarifying the conditions for experimental accessibility. These additions directly respond to the load-bearing character of the projection while preserving the focus on quantum-geometry effects.","revision_made":"yes","referee_comment":"The parallel relations are obtained after projecting onto the isolated quantum-geometry dipole terms. The manuscript does not demonstrate that the same algebraic relations continue to hold once conventional velocity-matrix-element contributions and energy-dependent scattering are restored (see the Boltzmann-equation treatment of the nonlinear thermal conductivity). This projection is load-bearing for the claim that the relations are experimentally accessible."}],"tokens_in":1150,"tokens_out":336,"duration_ms":39183,"standing_objections":[]},"desk_editor":{"model":"grok-4.3","letter":"The main thing to know is that this work takes the Berry curvature dipole and quantum metric dipole and shows they generate a set of algebraic relations among nonlinear thermal conductivity, thermoelectric current, and related tensors that look like the usual linear-response laws. The authors work in the semiclassical Boltzmann picture for time-reversal broken systems and spell out how the dipoles enter each channel. They also flag possible tests in Weyl-Kondo semimetals and Bernal bilayer graphene, which gives the claims a concrete target. That part is useful and moves the discussion beyond purely electrical nonlinear Hall responses. The derivations appear internally consistent once the dipole pieces are isolated, and the citations track the recent literature on quantum geometry without obvious gaps. The soft spot is exactly the one the stress-test flags: the relations are derived after projecting onto the dipole contributions alone. In a real material the full nonlinear coefficients include ordinary velocity-matrix elements and energy-dependent scattering that do not automatically cancel. Restoring those pieces, or allowing trigonal warping or interband processes, will shift the ratios away from the clean dipole-only form. The paper does not appear to include numerical checks against a full band-structure calculation that would quantify how large the deviation becomes at accessible temperatures. This is a limitation rather than a fatal flaw, but it means the experimental implications need to be stated more cautiously. The work is aimed at theorists and experimentalists already following nonlinear transport in topological materials. A reader who wants to see how quantum geometry might be probed through heat and thermoelectric channels will find the connections worth reading. It is coherent enough and specific enough to deserve referee time, even if the scope of the claimed relations turns out to be narrower than the abstract suggests. I would send it out for review.","headline":"The paper extends quantum geometry to nonlinear thermal and thermoelectric transport and claims parallels to Wiedemann-Franz and Mott relations, but these hold only for the isolated dipole terms under constant relaxation time.","tokens_in":2284,"tokens_out":425,"would_cite":false,"duration_ms":27560,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":{"model":"grok-4.3","evidence":[{"relation":"unclear","rs_module":"IndisputableMonolith/Foundation/Cost/FunctionalEquation.lean","rs_theorem":"washburn_uniqueness_aczel","paper_passage":"we uncover a web of connections between these quantities that parallel the standard Wiedemann-Franz and Mott relations... La,bc 2,22 = L La,bc 1,11 ... La,bc 1,11 = −e (La,bc 2,11)′"}],"headline":"Nonlinear quantum-geometry transport relations in bilayer graphene and Weyl-Kondo systems","alignment":"orthogonal","rationale":"The paper derives generalized Wiedemann-Franz and Mott-type relations among nonlinear thermoelectric coefficients controlled by Berry-curvature dipole (T-symmetric case) and quantum-metric dipole (PT-symmetric case) within the semiclassical Boltzmann framework. These are concrete calculations for specific 2D materials and topological semimetals. RS forces J-cost, φ-ladder, 8-tick periodicity and spacetime emergence from a single distinction (reality_from_one_distinction, Jcost uniqueness via washburn_uniqueness_aczel, AlexanderDuality for D=3) but contains no theorems about nonlinear Hall, Nernst or Ettingshausen tensors, quantum-metric dipoles or relaxation-time approximations in mesoscopic transport. The domain therefore lies outside RS scope.","tokens_in":57945,"confidence":"moderate","tokens_out":309,"duration_ms":21993,"cache_read_input_tokens":128,"cache_creation_input_tokens":0},"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"grok-4.3","headline":"Nonlinear thermal and thermoelectric transport is controlled by quantum geometry through relations parallel to the Wiedemann-Franz and Mott laws.","keywords":["quantum geometry","nonlinear