{"id":"f86d765d-65ed-4cfc-93f0-1744d9b296a8","arxiv_id":"2501.04345","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":1,"one_line_summary":"Bare PbTe nanowires show reproducible 45-degree g-factor anisotropy, and adding a Pb superconductor rotates and gate-tunes the magnetic-field anisotropy direction.","lead":"Experiments on lead telluride nanowires show that the magnetic-field direction that most strongly shifts electron energy levels is now reproducible across devices, a step forward for this Majorana platform. When the wire is coated with a superconductor, that preferred direction rotates, and the rotation can be tuned with a gate voltage.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The bare-PbTe g-factor map is extracted assuming pure Zeeman splitting, but the same data show spin-orbit anti-crossings; the 45° anisotropy may be an SO-coupling artifact rather than a g-tensor axis.","rationale":"The reader's weakest assumption was the pure-Zeeman interpretation of the peak splittings. I agree, and I sharpen it: the paper's own observation of spin-orbit-induced anti-crossings in exactly the levels used for g-factor extraction means that the splitting is not simply g μB B, but includes an SO coupling term. The Supplemental Material explicitly acknowledges level repulsion near the 45° minimum. This is load-bearing because the hybrid claim of a Pb-induced 23° deviation is defined relative to that 45° baseline; if the baseline angle already reflects SO coupling rather than a g-tensor principal axis, the deviation cannot be uniquely attributed to Pb or to gate-tunable SOI. The proposed test is a quantitative two-level fit to existing field-dependent data, which is feasible because the authors provide the raw data. The verdict remains CONDITIONAL: the qualitative reproducibility claim may survive, but the quantitative g-tensor direction and the hybrid mechanism attribution require this re-analysis or an equivalent control. I do not see a reason to move the verdict to accept or reject based on the text alone, so I leave it unchanged.","tokens_in":14128,"tokens_out":7213,"duration_ms":72038,"concrete_test":"Using the released raw data (Zenodo 14614293), re-analyze device A and B peak splittings at the nominal minimum and maximum directions as a function of |B| (e.g., 0.1–0.5 T). Fit the splitting to sqrt[(g μB B)^2 + Δ_SO^2] for each angle. If a nonzero Δ_SO is needed at the 45° minimum or if the angle of minimum splitting shifts with |B|, the reported g-tensor polar plot is not a pure Zeeman measurement and the 45° baseline for hybrids is compromised. If Δ_SO ≈ 0 at the minimum and the angle is |B|-independent, the concern is resolved.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central quantitative claim—reproducible g-factor anisotropy with extrema at ±45° to the wire axis—rests on converting conductance-peak splittings in Fig. 2(c) into g values via ΔE = g μB B. This assumes each splitting is the Zeeman energy of a spin-degenerate level. However, the paper itself reports avoided crossings in the same levels (Fig. 2(b), cyan arrows; Fig. S2; Fig. 2(f)) and attributes them to spin-orbit interaction. For two levels coupled by SO, the observed splitting is Δ = sqrt[(g μB B)^2 + Δ_SO^2], so the direction of minimal Δ is not necessarily the direction of minimal g; it is where the joint function is smallest. The Supplemental Material (Fig. S3 caption) concedes that 'The g factor may be underestimated near 45° due to level repulsion.' Underestimation is not the only possible distortion: anisotropic Δ_SO can shift the apparent extrema and produce non-zero apparent g where the Zeeman term vanishes. Since the hybrid analysis uses the 45° direction as the unperturbed baseline ('the 23° deviation is attributed to the presence of the superconductor'), a baseline corrupted by SO coupling would make the hybrid deviation, and its gate-tuning, ambiguous. The polar plots show no error bars, and the peak-finding step (Fig. S2(d)) discards 'noise or jumps' subjectively. The pattern's reproducibility across devices A–C therefore establishes reproducibility of the combined Zeeman+SO spectrum, not of the g-tensor orientation claimed in the abstract and conclusion.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper reports a systematic study of magnetic-field anisotropy in PbTe nanowire quantum dots and PbTe-Pb hybrid nanowires. In bare PbTe devices, the authors observe level splittings that depend on the direction of a fixed-magnitude magnetic field, and they convert these splittings into g-factors that are claimed to vary between 0 and 21 with extrema at approximately ±45° to the wire axis ([100]). This pattern is reported as reproducible across three devices. In PbTe-Pb hybrid devices, the paper shows that the direction of minimum zero-bias conductance in the xz plane deviates from 45°, falling in the range 9°-33° across devices, and that this direction shifts with side-gate voltage (for example, 