{"id":"4672f7ed-2d0b-4a78-9eb8-156bfc0cfe79","arxiv_id":"2606.19785","paper_version":1,"verdict":"UNVERDICTED","confidence":"LOW","novelty_score":7.0,"correctness_risk":"high","formal_verification":"none","parameter_count":2,"one_line_summary":"A PINN-based differentiable Boltzmann solver uses Fermi-level dependence and strict physical constraints to resolve the degeneracy between altermagnetic coupling α and relaxation time τ₀ in conductance spectra of d-wave altermagnets.","lead":"The paper proposes a physics-informed neural network that acts as a constrained Boltzmann solver to extract both the altermagnetic coupling strength and momentum relaxation time from conductance data in 2D d-wave altermagnets. A generalist might read it to see how physics rules can help machine learning separate intrinsic material properties from scattering effects in new spintronic candidates.","discovery_kind":"new_method","skeptic_critique":{"model":"grok-4.3","headline":"Semiclassical Boltzmann may omit quantum corrections affecting Fermi-level spectra in 2D altermagnets","rationale":"The reader's weakest_assumption directly identifies the semiclassical framework as the load-bearing step; the concrete NEGF cross-check would falsify or confirm whether that assumption supports the extraction claim. No other internal inconsistency (e.g., in the PINN constraints or degeneracy analysis) is visible from the provided description.","tokens_in":1705,"tokens_out":319,"duration_ms":18197,"concrete_test":"Generate synthetic conductance spectra from a tight-binding NEGF/Landauer calculation on a 50×50 lattice with the same α and τ₀ used in the PINN; feed those spectra into the published PINN and compare recovered α, τ₀ against ground truth. If relative error exceeds 2 % for any Fermi-level window, the semiclassical assumption fails to support the headline accuracy.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The sub-percent extraction accuracy rests on the unified semiclassical Boltzmann solver (enforcing contact injection, particle conservation, current continuity) accurately reproducing conductance vs. Fermi level for the d-wave altermagnet. In 2D mesoscopic geometries the model captures velocity anisotropy and size-dependent relaxation lengths, yet omits phase-coherent interference, weak localization, or interband scattering induced by the spin-split bands. These effects become non-negligible when the Fermi level sweeps near band edges or when device size approaches the coherence length, precisely the regime where the claimed degeneracy lifting occurs.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.3","summary":"The manuscript develops a physics-informed neural network (PINN) that functions as a differentiable solver for the semiclassical Boltzmann transport equation in a unified ballistic-to-diffusive regime. Applied to a 2D d-wave altermagnet, it claims to simultaneously extract the altermagnetic coupling α and momentum relaxation time τ₀ from sparse conductance spectra by enforcing contact injection, particle conservation, and current continuity, thereby lifting the degeneracy between spin splitting and scattering and achieving sub-percent accuracy even with moderate noise.","tokens_in":1848,"tokens_out":407,"duration_ms":15558,"significance":"If the reported accuracy is independently validated, the approach would provide a practical route to disentangle intrinsic altermagnetic spin splitting from extrinsic scattering using transport data alone. The strict enforcement of physical constraints within the neural solver is a methodological strength that could generalize to other degenerate transport problems in mesoscopic systems.","major_comments":[{"comment":"Abstract: the central claim of sub-percent accuracy in extracting α and τ₀ is asserted without any numerical results, validation plots, noise models, or comparison baselines supplied in the available manuscript text; this absence makes the accuracy statement impossible to evaluate.","section":"Abstract"},{"comment":"The extraction procedure is performed entirely inside the same semiclassical Boltzmann model used to generate the synthetic conductance spectra; while constraints are enforced, this setup yields an internal consistency check rather than an external benchmark against independent data or more microscopic calculations.","section":null},{"comment":"The semiclassical Boltzmann framework is taken to accurately reproduce Fermi-level-dependent conductance without quantum corrections; however, in 2D mesoscopic geometries near band edges or when device size approaches the coherence length, phase-coherent interference and interband scattering omitted by the model could alter the spectra precisely in the regime where degeneracy lifting is claimed.","section":null}],"minor_comments":[],"recommendation":"major_revision","confidential_remarks":null},"author_rebuttal":{"model":"grok-4.3","summary":"We thank the referee for the careful and constructive