{"id":"cc11c818-a761-47f8-aac4-21a24ebbc549","arxiv_id":"2607.21507","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":8,"one_line_summary":"In-plane magnetic fields break the C3v symmetry of charge-density-wave peak intensities in scanning-tunneling spectra of superconducting NbSe2, an effect the authors attribute to supercurrent-induced Doppler shifts of Bogoliubov quasiparticles.","lead":"An STM experiment on superconducting NbSe2 shows that an in-plane magnetic field changes the pattern of charge-density-wave ripples seen in electron spectra, breaking the three-fold symmetry. If confirmed, this gives a field-based handle to steer charge order in intertwined superconductors and a way to visualize how currents rebuild the electron energy bands.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Doppler-shift mechanism rests on an unvalidated Meissner-profile assumption and a ~30x field-scale mismatch between simulation (0.8Bc) and experiment (100 mT); vortex-state currents remain an uncontrolled alternative.","rationale":"The reader identified the same critical weakness I would: the experimental field regime is above Hc1, so the London Meissner vector potential of Methods Eq. (6) is not a controlled description of the actual current distribution, and the simulation operates at a much higher field (0.8Bc ≈ 3 T) than the 100–400 mT used in the experiment. The Discussion itself concedes this. My stress-test did not find a separate fatal flaw: the symmetry analysis connecting C3v-to-Cs peak locking is internally consistent, and the control topographs (Supplementary Fig. 12) rule out a trivial topographic artifact. The observation itself is reported carefully, with data deposited on Zenodo and multiple cross-checks (normal-state spectra unchanged, field-independent topographs, away-from-vortex acquisition). However, the central causal claim—'supercurrent effect'—is exactly the unproven part. The model reproduces a symmetry pattern under a large pair momentum, but the quantitative link to 100 mT is missing. I would therefore keep the CONDITIONAL verdict, requiring the authors to demonstrate the effect at the experimental field and/or in the Meissner state, or to provide a vortex-state calculation. My concern does not change the reader's verdict, so verdict_should_be is UNCHANGED.","tokens_in":23294,"tokens_out":5307,"duration_ms":54072,"concrete_test":"Recompute the CDW peak intensities P(d_i) from the same tight-binding model at B=100 mT (using the Doppler shift extracted from the measured coherence-peak shift, ~0.12 meV) and with a realistic vortex-state current profile for B>Hc1 (e.g., from a Ginzburg-Landau or London vortex-lattice calculation). If P(d1)>P(d2)=P(d3) is not reproduced at the experimental field, the model does not explain the data and the Doppler mechanism is unsupported. Alternatively, repeat the spectroscopic imaging at a field below Hc1 (Meissner regime): persistence of the field-orientation-dependent CDW asymmetry would support the Doppler interpretation, while its disappearance would implicate vortex effects.","verdict_should_be":"UNCHANGED","load_bearing_attack":"To establish the central claim—that the C3v-to-Cs CDW intensity asymmetry is caused by Doppler-shifted Bogoliubov quasiparticles—the paper needs (i) the actual surface current distribution at the experimental fields to be the Meissner screening current described by Methods Eq. (6), and (ii) the simulated field to be in the same regime as the experiment. Neither holds. The measurement is at 100–400 mT, above Hc1, so the sample is in the vortex state; the Discussion concedes that 'the current distribution near the surface may therefore differ from that in a simple Meissner-screening picture,' which is precisely the input of Eq. (6). The simulation uses B=0.8Bc (~3 T) (Supplementary Figs. 16–17), roughly 30 times larger than 100 mT, and the coherence-peak shift at 100 mT (~0.12 meV, Fig. 2h) implies a Doppler energy about an order of magnitude smaller than Δ≈1.28 meV used in the model. Consequently, the agreement between Figs. 4e–h and the experimental maps does not validate the Doppler mechanism at the experimental conditions; it only shows that a large pair momentum can produce such an asymmetry. Vortex-core or vortex-current pair-breaking, field-induced orbital effects, or other field-direction-dependent instrumental asymmetries could equally produce the observed peak selection without a supercurrent Doppler shift. The central claim therefore rests on an assumption that is both explicitly hedged and quantitatively untested.