{"id":"7b2e82dc-1e3b-420e-9613-67720cd3483b","arxiv_id":"2606.24108","paper_version":1,"verdict":"UNVERDICTED","confidence":"LOW","novelty_score":6.0,"correctness_risk":"unknown","formal_verification":"none","parameter_count":0,"one_line_summary":"NMR data on K2Cr3As3 reveal three spin-triplet superconducting phases with evolving d(k)-vector orientations and gap structures from helical to chiral to line-nodal.","lead":"The paper reports NMR measurements identifying three distinct superconducting phases in K2Cr3As3, with the d-vector rotating from in-plane to out-of-plane upon cooling in low fields and a line-nodal gap in high fields. This positions the material as a tunable platform for spin-triplet topological superconductivity studies.","discovery_kind":"new_application","skeptic_critique":{"model":"grok-4.3","headline":"NMR-to-d-vector mapping assumes unique correspondence between Knight shift/1/T1 behavior and specific helical/chiral/line-nodal states without quantitative model comparison.","rationale":"The reader's weakest_assumption correctly isolates the interpretive step that carries the entire phase diagram. Because the manuscript is experimental and the full data tables/figures are not reproduced here, no stronger internal inconsistency can be diagnosed; the concern remains exactly where the reader placed it.","tokens_in":1850,"tokens_out":320,"duration_ms":10981,"concrete_test":"Re-fit the published Knight-shift temperature dependence in the low-field phases using a fixed in-plane d-vector with only a temperature-dependent gap amplitude; if the fit quality (chi-squared) is statistically indistinguishable from the rotating-d-vector model across the reported transition, the directional-evolution claim is not uniquely required by the data.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim requires that observed field- and temperature-dependent changes in 77Se or 39K Knight shift and relaxation rates map one-to-one onto d-vector rotation (in-plane to out-of-plane) and node-type changes (point to line nodes). In practice this mapping depends on (i) the assumed form of the gap function and Fermi-surface anisotropy, (ii) negligible vortex or impurity contributions to the relaxation, and (iii) the absence of domain averaging or sample inhomogeneity that could mimic the reported phase boundaries. No independent verification (e.g., specific-heat node counting or directional thermal conductivity) is cited to anchor the assignment.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.3","summary":"The manuscript reports NMR measurements (Knight shift and spin-lattice relaxation) on K2Cr3As3 that identify three distinct superconducting phases: low-field Phase A (helical, point nodes, in-plane d-vector), Phase B (chiral, point nodes, out-of-plane d-vector upon cooling), and high-field Phase C (line-nodal gap, in-plane d-vector). These are presented as evidence for tunable spin-triplet topological superconductivity with manipulable d(k)-vector orientation and gap structure.","tokens_in":1955,"tokens_out":334,"duration_ms":14223,"significance":"If the phase assignments and d-vector identifications are robust, the results would establish K2Cr3As3 as a high-Tc (6.2 K) spin-triplet platform free of competing magnetic order, offering a cleaner system than U-based compounds for exploring topological superconductivity and Majorana states. The reported tunability across phases would be a notable experimental advance.","major_comments":[{"comment":"The central claim that observed field- and temperature-dependent changes in Knight shift and 1/T1 directly map onto specific d(k)-vector rotations (in-plane to out-of-plane) and node-type changes (point to line nodes) is load-bearing but rests on an assumed one-to-one correspondence. The manuscript provides no quantitative model comparisons (e.g., calculated relaxation rates for helical vs. chiral states including Fermi-surface anisotropy) or independent verification (specific-heat node counting or directional thermal conductivity) to rule out confounds such as impurities, vortex contributions, or domain averaging.","section":null}],"minor_comments":[],"recommendation":"major_revision","confidential_remarks":null},"author_rebuttal":{"model":"grok-4.3","summary":"We thank the referee for their careful review and constructive feedback on our manuscript. We address the major comment point by point below, providing clarifications on the basis of our interpretations while acknowledging areas where additional discussion can strengthen the presentation.","responses":[{"response":"We acknowledge that the phase assignments rely on established