{"id":"65918015-7dbe-4405-a0cb-705f21f548f0","arxiv_id":"1908.11625","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":2,"one_line_summary":"InSb nanowires coupled to Ising superconductors are predicted to host a topological superconducting gap that persists to fields near 10 T, giving a topological regime about ten times wider than standard InSb/Al nanowires.","lead":"A theoretical study proposes that placing InSb nanowires on Ising superconductors such as monolayer NbSe2 keeps the topological superconducting gap strong up to in-plane fields of about 10 tesla, far beyond the roughly 1 tesla limit of existing aluminum-based setups. The authors attribute this to equal-spin triplet Cooper pairs from the Ising superconductor, which are compatible with in-plane magnetization.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The 10 T topological window is extrapolated, not computed: the TB model omits Zeeman coupling and self-consistent gap suppression in parent NbSe2, and Appendix C derives the triplet d-vector from the zero-field parent Green's function, making the central robustness partly an artifact.","rationale":"The paper's main advance is the mechanism: equal-spin triplet pairs from an Ising superconductor induce a topological gap in the nanowire that survives in-plane Zeeman fields. I find that mechanism plausible, and the analytic projection in the V much greater than alpha limit is internally coherent provided the parent is treated as field-independent. The problem is that the headline quantitative claim requires the parent to remain effectively superconducting up to 10 T, and that is the least controlled step. The reader's verdict already flags this through orbital pair-breaking and the imported Ref. 32 endpoint. My stress test sharpens the concern: the omission is not only orbital; in both the tight-binding model and the self-energy derivation, the parent's Zeeman response is absent. Eq. C7 uses the zero-field Green's function, so the 'robust' d(kx) is not actually derived at finite V. This is a missing step rather than a demonstrated contradiction, and it can be addressed by a finite-V calculation, so a conditional verdict remains appropriate. I do not see a reason to reject: the mechanism is supported by the zero-field projection plus the finite-field band-basis argument, and the proposed numerical check would either confirm or falsify the 10 T window. Since the reader already arrived at a conditional verdict, I would not change it.","tokens_in":13174,"tokens_out":12415,"duration_ms":123880,"concrete_test":"Recompute the LDOS of Fig. 4(a) with the Zeeman term Vx sigma_x added to the NbSe2 monolayer (Eq. 17) and with the parent gap Delta(B) taken from the self-consistent solution of Eq. (B4) for the beta_so value used (or from measured Delta(B) of Ref. 32). Determine the field at which the end-of-wire topological gap closes; if it closes before about 10 T, or if the gap at B=5 T drops by more than about 30 percent relative to the constant-Delta calculation, the enlarged topological window is not established. To isolate the cause, rerun the same model with Delta fixed at the zero-field value but with the parent Zeeman term present.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The quantitative headline—topological regime from about 0.5 T to about 10 T, roughly ten times wider than InSb/Al—is not directly obtained from the calculation. In the tight-binding simulation of Sec. IIIB, the parent monolayer NbSe2 Hamiltonian (Eq. 17) contains no Zeeman term; only the nanowire (Eq. 18) is subjected to Vx. The parent order parameter is therefore held at its zero-field value over the computed field range. The LDOS shown in Fig. 4(a) extends only to about 5 T, and the 10 T endpoint is imported from Ref. 32 with the statement that the wire remains topological 'as long as the proximity gap is finite' and that the parent gap closes only near B~10 T. The same omission appears in the analytic derivation: Eq. (C7) evaluates d(kx) from Fs(k,iω), Ft(k,iω) with denominators xi_±^2 plus Delta^2 and no Zeeman argument, i.e. the zero-field parent Green's function (Eq. C1), even though the parent's own field response is shown in Fig. 1(b) and Eq. (B4) to reduce Delta(Vx) continuously. Thus the claimed V-insensitive triplet term in Eqs. (15)-(16) is partly baked in by computing the self-energy at V=0 rather than at finite V. Sec. II explicitly ignores orbital pair-breaking; even if that is valid for atomically thin NbSe2, the parent Zeeman/gap suppression is not obviously negligible in the same way, and the central 0.5-10 T window shrinks if the parent gap is reduced earlier.