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper reports a field-driven C3v-to-Cs symmetry breaking of the 3x3 CDW modulation in superconducting 2H-NbSe2, observed via STM/STS under in-plane magnetic fields of 100–400 mT. At zero field, the six CDW FFT peaks have equal intensity; under a field along Γ-M, the two CDW peaks centered along the field direction are enhanced while the other four are suppressed, yielding P(d1) > P(d2) = P(d3). The authors attribute this to a Meissner-current-induced Doppler shift of the Bogoliubov quasiparticle dispersion, which selectively modifies the CDW scattering at the precursor CDW wavevectors. A real-space tight-binding model with CDW and s-wave pairing, combined with a symmetry analysis, reproduces the observed anisotropy pattern and shows that the remaining symmetry is Cs. The paper concludes that supercurrents can tailor intertwined CDW order through momentum-space engineering.","tokens_in":23671,"tokens_out":5591,"duration_ms":57983,"significance":"The observation of magnetic-field-direction-dependent CDW peak weighting in a canonical intertwined superconductor is novel and potentially significant. The symmetry argument that an in-plane field reduces C3v to Cs, locking P(d2)=P(d3) while leaving P(d1) unconstrained, is elegant, parameter-free, and clearly presented. The experimental data are of good quality, and the paper includes data and code availability statements. If the Doppler-shift mechanism is quantitatively confirmed, this work would demonstrate a new handle for controlling charge order in superconductors. However, the quantitative link between experiment and model is not currently established: the simulations are run at a much larger field than the experiments, and the experimental field regime is above Hc1, where the assumed Meissner screening current profile is not guaranteed to hold. Thus the significance of the central claim is conditional on resolving these issues.","major_comments":[{"comment":"The central mechanism assumes that the in-plane field produces a well-defined Meissner screening current described by the vector potential A = (B λ_L sinh(z/λ_L)/cosh(d/2λ_L),0,0) (Methods Eq. (6)). The experiments, however, are performed at 100–400 mT, which the Discussion admits exceeds Hc1 and where vortices are present. The Discussion even concedes: \"the current distribution near the surface may therefore differ from that in a simple Meissner-screening picture.\" This concession directly undermines the applicability of Eq. (6) as the input for the model. To support the claim, the authors must either demonstrate that the actual surface current at these fields is the Meissner screening current (e.g., by local magnetic-field or current-density measurements) or modify the model to incorporate a vortex-state current profile. Without this, the agreement between Fig. 4 and experiment cannot","section":"Discussion; Methods Eq. (6)"},{"comment":"The simulations are run at B = 0.8Bc, which the paper states is about 3 T, while the key experimental data are taken at 100–400 mT. The coherence-peak shift at 100 mT (Fig. 2h) is ~0.12 meV, about an order of magnitude smaller than the superconducting gap Δ ≈ 1.28 meV used in the model. The simulation at 0.8Bc has a Doppler shift comparable to Δ, so the constant-energy contour at E = 0.5Δ is depleted on one side (Figs. 4c,d). At the experimental field, the Doppler energy is only ~0.1Δ, and the asymmetry of the constant-energy contour is correspondingly weak. No scaling argument is provided to show that the same qualitative pattern (P(d1)>P(d2)=P(d3)) persists at this smaller Doppler shift. The authors should either perform simulations at the experimental field strengths (increasing numerical accuracy as needed) or provide an analytical estimate of the field dependence of the intensity as","section":"Supplementary Figs. 16–17; Fig. 2h"},{"comment":"The expression for the CDW peak intensity P(d_i) is derived from first-order perturbation theory in the CDW potential, and the symmetry analysis in Supplementary Note 2 correctly shows that a mirror symmetry enforces P(d2)=P(d3). However, the actual magnitude and sign of the asymmetry, i.e., whether P(d1) is enhanced or suppressed relative to P(d2), depend on microscopic details encoded in the band structure and on the field strength. The model uses several free parameters (t1, t2, λ, Δsc, ΔCDW, μ, CDW phases, and the field B), and the CDW phases in Eq. (4) are chosen to reproduce the observed 3x3 pattern. Thus the agreement between Figs. 4e–h and experiment is partly a fit, not a parameter-free prediction. To strengthen the central claim, the authors should present the model's asymmetry ratio P(d1)/P(d2) as a function of field and compare it with the measured ratio extracted from the FF","section":"Eq. (1); Methods Eq. (12)"}],"minor_comments":[{"comment":"The abstract and introduction state unambiguously that the Meissner current is the cause, but the Discussion later concedes that vortices are present and the current distribution may differ. It would be more accurate to frame the Doppler-shift scenario as a plausible mechanism that needs verification, or to soften the wording throughout to match the caveat.","section":"Abstract and Introduction"},{"comment":"The coherence-peak shift at 100 mT is presented qualitatively. The authors could include the extracted Doppler shift as a function of field (shown in Supplementary Fig. 6e) in the main text to help the reader judge the magnitude of the effect.","section":"Fig. 1e"},{"comment":"The CDW phases (φ1=-2π/3, φ2=2π/3, φ3=0) are chosen to reproduce the observed 3x3 pattern. This should be explicitly acknowledged as an input rather than a prediction, as the reader might otherwise overestimate the model's