theoretical mappings between NMR observables and d-vector orientations/node structures in spin-triplet superconductors, rather than new material-specific quantitative calculations of relaxation rates that incorporate the full Fermi-surface anisotropy. Such calculations are complex for the multi-orbital, quasi-1D band structure of K2Cr3As3 and were not performed in this primarily experimental work. The interpretations are instead based on the standard NMR response functions for helical, chiral, and line-nodal triplet states as derived in the literature for similar systems, with the observed Knight-shift suppression and 1/T1 power laws matching the expected behaviors for in-plane vs. out-of-plane d-vectors and point vs. line nodes. Sample quality (sharp transitions, no magnetic order) and field-dependent data help mitigate confounds from impurities or vortices; domain averaging is unlikely given the consistent evolution across multiple samples. We have added an expanded discussion section with additional literature references and explicit consideration of alternative explanations in the revised manuscript. Independent probes such as directional thermal conductivity are valuable but outside the NMR scope of the present study.","revision_made":"partial","referee_comment":"The central claim that observed field- and temperature-dependent changes in Knight shift and 1/T1 directly map onto specific d(k)-vector rotations (in-plane to out-of-plane) and node-type changes (point to line nodes) is load-bearing but rests on an assumed one-to-one correspondence. The manuscript provides no quantitative model comparisons (e.g., calculated relaxation rates for helical vs. chiral states including Fermi-surface anisotropy) or independent verification (specific-heat node counting or directional thermal conductivity) to rule out confounds such as impurities, vortex contributions, or domain averaging."}],"tokens_in":1385,"tokens_out":423,"duration_ms":16767,"standing_objections":[]},"desk_editor":{"model":"grok-4.3","letter":"The core observation here is NMR data showing distinct temperature and field regimes in K2Cr3As3 that the authors label as helical (A), chiral (B), and line-nodal (C) states, with the d-vector rotating from in-plane to out-of-plane on cooling at low fields. This is presented as new, extending prior work on the same compound by adding phase boundaries and a specific evolution sequence.\n\nThe material choice is useful: higher Tc than the U-based candidates and no magnetic order removes some of the usual complications. The abstract indicates they tracked Knight shift and 1/T1 to track spin susceptibility and gap structure, which is the right experimental handle for spin-triplet claims.\n\nThe soft spot is the direct mapping from those NMR quantities to helical versus chiral versus line-nodal gaps and to the precise d-vector orientation. That step assumes the gap form, Fermi-surface details, and negligible impurity or vortex contributions produce unique signatures; the abstract does not cite cross-checks such as specific-heat node counting or directional thermal transport that would pin down the node type. The stress-test concern about one-to-one correspondence therefore lands on the presented evidence.\n\nThis is for groups already working on Cr- or U-based triplet candidates or on NMR in unconventional superconductors. A reader can extract the raw field-temperature phase diagram and the reported Knight-shift behavior even if they treat the d-vector and node assignments as working hypotheses. The work is coherent on its own terms and shows clear engagement with the literature on topological superconductivity, so it merits referee time rather than desk rejection, though the analysis section will need scrutiny on the uniqueness of the interpretations.","headline":"The paper reports NMR signatures for three SC phases in K2Cr3As3 with claimed d-vector rotation, but the node-type assignments rest on interpretive mappings that lack independent anchors.","tokens_in":2477,"tokens_out":412,"would_cite":false,"duration_ms":18276,"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":"K2Cr3As3 hosts three superconducting phases with evolving d-vector directions and gap nodes.","keywords":["spin-triplet superconductivity","topological superconductor","K2Cr3As3","d-vector","NMR","multiple phases","point nodes","line nodes"],"falsifier":"A temperature or field sweep in which the Knight shift or relaxation rate fails to show the expected drop or anisotropy pattern that would accompany a rotation of the d(k)-vector from in-plane to out-of-plane or a switch from point nodes to line