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes that proximity coupling an InSb nanowire to an Ising superconductor such as monolayer NbSe2 creates a topological superconducting gap that is robust against in-plane magnetic fields, yielding a topological regime from about 0.5 T to about 10 T. The mechanism is attributed to equal-spin triplet Cooper pairs in the Ising superconductor, which are compatible with large in-plane Zeeman fields. The authors support this proposal with an analytic projection of the induced pairing in Appendix C, which separates the effective p-wave pairing into three contributions (Eq. 15-16), and with a numerical tight-binding model of an InSb nanowire on monolayer NbSe2, presenting the local density of states at the wire end as a function of magnetic field in Fig. 4.","tokens_in":13486,"tokens_out":4713,"duration_ms":42567,"significance":"If the claimed robustness holds, this would be a significant step toward practical Majorana-based qubits, as the topological gap would survive fields far beyond the ~1 T limit of InSb/Al heterostructures. The analytic decomposition of the induced pairing into singlet and triplet channels is instructive and provides a clear physical picture. The numerical model uses realistic parameters and directly compares with the conventional s-wave case. However, the central quantitative claim of a 0.5-10 T window is only partially computed, and the field dependence of the parent superconductor is not included in the main calculations; these gaps must be addressed for the conclusion to be fully supported.","major_comments":[{"comment":"The calculated LDOS is shown only for fields up to B=5 T, yet the text states that the topological regime extends to B~10 T, citing Ref. 32. Since the 10 T endpoint is not computed in this manuscript, the headline claim rests on an extrapolation. The authors should either compute the LDOS at higher fields (including a field-dependent parent gap) or explicitly label the 0.5-10 T window as an estimate based on the prior result of Ref. 32.","section":"Sec. IIIB, Fig. 4(a)"},{"comment":"The parent NbSe2 Hamiltonian in the tight-binding model contains no Zeeman term, and the analytic self-energy is derived from the zero-field Green's function. Consequently, the parent order parameter is fixed at its B=0 value over the entire computed range, which suppresses the field-induced reduction of the proximity gap. This is inconsistent with the self-consistent equation Eq. (B4) that shows Δ(Vx) decreasing monotonically. The robustness of the triplet term Δ(p)t in Eq. (16) is therefore partially an artifact of the zero-field parent. The authors should re-evaluate the induced gap using a field-dependent parent order parameter, e.g., by inserting the self-consistent Δ(Vx) into the effective model, and determine whether the topological gap remains sizable at B~10 T.","section":"Sec. IIIB, Eq. (17); Appendix C, Eq. (C1)"},{"comment":"The paper explicitly ignores orbital pair-breaking in the Ising superconductor, but the comparison with Al in Fig. 4(b) includes orbital pair-breaking in the parent via Δ(B) = Δ√(1-(B/Bc)²). The authors do not discuss orbital pair-breaking in the nanowire itself, nor whether the assumption of negligible orbital effects remains valid for the composite heterostructure at B~10 T. Given that the main quantitative claim concerns high fields, this neglect should be justified more thoroughly or shown to be numerically unimportant.","section":"Sec. II and Sec. IIIB"}],"minor_comments":[{"comment":"There is a typo: 'nanaowire' should be 'nanowire'.","section":"Sec. IIIA"},{"comment":"The same paper (He et al., Communications Physics 1, 40 (2018)) appears as both Ref. 32 and Ref. 33; the citations should be consolidated or renumbered.","section":"References"},{"comment":"The caption states that the topological gap 'persists up to conventional Pauli limiting fields B~10T', but the plotted data range ends at 5 T; the caption should indicate that this is an extrapolation based on Ref. 32.","section":"Fig. 4 caption"},{"comment":"The notation Δ(p)s,α and Δ(p)s,β is used before the terms are