35° to 26° in device N and 32° to -27° in device O). The deviation is attributed to spin-orbit interaction induced by the superconductor and to orbital effects for out-of-plane fields. The manuscript includes SEM and STEM characterization of all devices and states that raw data and processing codes are available at a Zenodo DOI.","tokens_in":14414,"tokens_out":4609,"duration_ms":49432,"significance":"If the central claims hold, the paper would establish a useful empirical benchmark for PbTe-based hybrid quantum devices: reproducible anisotropy in nominally clean PbTe nanowires and gate-tunable modification of that anisotropy upon coupling to a superconductor. This addresses a known problem in PbTe devices, where earlier work showed device-to-device variation in g-factor anisotropy. The structural characterization of all nine devices and the public data repository are concrete strengths that support reproducibility. However, the quantitative interpretation of the bare-wire data as a pure g-tensor is undermined by the coexistence of spin-orbit-induced avoided crossings in the same levels, and the paper's own Supplemental Material concedes that level repulsion may distort the extraction near the claimed extrema. This weakens the load-bearing quantitative claim, although the qualitative observations of reproducible splitting anisotropy and gate-tunable gap anisotropy remain potentially valuable.","major_comments":[{"comment":"The g-factor extraction assumes that the conductance-peak splitting equals the Zeeman energy, ΔE = g μB B. However, the same data show avoided crossings attributed to spin-orbit interaction (Fig. 2(b) cyan arrows; Fig. 2(f); Fig. S2). For two spin-orbit-coupled levels, the observed splitting is expected to follow Δ = sqrt[(g μB B)^2 + Δ_SO^2], where Δ_SO is the spin-orbit gap. The minimal observed splitting therefore does not directly give the minimal g-factor; it gives the minimum of a combined function that also depends on the orientation-dependent Δ_SO. The SM Fig. S3 caption admits that the g-factor 'may be underestimated near 45° due to level repulsion,' which is exactly the direction claimed as a g-factor extremum. Underestimation is not the only possible distortion: anisotropic Δ_SO can shift the apparent extrema and can produce a nonzero apparent g where the true Zeeman term vanishes. The central claim that '±45° ... [is] the direction of minimum and maximum g-factors' is therefore not established by the presented analysis. The authors should either fit a coupled-level model that extracts both g and Δ_SO orientation dependence, or explicitly reframe the abstract and conclusion in terms of measured splitting anisotropy rather than g-tensor anisotropy.","section":"Section 2, Fig. 2(c-d) and SM Fig. S3"},{"comment":"The interpretation of the hybrid-device data uses the bare-wire 45° direction as the unperturbed baseline: 'The 23° deviation is attributed to the presence of the superconductor.' If the bare-wire baseline itself is contaminated by spin-orbit level repulsion, as argued above, then the apparent deviation in the hybrid cannot be unambiguously assigned to superconductor-induced spin-orbit coupling. Part or all of the deviation could reflect the same orientation-dependent spin-orbit physics already present in the bare wire, or could be an artifact of extracting a minimum from a gap-closure spectrum rather than from a clean Zeeman split. To support the attribution, the authors should quantify how the bare-wire splitting anisotropy would affect a gaplike observable (for example, by modeling the zero-bias conductance minimum with a two-level Hamiltonian including isotropic and anisotropic spin-orbit terms), and show that the observed hybrid angles are inconsistent with the bare-wire model alone.","section":"Section 3, paragraph beginning 'Building upon' and Fig. 3(e)"},{"comment":"The polar plots of g-factor and the reported hybrid minimum-conductance angles are presented without error bars or uncertainty estimates. The peak-finding procedure in SM Fig. S2(d) discards 'noise or jumps' subjectively, and the conductance-averaging method for the hybrid angle determination is not accompanied by a measure of how sensitive the extracted angle is to the chosen bias window or the smoothing procedure. Since the paper's main claim is reproducibility across devices, the authors should provide at least a quantitative estimate of the angular uncertainty for each extracted direction and for the g-factor values. Without this, the reader cannot distinguish genuine device-to-device consistency from the robustness of a curve-minimum routine.","section":"Fig. 2(d), SM Fig. S3(c), SM Fig. S4(e), and Fig. 4(b)"}],"minor_comments":[{"comment":"The statement that the diamonds in Fig. 2(a) 'correspond to quantized levels formed in the PbTe quantum dot, rather than Coulomb charging energy' is central to the argument that charging energy is negligible, but the text does not explain how the diamonds