{"id":"a350ee71-ea2a-4b2a-b194-822439d0f75a","arxiv_id":"2510.17674","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"Strongly disordered NbN films show a magnetic-field-insensitive third-harmonic signal above Tc that is unrelated to superconductivity, and a multi-peak spectrum below Tc attributed to interference between normal-state and Higgs channels.","lead":"In very disordered superconducting niobium-nitride films, a weak signal at three times the terahertz drive frequency survives above the superconducting temperature and in magnetic fields up to 9 tesla — behavior not seen in cleaner films. If confirmed, it shows that disorder, not superconducting fluctuations, can create this nonlinear terahertz response and offers a way to image nanoscale superconducting patches.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Matched-sensitivity check: the Tc=13 sample is a valid cleaner control, but the non-superconducting kFl<1 sample's internal pump field is unreported, leaving the negative-control half of the central claim unverified.","rationale":"The reader identified unequal pump fields as the weakest assumption, focusing on the Tc=15 sample's lower internal field. However, the paper also includes a Tc=13 sample whose internal field (2.12 kV/cm) is nearly identical to that of the Tc=5.9 sample (2.13 kV/cm) and whose normal-state THG is reported as vanishing completely. This provides a matched cleaner control, weakening the reader's specific example. The more serious remaining gap is that the non-superconducting kFl<1 sample's pump field is never stated, so the claim that THG is 'undetectable' in that sample cannot be separated from a possible sensitivity limitation. Since the central abstract claim is explicitly comparative ('absent in both cleaner superconducting and non-superconducting counterparts'), the unmatched kFl<1 control is load-bearing. A matched-field re-measurement or a cubic-scaling extrapolation would settle it. The other parts of the paper—field insensitivity of the normal-state THG, persistence to room temperature, and the disorder dome in Au—are independent and support the disorder-origin interpretation, so the verdict remains CONDITIONAL rather than being upgraded or rejected. I therefore agree with the reader's overall conditional stance but partially disagree with the diagnosis: the Tc=15 issue is largely mitigated, while the unreported kFl<1 pump field is the sharper concern.","tokens_in":15600,"tokens_out":5308,"duration_ms":46921,"concrete_test":"Re-measure the kFl<1 NbN film and the Tc=15 K film with 0.42 THz pump adjusted so the internal field (after Fabry-Pérot correction) is 2.13 kV/cm, matching the Tc=5.9 K sample; integrate the 1.26 THz peak and compare to the noise floor. If a 3ω peak emerges above noise in either sample, the 'absent in non-superconducting and cleaner counterparts' claim fails. If the full matching measurement is impractical, measure incident-field dependence on the kFl<1 sample and extrapolate the observed cubic scaling to 2.13 kV/cm; if the extrapolated THG exceeds the measured noise floor, the absence claim is sensitivity-limited.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim requires that normal-state THG is absent in both cleaner superconducting and non-superconducting controls. The Tc=13 sample was measured at an estimated internal field of 2.12 kV/cm vs 2.13 kV/cm for the Tc=5.9 sample, so it is a matched cleaner control and shows no normal-state signal; this partially answers the reader's sensitivity objection. The remaining problem is the non-superconducting kFl<1 sample: SM §IV lists internal fields only for the Tc=15, 13, and 5.9 K films, and no field is given for the Tc=0 K film. Since THG scales as E^3, a modest reduction in internal field (e.g., a factor of 2 in field) suppresses the signal 8-fold; without a stated field or a demonstrated noise floor at the matched 2.13 kV/cm condition, 'THG becomes undetectable' is not established as a material property. The Tc=15 sample at 1.29 kV/cm also cannot serve as a negative control because its expected signal for equal χ(3) would be ~0.22× that of the Tc=5.9 normal-state signal, likely below the noise floor. This is a load-bearing gap in the comparative claim, though the field-insensitivity, room-temperature persistence, and Au dome provide independent support for a disorder origin.