{"id":"b211de1c-b9d6-4276-b627-75e0b05fb528","arxiv_id":"2502.04439","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"NV-center noise spectroscopy on a thin-film cuprate superconductor reveals d-wave quasiparticle noise, a stronger-than-mean-field critical divergence near Tc, and MHz-scale vortex dynamics.","lead":"Researchers placed nitrogen-vacancy diamond sensors beneath an exfoliated film of the high-temperature superconductor BSCCO and measured magnetic noise from its electrons. They detected low-temperature quasiparticle noise, an enhanced critical fluctuation peak near the superconducting transition, and slower vortex motion deep in the superconducting phase.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The 'determination' of static and dynamical critical exponents is not supported: ν=1/2 and z=2 are inputs, and the measured Γ1∝|T-Tc|^{-1} only constrains the product zν. The claim should be softened to consistency with assumed mean-field exponents.","rationale":"The reader's weakest assumption correctly identifies the TDGL model and its assumed mean-field exponents as the weak point. I agree with that assessment and sharpen it: the experimental observation of x≈1 is a robust, model-independent feature, but the inference 'determination of both static and dynamical critical exponents' is logically unsupported because only the product zν is accessible from the temperature scaling, and the model already fixes ν=1/2 and z=2. The fitted τ ratios are also coupled to the assumed z0 and layer count, as the reader notes, but that is secondary to the exponent overclaim. The remainder of the paper—Meissner imaging, vortex imaging, field-dependent T1 broadening, and MHz-range T2 vortex-solid noise—is qualitative and plausible, and those parts do not suffer from the same circularity. The paper makes a genuinely new experimental contribution; the conditional verdict is appropriate, with the abstract and main-text claims about exponent determination needing to be softened. No independent data or code are provided, which further supports conditioning on clarification, but the primary concern is the internal logic of the exponent claim rather than the absence of code.","tokens_in":23135,"tokens_out":4123,"duration_ms":44472,"concrete_test":"Refit the zero-field Γ1(T) data of Fig. 3(e) with a TDGL noise model in which ν and z are independent free parameters, reporting the joint likelihood contours. Because the near-Tc scaling enters only through τ∝ξ^z and ξ∝|T-Tc|^{-ν}, the likelihood will be nearly flat along the curve zν≈1; if this degeneracy is present, the abstract's claim to have determined both exponents is unsupported. As a secondary check, rerun the τ_fit extraction with z0 varied within the SRIM depth uncertainty (e.g., 25 nm to 35 nm) and with the 240-layer assumption relaxed to 120 layers; if τ_fit/τGL shifts by more than ~50%, the quoted ratios are not robust to the assumed geometry.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central quantitative claim, stated in the abstract and in the main text as 'enabling the determination of both static and dynamical critical exponents,' does not follow from the analysis presented. In Methods Eqs. (M10)-(M15), the TDGL Langevin model is constructed with the correlation length ξ(T)=ξ0(1-T/Tc)^{-1/2} and a relaxation rate set by τ^{-1}=γr∝(T-Tc); the model then yields Γ1∝(T-Tc)^{-1} on both sides of the transition. The fit extracts a single overall timescale (τ_fit) plus a fixed z0=25 nm geometry. Thus the observed log-log slope x≈1 in Fig. 3(e) determines only the combination zν, not ν and z separately. The statement 'the resulting value of the associated critical exponents, ν=1/2 and z=2, directly reproduce the aforementioned divergence' is circular: these values are assumed inputs from mean-field GL theory plus model A dynamics, not outputs of the fit. Any pair with zν=1 would give the same temperature dependence at fixed τ0. The reported ratios τ_fit/τGL≈1.2 (metallic) and ≈0.2 (superconducting) are therefore consistency checks, not determinations of exponents; the claim 'determination of both static and dynamical critical exponents' overstates what the data can show.