are distinguished from Coulomb diamonds. A clearer discussion of the level-spacing extraction and its consistency with the lever-arm calibration would strengthen the paper.","section":"Section 2, first paragraph"},{"comment":"The g-factor conversion relies on a single lever arm α ~ 2.7 meV/V estimated from the diamond size. Since the g values scale linearly with α, an uncertainty in α directly changes the reported g range. Please provide an uncertainty estimate for α and state whether α was verified independently (for example, by bias spectroscopy at different gate voltages).","section":"Section 2, last paragraph and SM Fig. S3"},{"comment":"The even-odd peak-height pattern and the negative differential conductance in device B are noted as unexplained. This is acceptable if the effect is peripheral, but the text should clarify whether the spin-degeneracy assumption used for the splitting analysis could be affected by these features in the zero-field spectrum.","section":"Section 2, Fig. 2(e)"},{"comment":"The orientation ambiguity of ±z, ±x, and ±y is acknowledged, but the polar plots in Fig. 2(d) and SM S4(e) distinguish positive and negative directions. Since the directions are physically equivalent up to a global sign in a time-reversal-invariant system, the plots should either explicitly state that the two lobes are related by symmetry or indicate which sign convention is used.","section":"Footnotes 39-40"},{"comment":"The claim of gate tunability of spin-orbit interaction is based on the angular shift of the minimum of an averaged conductance curve. The paper does not discuss whether the gate voltage could also change the dot confinement potential, the tunnel coupling, or the induced gap, all of which could affect the position of the conductance minimum. A control measurement showing that the gap size or the zero-field spectroscopy remains similar at the different gate voltages would make the interpretation more robust.","section":"Section 3, Fig. 4"}],"recommendation":"major_revision","confidential_remarks":"The paper likely will interest the mesoscopic physics and Majorana-device community, and the dataset (with STEM/SEM on all devices and public data code) is a genuine asset. The main concern is not the quality of the measurements but the interpretation: the abstract and conclusion assert a clean g-factor anisotropy at ±45°, while the data themselves, and the SM text, indicate that spin-orbit avoided crossings are present in the same levels. This is a load-bearing issue because the hybrid-device claims are referenced to the 45° baseline. I believe the paper can be made publishable by either performing a two-level fit that separates Zeeman and spin-orbit contributions, or by carefully rewording the claims to describe the measured splitting anisotropy and the gate-induced shift of the gap-closure minimum without over-interpreting them as a pure g-tensor. I recommend major revision rather than rejection, since the qualitative reproducible anisotropy and the gate-tunable deviation are likely to survive a corrected analysis."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Here's my take. The paper's core observation—a consistent 45° g-factor anisotropy pattern across three bare PbTe nanowires—is a genuine improvement over the device-dependent scatter reported earlier. The STEM/SEM characterization of all nine devices is careful, and the raw data and processing code are posted. The hybrid part, using field-rotation of the superconducting gap, is a separate and more robust observable than the dot spectroscopy.\n\nThe soft spot is the g-factor extraction in Fig. 2(c-d). Peak splittings are converted to g values assuming a pure Zeeman effect, yet the same data show avoided crossings attributed to spin-orbit coupling. The Supplemental Materials admit 'the g factor may be underestimated near 45° due to level repulsion'—which is precisely where the stress-test concern lands. With SO coupling the observed splitting is sqrt[(gμB)^2 + Δ_SO^2]; anisotropic Δ_SO can shift the apparent extrema and produce non-zero apparent g where the Zeeman term vanishes. There are no error bars, and peak locating discards 'noise or jumps' subjectively. So the defensible claim is reproducibility of the combined Zeeman+SO spectrum, not of the bare g-tensor orientation.\n\nThat said, the qualitative 45° pattern is consistent across devices, the anti-crossings are small at the 0.3 T rotation field used, and the conclusion would likely survive a more careful analysis. The hybrid deviation (22° vs 45°) is measured via critical-field anisotropy, so it is less exposed to the dot-level fitting issue. The mechanism story—charge transfer controlling spin-orbit strength—is plausible but not directly tested.