nodes.","tokens_in":2736,"feed_emoji":"⚛️","tokens_out":762,"duration_ms":24645,"temperature":0.7,"pith_summary":"The paper establishes that K2Cr3As3 exhibits three distinct spin-triplet superconducting phases that can be tuned by temperature and magnetic field. Nuclear magnetic resonance tracks the d(k)-vector rotation and identifies point nodes in the low-field phases A and B versus a line-nodal gap in the high-field phase C. This provides evidence for helical and chiral states at low fields that evolve upon cooling and a different nodal structure at high fields. The material lacks competing magnetic orders and has a relatively high transition temperature, making the phases more accessible for study than in U-based compounds. A sympathetic reader would care because the findings position the compound as a tunable platform for exploring topological superconductivity.","feed_headline":"Three phases found in K2Cr3As3 with rotating d-vector","feed_subtitle":"NMR shows low-field helical and chiral states with point nodes evolving to a high-field line-nodal state, establishing a tunable spin-triple","key_machinery":"The d(k)-vector that encodes the spin orientation of the triplet Cooper pairs, mapped through NMR Knight shift and 1/T1 relaxation rate to distinguish helical, chiral, and line-nodal states.","core_discovery":"The authors report three distinct superconducting phases in K2Cr3As3. At low magnetic fields the system evolves from a helical phase A to a chiral phase B upon cooling, with the d(k)-vector rotating from in-plane to out-of-plane while both retain point nodes; a line-nodal gap appears in the high-field phase C where the d(k)-vector lies in the basal plane. These phases are identified through the internal spin degrees of freedom via NMR measurements of the Knight shift and relaxation rates.","pith_inferences":["Similar NMR protocols could be applied to related Cr- or As-based compounds to map additional phase diagrams.","Device structures incorporating K2Cr3As3 might exploit the field-tunable d-vector to control edge states or Majorana modes.","Pressure or chemical substitution experiments could extend the observed phases and test whether the line-nodal state persists or changes.","The higher Tc relative to U-based candidates suggests this platform could support experiments at more accessible temperatures."],"forward_implications":["K2Cr3As3 functions as a model spin-triplet superconductor free of coexisting magnetic order and with Tc near 6 K.","Magnetic field and temperature can be used to switch between helical, chiral, and line-nodal gap structures.","The point-node phases at low field versus line-node phase at high field allow direct comparison of different nodal topologies within one material.","The observed d(k)-vector rotation supplies a concrete example of how spin-triplet pairing can be manipulated internally."],"fun_headline_variants":["K2Cr3As3 d-vector rotates across three phases","Three phases evolve with rotating d-vector in K2Cr3As3","NMR maps d-vector shift in K2Cr3As3 phases A B C","K2Cr3As3 helical chiral line-nodal phases via NMR","d-vector rotates from in-plane to out-of-plane in K2Cr3As3 phases"],"cache_read_input_tokens":2112,"weakest_assumption_plain":"NMR signatures of the Knight shift and relaxation rates map directly onto specific d(k)-vector directions and gap node structures without major interference from impurities or sample inhomogeneity.","fun_headline_variants_meta":{"raw":{"variants":["K2Cr3As3 d-vector rotates across three phases","Three phases evolve with rotating d-vector in K2Cr3As3","NMR maps d-vector shift in K2Cr3As3 phases A B C","K2Cr3As3 helical chiral line-nodal phases via NMR","d-vector rotates from in-plane to out-of-plane in K2Cr3As3 phases"]},"model":"grok-4.3","cost_usd":0.004914,"raw_usage":{"total_tokens":2440,"prompt_tokens":734,"num_sources_used":0,"completion_tokens":90,"cost_in_usd_ticks":49137000,"prompt_tokens_details":{"text_tokens":734,"audio_tokens":0,"image_tokens":0,"cached_tokens":256},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":1616,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":734,"tokens_out":90,"duration_ms":12664,"temperature":1.0,"reasoning_tokens":1616,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-06-25T22:27:29.538248+00:00","model_set":{"reader":"grok-4.3"},"falsifier":"A temperature or field sweep in which the Knight shift or relaxation rate fails to show the expected drop or anisotropy pattern that would accompany a rotation of the d(k)-vector from in-plane to out-of-plane or a switch from point nodes to line nodes.","supporting_citations":[],"review_version":1}