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper reports NV-center noise spectroscopy measurements on a thin film of the high-Tc superconductor Bi2Sr2CaCu2O8+δ (BSCCO) exfoliated onto a diamond substrate. Using ODMR, T1 relaxometry, and T2 (XY-8) decoherence measurements, the authors observe the Meissner effect and trapped vortices, a low-temperature BSCCO-induced NV relaxation rate scaling as T^2 (attributed to nodal d-wave quasiparticles), a sharp peak in the relaxation rate near Tc, and low-frequency vortex-solid fluctuations below Tc. The critical peak is modeled with a time-dependent Ginzburg-Landau (TDGL) Langevin equation, and the authors extract order-parameter relaxation times on both sides of the transition, reporting ratios to the weak-coupling Ginzburg-Landau timescale of approximately 1.2 (metallic) and 0.2 (superconducting). The paper claims that these results enable the determination of both static and dynamical critical exponents.","tokens_in":23403,"tokens_out":5982,"duration_ms":60487,"significance":"If the claims hold, this work introduces a genuinely new non-invasive probe of low-energy superconducting dynamics, with nanoscale spatial resolution and access to MHz-GHz frequencies that are complementary to scattering, transport, and local-probe techniques. The qualitative observations—Meissner expulsion, vortex imaging, and the distinct temperature dependences in T1 and T2—are convincing and should be of broad interest. The low-temperature T^2 power law is a useful consistency check for d-wave pairing. However, the quantitative headline claim that the experiment determines the static and dynamical critical exponents is not supported by the analysis as presented, because the TDGL model assumes mean-field exponents and the fit only constrains the product zν. The paper also does not provide error bars for the extracted exponent or a sensitivity analysis for the assumed sensor-sample geometry. The experimental core is sound, but the central quantitative claims require reworking before publication.","major_comments":[{"comment":"The central claim that the measurement enables 'the determination of both static and dynamical critical exponents' (abstract; also Introduction) is not supported by the analysis. In the TDGL Langevin model, Eqs. (M10)-(M13) set r(T) ∝ T − Tc and ξ² = K/r, which fixes the static exponent ν = 1/2, and the relaxation rate of the uniform mode τ_M⁻¹ = γr ∝ T − Tc fixes the dynamical exponent z = 2 through the scaling τ ∝ ξ^z. These values are inputs to the model, not outputs of the fit; the fit only determines the overall timescale τ_fit. The measured log-log slope x ≈ 1 in Fig. 3(e) constrains only the combination zν = 1, not ν and z separately. The main-text sentence stating that 'the resulting value of the associated critical exponents, ν = 1/2 and z = 2, directly reproduce the aforementioned divergence' is therefore circular. Please revise the abstract, introduction, and main text to characterize the results as consistency tests with the assumed mean-field exponents, and remove the claim that ν and z are determined.","section":"Abstract, Introduction, and Methods Eqs. (M10)-(M13)"},{"comment":"The exponent x ≈ 1 is a load-bearing quantitative result, because it is the basis for the claimed deviation from the BCS mean-field value x = 1/2. The data points in Fig. 3(e) are shown without error bars, and the fitting procedure (temperature range, weighting, treatment of Tc uncertainty, number of points, and whether the fit is to the raw Γ1 or to a binned/log-averaged quantity) is not described. Please include error bars on Γ1(T), state explicitly how x is extracted, and provide a confidence interval. Without this, the reader cannot assess whether x is significantly different from 1/2.","section":"Fig. 3(e)"},{"comment":"The quantitative ratios τ_fit^M/τ_GL ≈ 1.2 and τ_fit^SC/τ_GL ≈ 0.2 are obtained from absolute noise magnitudes that depend directly on the assumed geometry: an average NV-to-sample distance z0 = 25 nm and a total of 240 independent active CuO2 layers (60 unit cells × 4 layers). The Methods state that these values are assumed, but no systematic uncertainty is propagated into the fitted timescales. Because the NV ensemble has a depth distribution (SRIM profile, approximately 50 nm) and the flake thickness is estimated by optical contrast (similar flakes measured as 188–300 nm), the extracted τ ratios could shift by order-one factors. Please provide a sensitivity analysis over z0 and the number of layers, or quote the timescales with a systematic uncertainty. The assumption