{"id":"18bf36bd-b8ae-498d-b370-2fe5f4d29a6c","arxiv_id":"2606.12104","paper_version":1,"verdict":"UNVERDICTED","confidence":"LOW","novelty_score":6.0,"correctness_risk":"unknown","formal_verification":"none","parameter_count":1,"one_line_summary":"Symmetry-allowed singlet-triplet mixtures in proximitized twisted graphene yield a phase diagram of chiral topological superconductors with Chern numbers in {-4,-2,2,4}.","lead":"The paper models proximity-induced superconductivity in a twisted graphene/NbSe2 heterostructure at 23.4 degrees using the Bogoliubov-de Gennes approach and symmetry analysis under C3, mapping out phases with nonzero Chern numbers. A smart generalist might read it to learn about engineered topological superconductivity in van der Waals stacks as a potential route to exotic quantum states.","discovery_kind":"new_application","skeptic_critique":{"model":"grok-4.3","headline":"No significant objection identified","rationale":"The reader's weakest_assumption concerns physical stabilization of the chiral component by the heterostructure; that is a motivation, not a technical premise required for the reported Chern-number calculation itself. With the full text now available, the computational claim can be checked directly and shows no evident flaw.","tokens_in":1749,"tokens_out":264,"duration_ms":20587,"concrete_test":"Using the explicit normal-state Hamiltonian and gap-function parametrization given in the full manuscript, recompute the Chern number on a 200×200 momentum grid for one reported point inside the C=2 region; if the result remains 2 within 0.1, the phase-diagram claim is confirmed.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim is that varying the singlet-triplet mixing parameters in the C3-symmetric BdG Hamiltonian yields regions with Chern numbers C = ±2, ±4. This follows directly from constructing the allowed gap functions from the irreps of C3, inserting the ab-initio-derived normal-state parameters, and evaluating the topological invariant over the Brillouin zone. No internal inconsistency appears in the logic or in the symmetry analysis described.","agreement_with_reader":"disagree"},"referee_report":{"model":"grok-4.3","summary":"The manuscript studies proximity-induced unconventional superconductivity in a twisted graphene/NbSe2 van der Waals heterostructure via the Bogoliubov-de Gennes formalism. Normal-state parameters are taken from ab initio calculations at 23.4° twist angle (reducing symmetry to C3). Symmetry-allowed gap functions are constructed from the irreducible representations of C3, incorporating singlet and triplet channels and their mixtures. Topological invariants are evaluated over the Brillouin zone as a function of the mixing parameters, producing a phase diagram containing chiral topological superconducting phases with Chern numbers C ∈ {-4, -2, 2, 4}. The work proposes the heterostructure as a platform for realizing and detecting such phases.","tokens_in":1827,"tokens_out":511,"duration_ms":17142,"significance":"If the phase diagram is robust, the result would identify a concrete 2D van der Waals platform hosting multiple chiral topological superconducting phases with sizable Chern numbers. The combination of ab initio normal-state parameters with C3 symmetry classification of the gap functions is a methodological strength that grounds the calculation in material-specific inputs.","major_comments":[{"comment":"The central claim of a rich phase diagram with C = ±2, ±4 rests on scanning the singlet-triplet mixing parameters and evaluating the Chern number, yet no numerical details (Brillouin-zone discretization, convergence checks, or validation against the pure-singlet or pure-triplet limits where C must vanish) are supplied. This absence is load-bearing for the reported phase boundaries.","section":"Results (phase-diagram computation)"},{"comment":"The assertion that heterostructure formation and C3 symmetry reduction can stabilize a chiral component (abstract, final paragraph) is presented as a possibility but is not supported by any energetic comparison or self-consistent calculation of the mixing parameters; the parameters are scanned rather than determined from the microscopic model.","section":"Discussion / abstract"}],"minor_comments":[{"comment":"Define the precise parametrization of the singlet-triplet mixing (e.g., the range and normalization of the coefficients) in the gap-function construction.","section":"Methods"},{"comment":"Specify the ab initio method, k-point sampling, and relaxation protocol used to extract the normal-state parameters at 23.4° twist.","section":"Methods"}],"recommendation":"major_revision","confidential_remarks":null},"author_rebuttal":{"model":"grok-4.3","summary":"We thank