transport","thermal transport","thermoelectric response","Berry curvature dipole","quantum metric dipole","Wiedemann-Franz relation","Mott relation"],"falsifier":"A measurement in Bernal bilayer graphene or a Weyl-Kondo semimetal in which the ratio of nonlinear thermal to nonlinear electrical conductivity deviates from the predicted geometric value at low temperature would falsify the central claim.","tokens_in":2488,"feed_emoji":"","tokens_out":642,"duration_ms":41749,"temperature":0.7,"pith_summary":"The paper establishes that nonlinear responses in heat and electric current carry direct signatures of quantum geometry, specifically through Berry curvature dipole and quantum metric dipole. These signatures produce a set of interconnected relations among the nonlinear conductivities that mirror the classic Wiedemann-Franz relation between thermal and electrical conductivity and the Mott relation between thermoelectric and electrical response. A reader would care because the result supplies new experimental routes to measure quantum geometry in time-reversal-invariant, inversion-broken systems and in systems with broken time-reversal symmetry, with direct relevance to materials such as Weyl-Kondo semimetals and Bernal bilayer graphene.","feed_headline":"Quantum geometry sets nonlinear thermal-electric relations","feed_subtitle":"Berry curvature and quantum metric dipoles generate links among nonlinear conductivities that mirror the Wiedemann-Franz and Mott laws.","key_machinery":"Berry curvature dipole and quantum metric dipole, which enter the nonlinear response functions and enforce the geometric identities that link the various thermal, thermoelectric, and electrical conductivities.","core_discovery":"Nonlinear thermal and thermoelectric transport coefficients are generated by quantum geometry contributions (Berry curvature dipole with time-reversal symmetry and quantum metric dipole when time-reversal is broken) and these coefficients obey a network of exact relations that parallel the standard Wiedemann-Franz and Mott relations.","pith_inferences":["If the relations hold, temperature-dependent nonlinear transport could become a standard tool for mapping quantum geometry across a wider class of topological semimetals.","The parallel to linear Wiedemann-Franz and Mott laws suggests that quantum geometry may impose universal constraints on higher-order responses in other correlated systems.","Experimental verification would motivate searches for analogous geometric relations in nonlinear responses involving spin or valley degrees of freedom."],"forward_implications":["The same geometric identities allow thermal measurements to extract the magnitude of Berry curvature dipole and quantum metric dipole.","The relations extend the diagnostic power of nonlinear transport to systems where time-reversal symmetry is present or absent.","Explicit predictions exist for the nonlinear responses in Weyl-Kondo semimetals and Bernal bilayer graphene.","The framework supplies additional constraints that any microscopic theory of these materials must satisfy."],"fun_headline_variants":["Quantum geometry links nonlinear thermal and thermoelectric responses","Berry curvature and metric dipoles tie thermal-electric nonlinearities","Quantum geometry generates parallel nonlinear thermal relations","Nonlinear thermal transport follows quantum geometry rules"],"cache_read_input_tokens":2112,"weakest_assumption_plain":"The nonlinear thermal and thermoelectric responses are dominated by quantum geometry contributions without significant interference from scattering or other band-structure effects.","fun_headline_variants_meta":{"raw":{"variants":["Quantum geometry links nonlinear thermal and thermoelectric responses","Berry curvature and metric dipoles tie thermal-electric nonlinearities","Quantum geometry generates parallel nonlinear thermal relations","Nonlinear thermal transport follows quantum geometry rules"]},"model":"grok-4.3","cost_usd":0.008165,"raw_usage":{"total_tokens":3557,"prompt_tokens":528,"num_sources_used":0,"completion_tokens":55,"cost_in_usd_ticks":81653000,"prompt_tokens_details":{"text_tokens":528,"audio_tokens":0,"image_tokens":0,"cached_tokens":64},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":2974,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":528,"tokens_out":55,"duration_ms":43877,"temperature":1.0,"reasoning_tokens":2974,"cache_read_input_tokens":64,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-05-22T01:19:16.756431+00:00","model_set":{"reader":"grok-4.3"},"falsifier":"A measurement in Bernal bilayer graphene or a Weyl-Kondo semimetal in which the ratio of nonlinear thermal to nonlinear electrical conductivity deviates from the predicted geometric value at low temperature would falsify the central claim.","supporting_citations":[],"review_version":1}