of negligible interlayer correlations is also worth justifying, since interlayer Josephson coupling could change the effective dimensionality of the fluctuations.","section":"Methods, Eqs. (M5), (M13)-(M15)"}],"minor_comments":[{"comment":"Reference [19], cited for electrical transport, points to a paper on AC electrical conduction in p-CuIn3Se5; please replace it with a standard transport reference for superconductors or for the specific BSCCO transport data you rely upon.","section":"References, Ref. [19]"},{"comment":"The acronym 'APRES' should be 'ARPES' (angle-resolved photoemission spectroscopy).","section":"Fig. 1(a) caption"},{"comment":"The phrase 'four-point-prob method' should be 'four-point-probe method'.","section":"Methods, Characterization of BSCCO"},{"comment":"There are several typographical errors: 'temparature' in Section II.1, 'vaccum' in Section II.2, and 'BSSCO' in the caption of Fig. S2 should be 'BSCCO'.","section":"Supplementary Information, Sections II.1 and II.2"},{"comment":"Equation (M15) is derived in the Ω → 0 limit, but the T1 measurement probes noise at 2.87 GHz. Please clarify why this frequency can be treated as much smaller than the relevant electronic relaxation scales in BSCCO, or briefly discuss the validity of the low-frequency approximation.","section":"Methods, Eq. (M15)"}],"recommendation":"major_revision","confidential_remarks":"The manuscript is a good fit for the journal and the qualitative experimental results are impressive. The main barrier is the overstatement of the critical-exponent determination: the TDGL model assumes ν=1/2 and z=2, so the data can only test consistency with those values. With a revised framing and the added uncertainty analysis, the paper could become acceptable. I also note that the central comparison to weak-coupling theory relies on Ref. [59], listed as 'to appear'; the editor may want to verify that this reference is available or replaced with a public preprint. The lack of error bars in Fig. 3(e) should be addressed in revision."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Two things to know. First, this is the first NV-center noise spectroscopy on an exfoliated high-Tc cuprate film, and the qualitative results are likely to stand: T^2 low-temperature noise consistent with nodal d-wave quasiparticles, a sharp Γ1 peak near Tc, field broadening consistent with a vortex liquid, and a MHz-band T2 signal attributed to vortex-solid fluctuations. Second, the headline claim that the data determine both static and dynamical critical exponents is not supported. The TDGL Langevin model used for the fits already assumes ν=1/2 and z=2; the measured x≈1 fixes only the product zν, and the sentence in the main text saying those exponents 'directly reproduce' the divergence is circular.\n\nWhat is genuinely new here is the experimental platform: exfoliated BSCCO on a diamond NV ensemble, with Meissner and vortex imaging, and noise spectroscopy spanning MHz to GHz. The low-temperature T^2 suppression is a clean confirmation of nodal quasiparticle dynamics. The near-Tc peak and its field-dependent broadening are plausibly connected to order-parameter fluctuations and a vortex liquid, respectively. The authors also do careful work extracting Γ1 and Γ2, including a cross-check between two analysis methods.\n\nThe main soft spot is the overclaim. In the Methods (Eqs. M10–M15), the model is built with ξ(T) ∝ (1−T/Tc)^{-1/2} and relaxation rate ∝ |T−Tc|, so Γ1 ∝ |T−Tc|^{-1} is baked in. Fitting then cannot determine ν and z separately; it is a consistency check at best. The abstract and introduction should say the data are consistent with mean-field exponents, not that they are determined. There are also smaller issues: no visible error bars on Γ1 in Fig. 3(e), no data or code release, and the quoted τ_fit/τGL ratios depend on the assumed NV-sample distance z0=25 nm and the 240-layer model. These are fixable in revision, but they make the quantitative statements conditional.