predictive power.","section":"Methods Eq. (4)"},{"comment":"The line-cut directions for the FFTs in Figs. 4g,h are described as \"dashed-arrow directions,\" but it is not clear from the figure which dashed arrows in the insets are being referenced. A clearer labeling would improve readability.","section":"Fig. 4g,h"}],"recommendation":"major_revision","confidential_remarks":"The paper presents a striking experimental observation and a clean symmetry argument, but the quantitative mismatch between the simulation field (0.8Bc) and the experimental field (100–400 mT) is a serious gap. The Discussion's concession about the Meissner-profile assumption is close to an admission that the central input is not justified. I would encourage the editor to invite a revision in which the authors either perform simulations at the experimental fields, provide a scaling argument, or otherwise demonstrate that the Doppler-shift mechanism is quantitatively viable in the measured regime. If such further evidence is not provided, the paper may need to be reframed as a proposal of a generic mechanism rather than a demonstration of the supercurrent effect in NbSe2."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Quick take: the central observation is real and worth knowing about — in-plane field rotates which CDW peaks win in dI/dV maps of superconducting NbSe2, C3v to Cs. The field-orientation dependence is clean and the symmetry argument (Doppler shift leaves a mirror plane, locking P(d2)=P(d3)) is basically parameter-free. That part is solid.\n\nWhat the paper does well: it connects a real-space LDOS modulation to a specific momentum-space mechanism, includes a careful symmetry analysis, and they've deposited data on Zenodo. The authors are also honest about the biggest caveat — they admit the sample is above Hc1 and the surface currents may not be a simple Meissner screening profile.\n\nThe soft spots are in the quantitative link. The simulation runs at B=0.8Bc (~3 T), but the data are at 100–400 mT. At 100 mT the coherence-peak shift is about 0.12 meV against a gap of 1.28 meV, so the Doppler energy is an order of magnitude smaller than the gap. Yet the model shows dramatic peak selection only when the Doppler energy is a substantial fraction of the gap. It's not obvious the same asymmetry appears at 100 mT with realistic parameters. That means Figs. 4e–h don't actually validate the mechanism at the experimental conditions; they show that a large pair momentum can produce the asymmetry. Combined with the vortex-state issue, the title's \"supercurrent effect\" is doing more work than the evidence supports.\n\nNone of this kills the observation. The symmetry breaking is new and likely correct. But as submitted, the paper over-attributes it to the Meissner Doppler shift without showing the effect at the measured fields. A serious referee should ask for either data or simulation at 100 mT, or at least a scaling argument that justifies extrapolating from 3 T down to 0.1 T.\n\nMy take: this deserves peer review. The observation is significant enough for the community, and the honesty of the Discussion is a good sign. I'd recommend acceptance after the quantitative gap is addressed. The authors should either soften the claim or show the model works at experimental fields.\n\nFor the reading group: maybe — the symmetry analysis is instructive, and it's a good example of how to think about field-induced symmetry breaking in intertwined orders.","headline":"New field-direction-selective CDW anisotropy in NbSe2 is likely real, but the supercurrent-Doppler mechanism is not quantitatively established and the title overclaims.","tokens_in":24283,"tokens_out":2535,"would_cite":true,"duration_ms":25919,"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":"An in-plane magnetic field breaks the threefold symmetry of charge-density-wave modulations in superconducting NbSe2 by Doppler-shifting quasiparticle excitations.","keywords":["superconductivity","charge density wave","Doppler shift","Meissner effect","scanning tunneling microscopy","NbSe2","symmetry breaking","Bogoliubov quasiparticles"],"falsifier":"Measure the CDW-peak anisotropy in a thin NbSe2 flake in a true Meissner state (no vortices, B < Hc1) and compare the Γ-M versus Γ-K enhancement patterns with the model prediction; if the field-direction selection rule is not reproduced, the Doppler-shift mechanism is not the cause.","tokens_in":23082,"feed_emoji":"🧲","tokens_out":6131,"duration_ms":55646,"temperature":0.7,"pith_summary":"An in-plane magnetic field breaks the threefold (C3v) symmetry of the charge-density-wave (CDW) modulations in superconducting 2H-NbSe2, lowering it to mirror-only (Cs) symmetry. The authors show that the Meissner screening current from the field Doppler-shifts the Bogoliubov quasiparticle dispersion, and only quasiparticle states with particular momenta remain at sub-gap energies. In spectroscopic dI/dV maps this appears as a selective enhancement of the CDW Fourier peaks aligned with the field: P(d1) > P(d2) = P(d3) for fields along Γ-M, with the reversed ordering for Γ-K. Rotating the field direction reorients the enhanced peaks, demonstrating