defined; consider providing brief definitions in the text for clarity.","section":"Eq. (15)-(16)"},{"comment":"The statement that 'for magnetic fields larger than 5T, the wire still remains a topological superconductor as long as the proximity gap is finite' would benefit from a numerical check, since the authors have the model at hand and could extend the simulation to verify the persistence.","section":"Sec. IIIB, text after Fig. 4"},{"comment":"The manuscript contains several grammatical errors (e.g., 'which results in a Kitaev chain' in the abstract, 'superductor' in Sec. IIIA); a careful proofreading pass is recommended.","section":"General"}],"recommendation":"major_revision","confidential_remarks":"The key external inputs (the equal-spin triplet mechanism, the 10 T nodal endpoint for NbSe2, and the Ising SOC parameter βso) come from the same group's previous papers (Refs. 23, 32, 33). This is not in itself a flaw, but it means the central quantitative claim depends on results that have not been independently reproduced. I would encourage the authors to perform a direct calculation of the topological gap at fields beyond 5 T using a field-dependent parent order parameter, which would also clarify the extent of the extrapolation."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The paper is worth a serious look. The analytic projection in Appendix C is coherent, and the separation of the induced p-wave gap into Rashba, induced Ising, and triplet contributions (Eqs. 15–16) is genuinely clarifying. The claim that the equal-spin triplet term, coming from the parent Ising superconductor, has a much weaker direct dependence on the in-plane Zeeman field than the singlet-derived terms is physically sound and is the paper's real contribution. The realistic tight-binding parameters and the comparison with InSb/Al are also well chosen.\n\nThat said, the headline quantitative claim is softer than it appears. The LDOS in Fig. 4(a) is computed with the parent NbSe2 Hamiltonian containing no Zeeman term, so the parent gap is artificially held at its zero-field value while only the nanowire is Zeeman-split. The LDOS is shown only up to about 5 T, and the persistence to ~10 T is imported from Ref. 32, the same group's earlier work. The analytic d-vector in Appendix C is evaluated from the zero-field parent Green's function (Eq. C1), so the \"insensitive to V\" result does not include the parent's own gap suppression, which Fig. 1(b) shows is real. The stress-test note largely lands: the mechanism is qualitative, and the 10 T endpoint is an estimate, not a computed result.\n\nThe orbital pair-breaking neglect is stated explicitly in Sec. II, which is fair, but it is not the only physics dropped. No code or data is shipped, and the tunnel coupling and chemical potentials are chosen rather than independently fixed. The two load-bearing inputs—the equal-spin triplet mechanism (Ref. 23) and the 10 T nodal endpoint (Ref. 32)—come from the same group's prior papers; that is not disqualifying, but the extrapolated endpoint has not been independently checked.\n\nWho should read it: anyone working on Majorana nanowires or Ising superconductor heterostructures will get a useful formalism and a clear conceptual takeaway. The paper deserves a serious referee. I would recommend acceptance after revision that either computes the parent gap suppression self-consistently in the tight-binding model and extends the LDOS, or explicitly reframes the claim as conditional on a weakly field-dependent parent gap. As is, the central mechanism stands, but the headline '10 T' should be treated as an estimate.","headline":"The analytic decomposition is clean and the mechanism is plausible, but the headline 0.5–10 T window is extrapolated rather than computed: parent Zeeman and gap suppression are left out of both the tight-binding simulation and the self-energy derivation.","tokens_in":14099,"tokens_out":2997,"would_cite":true,"duration_ms":30257,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"This paper claims that nanowires on Ising superconductors can keep their topological superconducting gap at in-plane magnetic fields near 10 T, roughly ten times the range for InSb/Al wires, because equal-spin triplet Cooper pairs from…","keywords":["Majorana zero modes","Ising superconductors","equal-spin triplet Cooper pairs","topological superconducting gap","nanowire