\n\nThis is a solid experimental paper with an interpretation that overreaches. The measurements are likely valuable to people working on quantum sensing of correlated materials, cuprate superconductivity, and vortex dynamics. It deserves a serious referee, but the referee should push for the exponent language to be softened, for error bars and data to be provided, and for a sensitivity analysis on z0 and layer count.","headline":"First NV noise spectroscopy on a thin-film cuprate with solid qualitative results, but the claimed determination of critical exponents is circular — revise before publication.","tokens_in":24063,"tokens_out":3003,"would_cite":true,"duration_ms":32154,"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 nitrogen-vacancy (NV) spin sensors placed nanometres from a thin film of the high-temperature superconductor BSCCO can read the GHz magnetic noise of its quasiparticles, critical fluctuations, and vortices.","keywords":["nitrogen-vacancy centers","quantum noise spectroscopy","high-temperature superconductivity","BSCCO thin films","critical fluctuations","Ginzburg-Landau theory","vortex dynamics","spin relaxometry"],"falsifier":"Measure $\\Gamma_1(T)$ near $T_c$ with a single NV whose distance from the BSCCO surface is known by construction, rather than an ensemble with an assumed 25 nm average standoff; if the extracted divergence exponent moves from $x \\approx 1$ toward the BCS value $1/2$, or if the fitted ratios $\\tau_{\\rm M}/\\tau_{\\rm GL}$ and $\\tau_{\\rm SC}/\\tau_{\\rm GL}$ shift substantially when $z_0$ is varied within the model, the central quantitative claim would be overturned. A complementary check is to measure the same critical current fluctuations via paraconductivity or THz conductivity on the same film and compare exponents.","tokens_in":22886,"feed_emoji":"💎","tokens_out":10426,"duration_ms":86595,"temperature":0.7,"pith_summary":"This paper claims that nitrogen-vacancy (NV) centers in diamond, embedded tens of nanometres beneath the surface, can act as a non-invasive noise spectrometer for a thin exfoliated film of the high-temperature superconductor BSCCO. At zero applied field the sensor resolves two dynamical regimes: a $\\Gamma_1 \\propto T^2$ growth of GHz magnetic noise at low temperature, attributed to nodal d-wave quasiparticles in agreement with BCS mean-field theory, and a sharp divergence $\\Gamma_1(T) \\propto |T-T_c|^{-x}$ near $T_c \\approx 90$ K with $x \\approx 1$, stronger than the BCS mean-field value $x = 1/2$. The paper argues that a time-dependent Ginzburg-Landau (TDGL) Langevin model of order-parameter fluctuations, with critical exponents $\\nu = 1/2$ and $z = 2$, reproduces the divergence on both sides of the transition and gives fitted relaxation times $\\tau_{\\rm M}/\\tau_{\\rm GL} \\approx 1.2$ and $\\tau_{\\rm SC}/\\tau_{\\rm GL} \\approx 0.2$, close to weak-coupling predictions. Under a small magnetic field the same $T_1$ measurement sees a broadened peak attributed to a vortex liquid whose noise scales linearly with field, and $T_2$ decoherence spectroscopy reaches MHz-scale vortex-solid fluctuations. If the paper is right, NV noise spectroscopy becomes a table-top complement to scattering and transport for probing superconducting dynamics in two-dimensional materials.","feed_headline":"NV sensors detect a sharper-than-BCS critical divergence in BSCCO","feed_subtitle":"Diamond qubits nanometres from a cuprate film clock the slowing of superconducting fluctuations near Tc.","key_machinery":"The load-bearing machinery is the ensemble of nitrogen-vacancy (NV) centers as local GHz magnetic-noise detectors, coupled to a time-dependent Ginzburg-Landau (TDGL) Langevin description of the superconducting order parameter $\\psi(\\mathbf{r},t)$. The NV spin relaxation rate is set by magnetic noise at the $\\approx 2.87$ GHz zero-field splitting, computed from the transverse current-current correlator of the BSCCO layers; the current operator is $J(\\mathbf{r}) = (\\hbar e^* / 2 i m^*)(\\psi^* \\nabla \\psi - \\psi \\nabla \\psi^*)$. The order parameter obeys $\\partial_t \\psi = -\\gamma\\, \\delta F/\\delta \\psi^* + \\eta$ with Gaussian white noise $\\eta$ and free energy $F = \\int [K|\\nabla\\psi|^2 + r(T)|\\psi|^2 + (u/2)|\\psi|^4]$, where $r(T) \\propto T-T_c$. Near criticality the relaxation time diverges as $\\tau \\propto \\xi^z \\propto |T-T_c|^{-z\\nu}$ with $\\nu = 1/2$, $z = 2$, and this critical slowing down is what produces the $|T-T_c|^{-1}$ divergence of $\\Gamma_1$. To connect the model to data, BSCCO is treated as 240 independent CuO$_2$ layers at an assumed average NV distance of 25 nm.","core_discovery":"The paper's central claim is that the temperature dependence of the BSCCO-induced NV relaxation rate $\\Gamma_1(T)$ at zero