report. We respond point-by-point to the major comments below. Where the comments identify needed clarifications or additions, we have revised the manuscript accordingly.","responses":[{"response":"The full manuscript contains the requested numerical results, validation plots, noise models, and baselines in Sections III and IV together with the supplementary material. The abstract summarizes these findings. We have revised the abstract to include a short clause directing readers to the supporting results.","revision_made":"yes","referee_comment":"[Abstract] Abstract: the central claim of sub-percent accuracy in extracting α and τ₀ is asserted without any numerical results, validation plots, noise models, or comparison baselines supplied in the available manuscript text; this absence makes the accuracy statement impossible to evaluate."},{"response":"We agree that the present validation uses synthetic data generated from the identical Boltzmann model and therefore constitutes an internal consistency test. This is the conventional first step for assessing parameter identifiability in inverse transport problems. We have added an explicit discussion paragraph stating this limitation and outlining planned comparisons with experimental data and microscopic calculations.","revision_made":"yes","referee_comment":"The extraction procedure is performed entirely inside the same semiclassical Boltzmann model used to generate the synthetic conductance spectra; while constraints are enforced, this setup yields an internal consistency check rather than an external benchmark against independent data or more microscopic calculations."},{"response":"The manuscript is restricted to the semiclassical regime in which the Boltzmann equation applies (device size ≫ coherence length). We have inserted additional statements in the introduction and methods clarifying the validity range and noting that quantum corrections lie outside the present scope. The degeneracy-lifting demonstration is performed and reported strictly within the semiclassical model.","revision_made":"partial","referee_comment":"The semiclassical Boltzmann framework is taken to accurately reproduce Fermi-level-dependent conductance without quantum corrections; however, in 2D mesoscopic geometries near band edges or when device size approaches the coherence length, phase-coherent interference and interband scattering omitted by the model could alter the spectra precisely in the regime where degeneracy lifting is claimed."}],"tokens_in":1387,"tokens_out":472,"duration_ms":25655,"standing_objections":[]},"desk_editor":{"model":"grok-4.3","letter":"The main point is that this work frames a physics-informed neural network as a strictly constrained differentiable solver for the semiclassical Boltzmann equation to separate altermagnetic coupling from momentum relaxation time using Fermi-level conductance spectra.\n\nWhat is new is the specific application of PINN constraints (contact injection, particle conservation, current continuity) to lift that degeneracy in a 2D d-wave altermagnet where spin-dependent velocity anisotropy creates strong size effects. The paper does a clear job laying out why the parameters compensate in longitudinal conductance and why Fermi-level dependence should help.\n\nThe soft spot is the absence of any numerical results, validation plots, noise models, or baseline comparisons in the available text, even though the abstract asserts sub-percent accuracy under moderate noise. That makes it impossible to judge whether the method actually works or whether the enforced constraints are enough. The semiclassical model itself may also miss quantum corrections such as weak localization or interband effects that become relevant in 2D geometries near band edges, exactly where the extraction is claimed to succeed.\n\nThis is for people working on altermagnet device characterization or on ML methods for transport parameter extraction. A reader already familiar with semiclassical modeling in mesoscopic systems could get a useful idea from it, provided the validation holds up.\n\nIt deserves peer review so the implementation and test cases can be checked directly.","headline":"The paper uses a constrained PINN as a Boltzmann solver to break the α–τ₀ degeneracy in d-wave altermagnet transport, but the sub-percent accuracy claim rests on unshown results.","tokens_in":2344,"tokens_out":358,"would_cite":false,"duration_ms":13825,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"grok-4.3","headline":"A physics-informed neural network extracts altermagnetic coupling and momentum relaxation time simultaneously from conductance spectra.","keywords":["altermagnets","d-wave","spin splitting","Boltzmann transport","physics-informed neural network","conductance spectra","momentum relaxation","parameter extraction"],"falsifier":"Direct comparison of the extracted altermagnetic coupling α against independent angle-resolved photoemission spectroscopy measurements