proximity effect","NbSe2","in-plane magnetic field","Kitaev chain"],"falsifier":"Measure the local density of states at the end of an InSb nanowire on monolayer NbSe2 as a function of in-plane field: if the induced gap fails to reopen or the zero-bias peak disappears well below 10 T—on the ~1 T scale characteristic of aluminum-contacted wires—then the triplet-pairing mechanism is not enough to protect the topological phase; a hard gap persisting past roughly 5 T would support the claim.","tokens_in":12903,"feed_emoji":"🧲","tokens_out":9409,"duration_ms":82013,"temperature":0.7,"pith_summary":"The paper argues that a semiconducting nanowire placed on an Ising superconductor—an atomically thin superconductor whose spin-orbit coupling locks electron spins out of plane—keeps its proximity-induced topological gap almost unchanged as an in-plane magnetic field grows. The reason is that the parent material supplies equal-spin triplet Cooper pairs, which align with the field instead of being broken by it. For a realistic InSb nanowire on monolayer NbSe2, the topological regime runs from about 0.5 T to about 10 T, roughly ten times the window seen in InSb wires on aluminum. If correct, this removes the main practical ceiling on Majorana-based qubits: the field that creates the topological phase no longer destroys the superconducting gap that protects it.","feed_headline":"Ising superconductor keeps nanowire Majorana gap to 10 T","feed_subtitle":"Equal-spin triplet pairs from NbSe2 survive fields that kill aluminum-based Majorana wires.","key_machinery":"The load-bearing object is the decomposition of the effective proximity-induced p-wave pairing in Eqs. (15)–(16). The total induced p-wave gap is split as $\\Delta^{(p)}=\\Delta^{(p)}_{s,\\alpha}+\\Delta^{(p)}_{s,\\beta}+\\Delta^{(p)}_t$: the first two terms come from singlet Cooper pairs combined with Rashba or induced Ising spin-orbit coupling and vanish when the Zeeman energy $V$ dominates the spin-orbit scales $\\alpha,\\beta$; the third term, $\\Delta^{(p)}_t$, is the projection of the parent Ising superconductor's equal-spin triplet pairs, with $d_z(k_x)\\propto k_x$ fixed by the $D_{3h}$ symmetry of monolayer NbSe2. In the strong-field limit $\\Delta^{(p)}_t\\approx -d_z(k_x)/2$, so the triplet channel keeps the wire topological even after the singlet channels have died. The self-energy calculation that produces this decomposition carries the argument from the parent superconductor's Gor'kov equations to the nanowire's effective Hamiltonian.","core_discovery":"The central claim is that the effective p-wave pairing which makes the nanowire topological has three contributions, and only the two singlet-derived ones—one from the wire's Rashba spin-orbit coupling and one from the Ising spin-orbit coupling induced into the wire—are suppressed by the Zeeman field. The third contribution, $\\Delta_t^{(p)}$, comes from equal-spin triplet Cooper pairs tunneling out of the Ising superconductor and, in the limit $V \\gg \\alpha,\\beta$, approaches $-d_z(k_x)/2$, where $d_z(k_x) \\propto k_x$ is a p-wave triplet pairing term inherited from the parent. Because this term does not rely on pairing opposite spins, the induced topological gap survives in-plane fields that would destroy singlet proximity pairing. In the specific InSb/NbSe2 heterostructure, the topological gap closes and reopens near 0.5 T, remains sizable to at least 5 T in the numerical local density of states, and persists until the parent NbSe2 itself reaches its Pauli-limited critical field near 10 T, giving a topological window about ten times wider than InSb/Al wires.","pith_inferences":["A direct experimental signature would be a hard induced gap that persists well past 1 T in tunneling spectroscopy at the wire end, with the zero-bias peak surviving as the field is raised; this is what distinguishes the triplet mechanism from the behavior of aluminum-contacted wires.","The same robustness is likely to extend to gated MoS2 and to Shiba chains on Ising superconductors, since both rely on the same equal-spin triplet pairing rather than on the specific NbSe2 band structure.","One could test the mechanism's field-insensitivity by measuring the gap at fixed chemical potential as a function of field angle: if the protection comes from in-plane equal-spin pairs, the gap should show the predicted flatness only for in-plane fields, not