\n\nWho gets value? Groups designing PbTe or PbTe-Pb Majorana devices: the paper gives practical design rules even if the exact g-tensor is not pinned down. It deserves serious review, but referees should ask for uncertainty estimates, a defense or qualification of the pure-Zeeman assumption, and a softer mechanism claim. I'd engage with it.","headline":"Reproducible 45° anisotropy in PbTe nanowires is a real advance, but the pure-Zeeman g-factor extraction is strained by the paper's own anti-crossing data.","tokens_in":44,"tokens_out":3112,"would_cite":true,"duration_ms":76391,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"Bare PbTe nanowires show a reproducible 45-degree g-factor anisotropy, and adding a Pb superconductor shifts that anisotropy in a gate-tunable way.","keywords":["PbTe nanowires","g-factor anisotropy","spin-orbit interaction","superconducting proximity effect","quantum dots","gate tunability","Majorana zero modes","orbital effect"],"falsifier":"Repeat the fixed-field rotation on the same PbTe dot for two different orbital levels, or on a dot small enough that charging energy is visible; if the direction of minimum splitting moves with the orbital state or with gate voltage while the magnetic field direction is fixed, the peak-splitting readout is not a clean single-particle g-tensor and the reported 45° pattern would not be the intrinsic anisotropy.","tokens_in":13920,"feed_emoji":"🧲","tokens_out":12258,"duration_ms":109928,"temperature":0.7,"pith_summary":"The paper tries to establish that the magnetic anisotropy of PbTe nanowires can be made reproducible, and that it changes in a controlled way once the wire is coupled to a superconductor. In bare PbTe quantum dots, the electron g-factor (how strongly a spin responds to a magnetic field) has its minimum and maximum along directions 45 degrees off the wire axis, not along the axis, and the same pattern repeats across devices. In PbTe-Pb hybrids, the direction in which the superconducting gap closes most easily under a magnetic field moves away from that 45-degree reference, and the move can be adjusted with gate voltage. The paper attributes the deviation to spin-orbit interaction and orbital effects set by charge transfer between Pb and PbTe. If this is right, the platform offers a reproducible spin geometry plus an electrical knob for spin-orbit effects, which matters for efforts to engineer Majorana zero modes.","feed_headline":"PbTe's 45-degree spin anisotropy shifts when Pb is added","feed_subtitle":"The shift is gate-tunable, giving a direct electrical handle on spin-orbit effects in the nanowire platform.","key_machinery":"The central object is the angle-resolved magnetic-field rotation, read through two complementary observables. In bare PbTe, a quantum dot's conductance peaks split under the field, and because the stability diamonds are quantized single-particle levels rather than Coulomb charging diamonds, the splitting is converted directly into a g-factor using a lever arm of about 2.7 meV/V. In PbTe-Pb hybrids the same rotation is read through the softness of the induced superconducting gap (zero-bias and near-zero-bias conductance). The explanatory mechanism is a competition: the anisotropic Zeeman effect alone would keep the weakest-gap direction at 45° to the wire axis, the spin-orbit interaction pushes it toward 0° (the wire axis), and out-of-plane field components bring in an orbital effect that dominates the gap closure. Gate voltage and the Pb0.99Eu0.01Te interlayer thickness tune the spin-orbit strength through charge transfer.","core_discovery":"With disorder reduced, PbTe nanowire quantum dots show a reproducible anisotropic Zeeman response: rotating a fixed-magnitude magnetic field through three orthogonal planes maps out a g-factor that runs from 0 to 21, with its minimum and maximum at roughly ±45° to the [100] wire axis rather than along any crystal axis. The same directional pattern appears across multiple devices, though the magnitude varies with wire thickness. When PbTe is proximitized with Pb through a Pb0.99Eu0.01Te interlayer, the anisotropy of the induced superconducting gap deviates from that bare-PbTe reference: the direction of softest gap under an in-plane field sits at angles such as 9°, 21°, 22°, and 33° to the wire axis in different devices, and for one device the angle moves from 32° to -27° as the gate voltage is changed. The paper attributes this deviation to spin-orbit interaction and orbital effects arising from charge transfer between Pb and PbTe, with interlayer thickness and gates controlling the coupling.","pith_inferences":["A natural test beyond this paper would be to grow PbTe nanowires along a different crystal direction: if the 45° pattern follows the crystal lattice rather than the wire shape, it is an intrinsic band-structure fingerprint.","The gate-driven shift of the gap anisotropy could serve as a practical proxy for spin-orbit strength in future device work, but it has not been independently cross-checked against, for example, weak-antilocalization or Josephson critical-field measurements.","If the shift angle really tracks charge transfer between Pb and PbTe, systematic