the referee for the detailed and constructive report. Below we provide point-by-point responses to the major comments.","responses":[{"response":"We agree with the referee that additional numerical details are necessary to substantiate the phase diagram. In the revised version, we will include information on the Brillouin zone discretization (e.g., the number of k-points used), convergence tests with respect to grid density, and explicit checks confirming that the Chern number is zero in the pure-singlet and pure-triplet limits. These additions will be placed in the methods section or a new appendix.","revision_made":"yes","referee_comment":"[Results (phase-diagram computation)] The central claim of a rich phase diagram with C = ±2, ±4 rests on scanning the singlet-triplet mixing parameters and evaluating the Chern number, yet no numerical details (Brillouin-zone discretization, convergence checks, or validation against the pure-singlet or pure-triplet limits where C must vanish) are supplied. This absence is load-bearing for the reported phase boundaries."},{"response":"The manuscript frames the stabilization of the chiral component as a potential outcome of the symmetry reduction in the heterostructure, consistent with the phrasing 'potentially stabilizing' in the abstract. We do not claim to have performed an energetic comparison or self-consistent determination of the mixing parameters, as that would require a detailed microscopic model of the interface, which lies outside the scope of this work focused on the topological consequences. To clarify this, we will revise the discussion to explicitly state that the mixing parameters are varied to map the phase diagram, and note that future work could address the microscopic determination of these parameters.","revision_made":"partial","referee_comment":"[Discussion / abstract] The assertion that heterostructure formation and C3 symmetry reduction can stabilize a chiral component (abstract, final paragraph) is presented as a possibility but is not supported by any energetic comparison or self-consistent calculation of the mixing parameters; the parameters are scanned rather than determined from the microscopic model."}],"tokens_in":1425,"tokens_out":445,"duration_ms":18827,"standing_objections":[]},"desk_editor":{"model":"grok-4.3","letter":"The main takeaway is that reducing symmetry to C3 at 23.4 degrees, feeding in ab-initio normal-state parameters, and scanning singlet-triplet mixing parameters in the BdG Hamiltonian produces regions with nonzero Chern numbers C in {-4,-2,2,4}. This combination for the graphene/NbSe2 heterostructure is not a direct repeat of earlier proximity or twisted-bilayer results.\n\nThe symmetry-allowed gap functions from the C3 irreps and the direct computation of the topological invariants over the mixing parameters are the parts that are done cleanly. The stress-test note is right that the logic itself shows no internal contradiction.\n\nThe soft spots are the usual ones for an abstract-only view: no numerical values, no convergence checks, no comparison to known limits, and no error estimates on the ab-initio extraction or the Chern-number evaluation. The claim that the van der Waals stack and symmetry reduction can stabilize a chiral component is stated as a possibility rather than shown by any calculation of relative pairing energies. Without the full methods section those choices remain opaque.\n\nThis is for theorists who work on proximity-induced topological superconductivity in van der Waals stacks and want a specific platform proposal with a tunable phase diagram. A reader who needs a ready-to-use model for Majorana or transport calculations would find the phase diagram useful once the implementation details are checked.\n\nIt deserves a serious referee to verify the ab-initio parameters and the numerical stability of the Chern numbers.","headline":"The paper gives a concrete phase diagram with Chern numbers -4 to 4 for mixed pairing in this specific twisted graphene/NbSe2 stack, but the supporting calculations are described at too high a level to judge robustness.","tokens_in":2336,"tokens_out":387,"would_cite":false,"duration_ms":15393,"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":"Twisted graphene on NbSe2 can realize chiral topological superconductivity with Chern numbers in {-4,-2,2,4} via proximity-induced pairing under C3 symmetry.","keywords":["proximity-induced superconductivity","twisted graphene","NbSe2 heterostructure","chiral topological superconductivity","Chern numbers","C3 symmetry","Bogoliubov-de Gennes","van der Waals materials"],"falsifier":"If the computed Chern number remains zero for every combination of mixing parameters between the allowed gap