out-of-plane ones."],"forward_implications":["In an InSb nanowire on monolayer NbSe2, the topological regime should extend from the gap closing near 0.5 T up to the Pauli-limited parent gap near 10 T, about ten times the range of InSb/Al wires.","A large Zeeman splitting is no longer a liability: the topological gap stays sizable as the field grows, so the Majorana qubit operating point can sit at high field where the single-mode window is wide.","The same equal-spin triplet proximity mechanism should transfer to other nanowire/Ising-superconductor combinations, so the protection is a property of the pairing channel rather than of NbSe2 specifically.","At the 10 T ceiling the parent NbSe2 becomes a nodal topological superconductor, so the wire loses its gapped topological phase only through the parent's own superconducting transition."],"supporting_citations":[{"why":"Establishes that Ising spin-orbit coupling converts s-wave pairing into equal-spin triplet Cooper pairs, the ingredient the proposal relies on.","marker":"[23]"},{"why":"Reports atomically thin NbSe2 as an Ising superconductor with a strongly enhanced in-plane critical field, supplying the parent material.","marker":"[22]"},{"why":"Provides the band-basis projection used to derive the effective p-wave decomposition in Eqs. (15)-(16).","marker":"[30]"},{"why":"Supplies the realistic tight-binding model of monolayer 2H-NbSe2 used for the numerical local density of states.","marker":"[31]"},{"why":"Gives the first-principles Ising spin-orbit coupling strength used in the tight-binding simulation.","marker":"[33]"},{"why":"Sets the claimed 10 T endpoint by predicting that NbSe2 becomes a nodal topological superconductor near the Pauli limit.","marker":"[32]"},{"why":"Provides the InSb/Al experimental baseline whose gap collapses near 1 T, the comparison that defines the enlarged window.","marker":"[12]"},{"why":"Provides the spin-susceptibility formalism used to estimate the enhanced in-plane critical field of Ising superconductors.","marker":"[26]"},{"why":"Supplies the field-dependent parent gap model for aluminum used in the comparison calculation of Fig. 4(b).","marker":"[34]"}],"fun_headline_variants":["Ising superconductor lifts nanowire topological limit to 10 T","Triplet Cooper pairs from NbSe2 push nanowire topological gap to 10 T","Nanowire topological regime ten times larger via Ising superconductor","Equal-spin triplets preserve nanowire Majorana gap to 10 T"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The claim that the topological regime reaches about 10 T assumes that in-plane magnetic fields do not break apart the Cooper pairs in the NbSe2 itself or in the nanowire before that field strength, so the parent superconducting gap remains open and the only ceiling is the spin-alignment limit.","fun_headline_variants_meta":{"raw":{"variants":["Ising superconductor lifts nanowire topological limit to 10 T","Triplet Cooper pairs from NbSe2 push nanowire topological gap to 10 T","Nanowire topological regime ten times larger via Ising superconductor","Equal-spin triplets preserve nanowire Majorana gap to 10 T"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000478,"raw_usage":{"total_tokens":2386,"prompt_tokens":981,"completion_tokens":1405,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":597,"completion_tokens_details":{"reasoning_tokens":1322}},"tokens_in":597,"tokens_out":1405,"duration_ms":10559,"temperature":1.0,"reasoning_tokens":1322,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-14T10:10:15.216377+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure the local density of states at the end of an InSb nanowire on monolayer NbSe2 as a function of in-plane field: if the induced gap fails to reopen or the zero-bias peak disappears well below 10 T—on the ~1 T scale characteristic of aluminum-contacted wires—then the triplet-pairing mechanism is not enough to protect the topological phase; a hard gap persisting past roughly 5 T would support the claim.","supporting_citations":[{"cited_title":"\\ He , author B","cited_arxiv_id":null,"evidence_quote":"Gives the first-principles Ising spin-orbit coupling strength used in the tight-binding simulation."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the spin-susceptibility formalism used to estimate the enhanced in-plane critical field of Ising superconductors."}],"review_version":1}