interlayer-thickness sweeps could locate an optimum spin-orbit regime for Majorana experiments, a knob the paper opens up but does not fully explore."],"forward_implications":["In bare PbTe nanowires, the direction of minimum and maximum g-factor is pinned at about ±45° to the [100] wire axis and repeats across devices.","Coupling PbTe to Pb rotates the magnetic anisotropy of the induced superconducting gap away from that 45° reference, with the rotation angle differing from device to device.","The rotation angle is gate-tunable, with one device shifting from 32° to -27°, showing that spin-orbit coupling in the proximitized region can be controlled electrostatically.","The Pb0.99Eu0.01Te interlayer thickness acts as a second control over the spin-orbit interaction strength.","For fields with out-of-plane components, orbital effects dominate the gap closure, so the spin-orbit/Zeeman competition is best studied with in-plane fields."],"supporting_citations":[{"why":"Reports the reduced-disorder PbTe nanowire growth and device process that makes the reproducible anisotropy possible.","marker":"[15]"},{"why":"Documents the earlier device-dependent g-factor anisotropy and small charging energies that this work aims to overcome.","marker":"[8]"},{"why":"Underpins the assignment of PbTe dot diamonds to quantized single-particle levels rather than Coulomb charging, the premise for extracting g-factors from peak splitting.","marker":"[7]"},{"why":"Supplies the spin-orbit-protection model used to interpret why the gap-closure direction shifts in PbTe-Pb hybrids.","marker":"[41]"},{"why":"Describes the selective-area, lattice-matched growth that fixes the [100] nanowire orientation.","marker":"[4]"},{"why":"Demonstrates the PbTe-Pb proximity effect in Josephson junctions, the baseline hybrid platform extended here.","marker":"[9]"}],"fun_headline_variants":["PbTe anisotropy reproducible; adding Pb makes it gate-tunable","Gate-tunable anisotropy shift in PbTe-Pb nanowires","PbTe anisotropy becomes reproducible, then Pb coupling shifts it","Reproducible PbTe anisotropy shifts when Pb is added","PbTe anisotropy made reproducible; Pb then tunes it"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The g-factor map rests on assuming that the field-induced conductance-peak splitting is a Zeeman effect of a spin-degenerate single-particle level, with charging energy and orbital effects negligible; the authors themselves note that level repulsion may underestimate the g-factor near 45°, so the pattern's sharp minimum is the most assumption-sensitive feature.","fun_headline_variants_meta":{"raw":{"variants":["PbTe anisotropy reproducible; adding Pb makes it gate-tunable","Gate-tunable anisotropy shift in PbTe-Pb nanowires","PbTe anisotropy becomes reproducible, then Pb coupling shifts it","Reproducible PbTe anisotropy shifts when Pb is added","PbTe anisotropy made reproducible; Pb then tunes it"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000869,"raw_usage":{"total_tokens":3726,"prompt_tokens":870,"completion_tokens":2856,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":486,"completion_tokens_details":{"reasoning_tokens":2785}},"tokens_in":486,"tokens_out":2856,"duration_ms":22442,"temperature":1.0,"reasoning_tokens":2785,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-10T21:35:05.937438+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Repeat the fixed-field rotation on the same PbTe dot for two different orbital levels, or on a dot small enough that charging energy is visible; if the direction of minimum splitting moves with the orbital state or with gate voltage while the magnetic field direction is fixed, the peak-splitting readout is not a clean single-particle g-tensor and the reported 45° pattern would not be the intrinsic anisotropy.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Reports the reduced-disorder PbTe nanowire growth and device process that makes the reproducible anisotropy possible."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Documents the earlier device-dependent g-factor anisotropy and small charging energies that this work aims to overcome."},{"cited_title":"Gomanko, E","cited_arxiv_id":null,"evidence_quote":"Underpins the assignment of PbTe dot diamonds to quantized single-particle levels rather than Coulomb charging, the premise for extracting g-factors from peak splitting."},{"cited_title":"Anisotropy of PbTe nanowires with and without a superconductor","cited_arxiv_id":null,"evidence_quote":"Supplies the spin-orbit-protection model used to interpret why the gap-closure direction shifts in PbTe-Pb hybrids."},{"cited_title":"Jiang, S","cited_arxiv_id":null,"evidence_quote":"Describes the selective-area, lattice-matched growth that fixes the [100] nanowire orientation."},{"cited_title":"Zhang, W","cited_arxiv_id":null,"evidence_quote":"Demonstrates the PbTe-Pb proximity effect in Josephson junctions, the baseline hybrid platform extended here."}],"review_version":1}