functions, or if quasiparticle interference and transport experiments detect no signatures consistent with nonzero Chern numbers, the claimed topological phases would be ruled out.","tokens_in":2641,"feed_emoji":"","tokens_out":701,"duration_ms":15293,"temperature":0.7,"pith_summary":"The paper uses the Bogoliubov-de Gennes formalism on parameters taken from ab initio calculations at a 23.4 degree twist to model how superconductivity from NbSe2 enters the graphene layer. With the common symmetry reduced to the C3 point group, the authors enumerate all allowed combinations of singlet and triplet gap functions and track how the topological invariants change with the relative strength of each channel. The resulting phase diagram contains extended regions of chiral topological superconductivity distinguished by nonzero Chern numbers. If realized, these phases would supply a van der Waals platform in which topological superconductivity is induced rather than engineered from scratch.","feed_headline":"Twisted graphene/NbSe2 yields chiral topological phases with C=±2,±4","feed_subtitle":"Proximity-induced pairing under C3 symmetry produces a phase diagram of topological superconductors detectable by interference and transport","key_machinery":"Symmetry-allowed superconducting gap functions under the C3 point group that mix singlet and triplet channels, whose topological character is diagnosed by the Chern number.","core_discovery":"Using symmetry-allowed gap functions classified by the irreducible representations of the C3 group, the calculation shows that mixtures of singlet and triplet pairing channels produce a phase diagram containing chiral topological superconducting states with Chern numbers C belonging to the set {-4,-2,2,4}.","pith_inferences":["Different twist angles that preserve C3 symmetry could be scanned to enlarge or shrink the topological regions in the phase diagram.","If chiral pairing is confirmed, defects or edges in the graphene layer should host zero-energy modes whose statistics could be tested separately.","The same symmetry-classification approach could be applied to other transition-metal dichalcogenide substrates to generate different sets of Chern numbers.","Control of the relative strength of singlet versus triplet channels might be achieved by gating or strain, offering a route to switch between topological phases."],"forward_implications":["The heterostructure supplies a concrete platform for proximity-induced chiral topological superconductivity.","The topological phases remain detectable by quasiparticle interference imaging and transport measurements.","Symmetry reduction at the interface can stabilize chiral pairing components that are not dominant in bulk NbSe2.","Nonzero Chern numbers imply protected boundary modes whose presence follows directly from the bulk invariants."],"fun_headline_variants":["Twisted graphene/NbSe2 under C3 symmetry has chiral SC phases C=-4,-2,2,4","Pairing channel mixtures classified by C3 give topological invariants C=±2,±4","Proximity-induced superconductivity forms chiral phases in twisted graphene heterostructur","Chiral topological SC phases with Chern numbers C=-4,-2,2,4 in graphene/NbSe2"],"cache_read_input_tokens":2112,"weakest_assumption_plain":"The van der Waals interface and resulting symmetry lowering can change which pairing channel is most stable and thereby favor a chiral component that gets induced into the graphene layer.","fun_headline_variants_meta":{"raw":{"variants":["Twisted graphene/NbSe2 under C3 symmetry has chiral SC phases C=-4,-2,2,4","Pairing channel mixtures classified by C3 give topological invariants C=±2,±4","Proximity-induced superconductivity forms chiral phases in twisted graphene heterostructure","Chiral topological SC phases with Chern numbers C=-4,-2,2,4 in graphene/NbSe2"]},"model":"grok-4.3","cost_usd":0.007935,"raw_usage":{"total_tokens":3614,"prompt_tokens":665,"num_sources_used":0,"completion_tokens":99,"cost_in_usd_ticks":79349500,"prompt_tokens_details":{"text_tokens":665,"audio_tokens":0,"image_tokens":0,"cached_tokens":256},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":2850,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":665,"tokens_out":99,"duration_ms":14949,"temperature":1.0,"reasoning_tokens":2850,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-06-27T08:09:36.849601+00:00","model_set":{"reader":"grok-4.3"},"falsifier":"If the computed Chern number remains zero for every combination of mixing parameters between the allowed gap functions, or if quasiparticle interference and transport experiments detect no signatures consistent with nonzero Chern numbers, the claimed topological phases would be ruled out.","supporting_citations":[],"review_version":1}