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper reports THz third-harmonic generation (THG) measurements on NbN thin films with four disorder levels (kFl ≈ 7.2, 5.5, 2.5, and <1) plus a series of disordered Au films. The central observation is that a weakly disordered clean sample (kFl≈7.2) shows no normal-state THG, moderate disorder (kFl≈5.5) shows none, but a strongly disordered sample near the SIT (kFl≈2.5, Tc=5.9 K) exhibits a weak THG signal above Tc that persists to high temperature and is insensitive to a 9 T magnetic field. The authors interpret this normal-state nonlinearity as a disorder-induced material property (band anharmonicity or τE/τM disparity) rather than superconducting fluctuations. Below Tc, the THG intensity increases sharply and is attributed to a dominant Higgs-mode contribution; in the strongly disordered sample, the THG spectrum develops a multi-peak structure attributed to quantum-path interference between normal-state and superconducting channels. The paper includes supporting measurements: fluence scaling (E^3), magnetic-field-dependent optical conductivity, LO-model fits to determine gap inhomogeneity, and Au-film controls.","tokens_in":15988,"tokens_out":10302,"duration_ms":89492,"significance":"If the central observation is correct, this is a significant experimental result: it identifies a normal-state THG response that appears only in strongly disordered superconductors near the SIT, independent of superconducting correlations, and it shows that disorder can non-monotonically tune the nonlinear THz response. The paper has several notable strengths: the THG signal is verified by cubic fluence scaling (SM Fig. S6); the Tc=13 K film provides a cleaner superconducting control measured at nearly identical internal field (2.12 vs 2.13 kV/cm); the field-insensitivity and room-temperature persistence independently argue against a superconducting-fluctuation origin; the Au dome-shaped response, though in a different disorder range, supports a universal disorder-driven effect; and echo simulations rule out spurious reflections. These elements make the core observation credible. However, the negative-control claim for the non-superconducting kFl<1 film is not yet supported at matched sensitivity, and the Higgs-mode and strong-coupling interpretations are more speculative than the abstract suggests. The paper is a strong candidate for publication after revision.","major_comments":[{"comment":"The claim that normal-state THG is absent in the non-superconducting kFl<1 sample is not supported at matched sensitivity. SM §IV lists internal pump fields for the Tc=15, 13, and 5.9 K films only; no internal field or noise floor is given for the Tc=0 K film. Since THG ∝ E^3, a factor-of-two reduction in internal field suppresses the signal ~8-fold. Without a stated internal field (ideally 2.13 kV/cm) and a demonstrated noise floor, \"THG becomes undetectable\" is not established as a material property. Please provide this information or explicitly weaken the negative-control claim.","section":"SM §IV and Fig. 1(d)"},{"comment":"The Tc=15 K sample was pumped at 1.29 kV/cm internal field versus 2.13 kV/cm for the kFl~2.5 sample; at equal χ(3), its normal-state THG would be ~0.22× that of the disordered film, likely below noise. The matched cleaner control is the Tc=13 K sample at 2.12 kV/cm. The statement \"absent in both cleaner superconducting counterparts\" is therefore stronger than the data warrant. Please present the Tc=15 K result as consistent with, but not independently decisive for, the absence claim.","section":"Fig. 1(e,g) and SM §IV"},{"comment":"The field-insensitivity experiment is cited as excluding superconducting fluctuations as the origin of normal-state THG. However, no quantitative estimate is given for how much a 9 T field should suppress the fluctuation-induced THG; within the stated noise floor, a partial suppression would not be detected. The room-temperature persistence at 0.7 THz (SM Fig. S5) independently disfavors the fluctuation scenario, but the wording \"excludes\" is too strong. Please soften or add an estimate of the expected suppression.","section":"Fig. 2(e) and §2"},{"comment":"The claim that the low-temperature THG is dominated by the driven Higgs mode is not directly established. For the kFl~2.5 sample, the LO fit gives 2Δ=0.31 THz, well below 2ω=0.84 THz, so the enhancement below Tc is off-resonance. No resonance condition is shown for this sample, and the sharp increase at Tc is also consistent with other superconducting nonlinearities. The paper's own statement that a THz pump-probe study is needed to resolve the Higgs oscillation supports this concern. Please either provide resonant evidence or soften the Higgs attribution.","section":"Fig. 1(c),(g); Fig. 4(a)"},{"comment":"The interpretation of the multi-peak structure as quantum-path interference between normal-state and Higgs channels, and the abstract's \"strong coupling\" claim, are presented without a quantitative model. The echo analysis rules out reflections, but inhomogeneous gap distributions or multiple superconducting islands could produce split peaks without invoking strong interference. Since the authors note that \"complementary theoretical studies are essential,\" this should be framed as a hypothesis rather than an established finding.","section":"Fig. 2(c,d) and §4"}],"minor_comments":[{"comment":"The Tc=0 K sample is normalized using Tc=5.9 K, which is confusing since this film has no superconducting transition. Please clarify the convention.","section":"Fig. 1(h)"},{"comment":"The text states the THG persists up to 100 K and also up to 10Tc; for Tc=5.9 K these are inconsistent (10Tc≈59 K). Please reconcile.","section":"§2"},{"comment":"The refractive