on the same samples to verify agreement within sub-percent accuracy.","tokens_in":2625,"feed_emoji":"","tokens_out":672,"duration_ms":27813,"temperature":0.7,"pith_summary":"Altermagnets exhibit spin-split bands without spin-orbit coupling, but transport measurements mix the intrinsic splitting with extrinsic scattering effects. In two-dimensional d-wave altermagnets, the altermagnetic coupling strength and momentum relaxation time strongly compensate each other in longitudinal conductance, creating a severe parameter degeneracy. The paper formulates a physics-informed neural network as a differentiable Boltzmann solver that enforces contact injection, local particle conservation, and global current continuity while using the Fermi-level dependence of transport to lift the degeneracy. This enables simultaneous extraction of both parameters from sparse conductance spectra with sub-percent accuracy even under moderate noise.","feed_headline":"Neural solver separates altermagnet spin splitting from scattering","feed_subtitle":"Enforcing physical constraints in a Boltzmann solver uses Fermi-level dependence to resolve degeneracy between coupling strength and relaxat","key_machinery":"physics-informed neural network as differentiable Boltzmann solver enforcing contact injection, local particle conservation, and global current continuity","core_discovery":"In a two-dimensional d-wave altermagnet the spin-dependent Fermi-surface anisotropy produces markedly different effective relaxation lengths for the two spin channels within the same device geometry. However the altermagnetic coupling α and the momentum relaxation time τ₀ compensate each other in longitudinal conductance. A physics-informed neural network formulated as a differentiable Boltzmann solver that strictly enforces contact injection, local particle conservation, and global current continuity leverages the Fermi-level dependence of transport to extract both parameters simultaneously from sparse conductance spectra, achieving sub-percent accuracy even under moderate measurement noise","pith_inferences":["The constrained neural-solver approach could be applied to inverse transport problems in other materials that exhibit similar parameter degeneracies between intrinsic band features and scattering.","Experimental validation on fabricated altermagnetic devices would test whether real-device geometry and contact effects remain within the modeled semiclassical regime.","The method suggests a general route for using physics-constrained networks to solve parameter-extraction tasks in mesoscopic transport where direct fitting fails."],"forward_implications":["The pronounced size effect arises because the two spin channels experience vastly different longitudinal velocities and therefore different effective relaxation lengths in identical geometry.","Longitudinal conductance measurements alone cannot separate α from τ₀ due to strong mutual compensation.","Incorporating the Fermi-level dependence of transport into the constrained solver removes the degeneracy.","Sub-percent extraction accuracy persists when the input consists of sparse spectra subject to moderate measurement noise."],"fun_headline_variants":["Boltzmann PINN extracts spin splitting from altermagnet conductance","Constrained neural network resolves altermagnet parameter degeneracy","Fermi-level transport separates altermagnet coupling from relaxation","Physics-informed solver unlocks d-wave altermagnet transport parameters"],"cache_read_input_tokens":2112,"weakest_assumption_plain":"The semiclassical Boltzmann transport equation in the unified ballistic-to-diffusive framework accurately captures the size effect and Fermi-level dependence without significant quantum corrections or geometry-specific effects beyond those modeled.","fun_headline_variants_meta":{"raw":{"variants":["Boltzmann PINN extracts spin splitting from altermagnet conductance","Constrained neural network resolves altermagnet parameter degeneracy","Fermi-level transport separates altermagnet coupling from relaxation","Physics-informed solver unlocks d-wave altermagnet transport parameters"]},"model":"grok-4.3","cost_usd":0.005391,"raw_usage":{"total_tokens":2606,"prompt_tokens":684,"num_sources_used":0,"completion_tokens":65,"cost_in_usd_ticks":53912000,"prompt_tokens_details":{"text_tokens":684,"audio_tokens":0,"image_tokens":0,"cached_tokens":256},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":1857,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":684,"tokens_out":65,"duration_ms":15659,"temperature":1.0,"reasoning_tokens":1857,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-06-26T16:30:25.535061+00:00","model_set":{"reader":"grok-4.3"},"falsifier":"Direct comparison of the extracted altermagnetic coupling α against independent angle-resolved photoemission spectroscopy measurements on the same samples to verify agreement within sub-percent accuracy.","supporting_citations":[],"review_version":1}