on-demand control of the CDW pattern in momentum space. Tight-binding simulations incorporating a triple-Q CDW potential, s-wave pairing, and the Peierls phase reproduce the observed anisotropy and place the effect inside the superconducting gap.","feed_headline":"Magnetic field breaks threefold symmetry of charge order in superconductor","feed_subtitle":"In superconducting NbSe2, an in-plane field selectively boosts charge-density-wave peaks by Doppler-shifting quasiparticles.","key_machinery":"The machinery is the Doppler-shifted Bogoliubov dispersion produced by the Meissner screening current (via Peierls substitution, p → p + eA), together with a first-order perturbation formula for how CDW peak intensities depend on energy denominators ΔE(k ± d_i) between states coupled by the CDW wavevectors.","core_discovery":"The central claim is that the diamagnetic Meissner current generated by an in-plane magnetic field acts as a momentum-space handle on a superconductor intertwined with charge order. The Doppler shift e v_k · A adds to the Bogoliubov dispersion, selectively depopulating quasiparticle branches on one side of the constant-energy contour for energies between the Doppler-shift energy and the gap. Because the CDW peak intensity in the local-density-of-states Fourier transform is controlled by energy denominators ΔE(k ± d_i) between states connected by the CDW wavevectors, the reconstructed contours enhance some CDW peaks and suppress others. The authors observe exactly this: a C3v-to-Cs transition","pith_inferences":["If the Doppler-shift attribution is correct, the same mechanism should imprint directional anisotropy on other intertwined orders in superconductors, such as pair-density waves or spin-density waves, when an in-plane field is applied.","The effect could be leveraged as an imaging probe of the local Meissner screening current: the pattern of enhanced CDW peaks should map the local supercurrent direction and magnitude at the surface, complementing vortex imaging.","A sharper test would be to repeat the measurement in a vortex-free slab below Hc1; if the anisotropy pattern changes or disappears, the simple Doppler picture would need revision in favor of vortex-modified currents.","The symmetry-locking argument implies that any perturbation that lowers C3v to Cs yields P(d2)=P(d3), so the observed peak equality is not by itself evidence for the Doppler mechanism, but the field-direction reversal (Γ-M vs Γ-K) is."],"forward_implications":["Rotating the in-plane field direction reorients the enhanced CDW peaks, so the emergent CDW anisotropy can be tuned on demand.","The field-driven symmetry breaking is confined to sub-gap energies (roughly 0.2–0.6 meV at 100–400 mT); above the coherence peaks the CDW retains C3v symmetry, and normal-state topography is unaffected.","The same Doppler-shift mechanism should apply to any superconductor with coexisting charge order whose CDW wavevectors connect states on the constant-energy contour.","The CDW-peak anisotropy provides a direct momentum-space visualization of the Doppler-shift-modified contour, offering a new probe of supercurrent flow.","Because the CDW peak intensity formula is generic, the field-direction selection rules (P(d2)=P(d3) locked by a mirror plane) follow from symmetry alone and should be robust to the microscopic details."],"fun_headline_variants":["Meissner current bends charge order in NbSe2","Doppler shift flips symmetry of CDW in superconductor","Field-tuned quasiparticles steer charge waves in NbSe2","Supercurrent reshapes CDW order in superconductor"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"The paper's explanation assumes that the in-plane field generates a clean Meissner screening current with a well-defined London vector potential that uniformly Doppler-shifts the quasiparticle dispersion at the experimental fields; the authors concede in the Discussion that the fields exceed Hc1, vortices are present, and the surface current distribution may differ from the simple Meissner picture, while the numerical simulation is run at 0.8Bc (~3 T) rather than at 100–400 m","fun_headline_variants_meta":{"raw":{"variants":["Meissner current bends charge order in NbSe2","Doppler shift flips symmetry of CDW in superconductor","Field-tuned quasiparticles steer charge waves in NbSe2","Supercurrent reshapes CDW order in superconductor"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000161,"raw_usage":{"total_tokens":1063,"prompt_tokens":722,"completion_tokens":341,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":466,"completion_tokens_details":{"reasoning_tokens":270}},"tokens_in":466,"tokens_out":341,"duration_ms":4138,"temperature":1.0,"reasoning_tokens":270,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-01T07:13:41.743442+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure the CDW-peak anisotropy in a thin NbSe2 flake in a true Meissner state (no vortices, B < Hc1) and compare the Γ-M versus Γ-K enhancement patterns with the model prediction; if the field-direction selection rule is not reproduced, the Doppler-shift mechanism is not the cause.","supporting_citations":[],"review_version":1}