index used for the Fabry-Pérot correction is only cited as \"Ref. [64]\"; provide the numerical value used in the estimate.","section":"SM §IV"},{"comment":"The axis label appears garbled (\"THG/s32/s124/s967(3)|\"); please fix the encoding.","section":"Fig. 3(b)"},{"comment":"If a published version of the arXiv paper exists, cite it instead of the preprint.","section":"Reference [42]"}],"recommendation":"major_revision","confidential_remarks":"The paper is likely to be of broad interest to the nonlinear THz and disordered superconductivity communities. The main risk is the unmatched negative control for the non-superconducting film; this should be resolved or explicitly acknowledged. The Higgs and strong-coupling claims are somewhat ahead of the evidence but can be softened without losing the paper's core value. No concerns about novelty or author conduct."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The short version: this is a careful THG study of disordered NbN that gives the best evidence yet that the normal-state THG in strongly disordered films is not from superconducting fluctuations. The magnetic-field insensitivity, persistence to 300 K, and the disordered-Au dome are independent strands that hold up. The weakest link is the negative control: the kFl<1 film's pump field is never stated, so \"undetectable\" is not established as a material property.\n\nWhat's new: Ref. 42 already saw normal-state THG in disordered NbN and blamed fluctuations. This paper discriminates by field, temperature, and a universal disorder comparison. The Tc=13 K sample is a well-matched cleaner control (2.12 kV/cm vs 2.13 kV/cm internal field) and shows no normal-state signal, which directly answers the sensitivity concern for that half of the claim. The 0.7 THz data with THG up to 300 K is a clean demonstration that this is not a low-temperature artifact. The Au data is a nice universality check.\n\nSoft spots: (1) The kFl<1 sample's internal field is unreported, so the \"absent in non-superconducting\" claim is unquantified. The authors should either give the field or show the noise floor at matched sensitivity. (2) The Tc=15 K sample at 1.29 kV/cm is not a valid negative control; the authors don't lean on it much, but they should not count it as \"cleaner\" evidence. (3) The multi-peak interference picture is qualitative; they label it as attribution and call for theory, which is honest, but the claim that it is a probe of inhomogeneity is speculative at this point.\n\nThe fits to the LO model are reasonable and the parameters aren't used to predict THG, so no circularity.\n\nOverall: the central observation (normal-state THG in strongly disordered NbN, field-insensitive, persistent to high T) is solid and worth publishing. The comparative and interpretive claims need tightening. A serious referee should get it.\n\nCheers.","headline":"Solid experimental evidence that normal-state THG in disordered NbN is not from superconducting fluctuations; the negative control needs a stated pump field.","tokens_in":16486,"tokens_out":1772,"would_cite":true,"duration_ms":15685,"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":"Strong disorder in NbN films produces a third-harmonic terahertz signal above the superconducting critical temperature, a signal that persists in high magnetic fields and is attributed to disorder-modified electron dynamics; below T_c, the","keywords":["terahertz nonlinearity","third-harmonic generation","Higgs mode","superconductor-insulator transition","disorder","NbN","Ioffe-Regel parameter","mesoscopic inhomogeneity"],"falsifier":"Measure the cleanest NbN sample (T_c=15 K) with an internal 0.42 THz field of at least 2 kV/cm, matching the strongly disordered sample's pump strength; if a THG signal appears above T_c, the central claim that normal-state THG is specific to strongly disordered films would be falsified.","tokens_in":15465,"feed_emoji":"⚡","tokens_out":9668,"duration_ms":73566,"temperature":0.7,"pith_summary":"The paper investigates how disorder affects the terahertz third-harmonic generation (THG) of superconducting NbN films with different Ioffe-Regel parameters k_Fl. It finds that in strongly disordered films near the superconductor-insulator transition, a weak THG signal appears above the superconducting critical temperature T_c, whereas cleaner superconducting and non-superconducting films show none. Because this signal is insensitive to magnetic fields up to 9 T, the authors rule out superconducting fluctuations as its origin; they attribute it to disorder-induced electronic structure modifications or to the disparity between energy and momentum relaxation times. Below T_c, THG increases sharply, indicating a dominant Higgs-mode contribution, and the spectrum develops a multi-peak structure with time-domain beating, which they interpret as quantum path interference between normal-state and Cooper-pair channels within emergent superconducting islands. These results show that disorder tunes nonlinear terahertz response and that normal-state nonlinearity can couple to the Higgs mode, offering a new probe of mesoscopic superconducting inhomogeneity.","feed_headline":"Disorder yields third-harmonic signal above T_c in superconductors","feed_subtitle":"Persists in high fields, ruling out superconducting fluctuations; reveals coupling of normal electrons to the Higgs mode.","key_machinery":"The central mechanism is the coexistence and coupling of two THG channels: (1) the disorder-enhanced normal-state nonlinearity, which the authors attribute to band anharmonicity or to the ratio of energy to momentum relaxation times, and (2) the driven Higgs mode of the superconductor. In the strongly disordered sample, the THz electric field at 0.42 THz generates a third harmonic at 1.26 THz; below T_c, the two channels interfere, producing a time-domain beating and spectral peak splitting (energy repulsion). The level of inhomogeneity is quantified via a depairing parameter η extracted from a coherence-factor fit to the optical conductivity.","core_discovery":"The authors report that in NbN with k_Fl~2.5, a THG signal persists above the global T_c (up to ~100 K, and up to room temperature with stronger drive), while samples with k_Fl~7.2, 5.5, and <1 show no such normal-state signal. The signal's intensity is unchanged in magnetic fields up to 9 T, which would suppress superconducting fluctuations, so the authors conclude it is a material property of strongly disordered metal, not a precursor of superconductivity. Below T_c, THG intensity rises sharply consistent with resonant driving of the Higgs amplitude mode, and the THG spectrum exhibits a broadened, multi-peak structure with a beating in the time domain. Using a depairing-parameter analysis","pith_inferences":["If the normal-state nonlinearity indeed scales with the energy-to-momentum relaxation time ratio, then films with tailored electron-phonon coupling (e.g., varying thickness or substrate) should show corresponding changes in the THG dome; this could separate the relaxation-disparity mechanism from band-anharmonicity.","The interference peak separation and its temperature dependence may be used to extract the typical size or coupling strength of superconducting islands; a quantitative theory linking peak splitting to the spatial distribution of the pairing gap would be a testable extension.","The magnetic-field-insensitive THG in the normal state could serve as a background-free probe of local electronic correlations in other disordered systems, independent of macroscopic superconductivity."],"forward_implications":["The Higgs mode remains a dominant contributor to nonlinear terahertz response even in strongly disordered superconducting films near the SIT, not just in clean superconductors.","Normal-state THG signals observed previously in disordered superconductors cannot be automatically assigned to superconducting fluctuations; magnetic-field dependence can distinguish the two origins.","The multi-peak/beating pattern in THG spectra is a new indicator of mesoscopic superconducting inhomogeneity, supplementing linear conductivity measurements.","The dome-shaped disorder dependence of THG in both NbN and Au suggests a universal disorder-enhanced nonlinearity in metals, relevant for any strongly disordered conductor."],"fun_headline_variants":["Disordered NbN emits THG above Tc, even in 9T field","THG above Tc in dirty superconductor ties electrons to Higgs","Unexpected terahertz signal in disordered superconductor above Tc","Disorder exposes Higgs-mode coupling via normal-state THG","Superconductor's odd THG above Tc withstands high magnetic field"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"The claim that normal-state THG is absent in cleaner NbN relies on measurements at roughly 4.5 times lower pump intensity than that used for the strongly disordered sample, so the apparent absence might be a sensitivity limit rather than a real material difference.","fun_headline_variants_meta":{"raw":{"variants":["Disordered NbN emits THG above Tc, even in 9T field","THG above Tc in dirty superconductor ties electrons to Higgs","Unexpected terahertz signal in disordered superconductor above Tc","Disorder exposes Higgs-mode coupling via normal-state THG","Superconductor's odd THG above Tc withstands high magnetic field"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000915,"raw_usage":{"total_tokens":3775,"prompt_tokens":765,"completion_tokens":3010,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":509,"completion_tokens_details":{"reasoning_tokens":2917}},"tokens_in":509,"tokens_out":3010,"duration_ms":18461,"temperature":1.0,"reasoning_tokens":2917,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-04T08:58:37.706544+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure the cleanest NbN sample (T_c=15 K) with an internal 0.42 THz field of at least 2 kV/cm, matching the strongly disordered sample's pump strength; if a THG signal appears above T_c, the central claim that normal-state THG is specific to strongly disordered films would be falsified.","supporting_citations":[],"review_version":1}