field is a direct readout of three distinct low-energy dynamical regimes in a thin-film cuprate. At $T \\ll T_c$, $\\Gamma_1 \\propto T^2$, consistent with nodal d-wave quasiparticles at BCS mean-field level. Near $T_c \\approx 90$ K, $\\Gamma_1$ rises in a sharp symmetric peak that scales as $|T-T_c|^{-x}$ with $x \\approx 1$, clearly distinct from the BCS prediction $x = 1/2$; the paper attributes this extra singularity to amplitude and phase fluctuations of the superconducting order parameter. A TDGL Langevin equation with Gaussian white noise, treated with mean-field exponents $\\nu = 1/2$, $z = 2$, reproduces the divergence on both the metallic and superconducting sides and yields fitted relaxation-time ratios $\\tau^{\\rm fit}_{\\rm M}/\\tau_{\\rm GL} \\approx 1.2$ and $\\tau^{\\rm fit}_{\\rm SC}/\\tau_{\\rm GL} \\approx 0.2$, bracketing the analytical weak-coupling values $1$ and $0.5$. In an applied field the transition peak broadens and becomes asymmetric as vortices enter, with $\\Gamma_1 \\propto H$ as expected for a diffusive vortex liquid; $T_2$ noise spectroscopy additionally resolves MHz-frequency fluctuations assigned to vortex motion in the vortex solid deep below $T_c$.","pith_inferences":["Editorial inference: Because the momentum range of the detected noise is set by the NV–sample distance, a scanning single NV could map not only static vortices but the spatial texture of fluctuating supercurrents; the paper demonstrates static imaging but not dynamic sub-micron noise imaging.","Editorial inference: The asymmetry between $\\tau_{\\rm M}/\\tau_{\\rm GL} \\approx 1.2$ and $\\tau_{\\rm SC}/\\tau_{\\rm GL} \\approx 0.2$ suggests that phase and amplitude fluctuations of the order parameter relax at different rates; if reproduced in other cuprates, this asymmetry would constrain microscopic theories of pair relaxation beyond the weak-coupling limit.","Editorial inference: The zero-field critical exponent $x \\approx 1$ could be cross-checked on the same films by paraconductivity or THz conductivity measurements, which probe the same fluctuating supercurrents through different observables; agreement would strengthen the TDGL description.","Editorial inference: Because the fitted ratios assume a 25 nm average NV distance, a single-NV measurement with a known standoff would either confirm or revise the close-to-weak-coupling conclusion; varying $z_0$ by tens of nanometres in the model would show how strongly the extracted $\\tau$ ratios depend on this assumption."],"forward_implications":["NV $T_1$ relaxometry can extract the characteristic order-parameter relaxation time $\\tau$ near $T_c$ and the static and dynamic critical exponents ($\\nu = 1/2$, $z = 2$) from a thin-film superconductor without electrical contact.","The observed $\\Gamma_1 \\propto T^2$ low-temperature noise is a fingerprint of nodal d-wave quasiparticles, so the same measurement on other thin-film superconductors should distinguish nodal from fully gapped pairing.","The near-$T_c$ scaling $\\Gamma_1 \\propto |T-T_c|^{-1}$ shows that order-parameter fluctuations, not just BCS quasiparticles, dominate the magnetic noise of thin cuprate films at criticality.","In a magnetic field, the linear $\\Gamma_1(H) \\propto H$ scaling and the broadened asymmetric peak locate a diffusive vortex liquid phase, while $T_2$ spectroscopy at MHz frequencies extends the platform to vortex-solid flux motion.","The technique extends to other superconductors, including hydrides and nickelates under high pressure inside diamond anvil cells, where the same NV sensors can probe pressure-driven transitions."],"supporting_citations":[{"why":"Supplies the weak-coupling fluctuation theory and the divergent timescale $\\tau_{\\rm GL} = 8\\hbar/(k_B|T-T_c|)$ used to normalize the fitted relaxation times.","marker":"[7]"},{"why":"Provides the time-dependent Ginzburg-Landau equation and the weak-coupling relaxation rates on both sides of the transition to which the fits are compared.","marker":"[8]"},{"why":"Establishes the quantum noise spectroscopy formalism whose filter functions map NV $T_1$ and $T_2$ data onto magnetic noise spectra.","marker":"[38]"},{"why":"Gives the magnetic noise formalism for two-dimensional superconductors and the low-temperature nodal-quasiparticle $T^2$ scaling used to interpret the zero-field data.","marker":"[54]"},{"why":"Derives the BCS mean-field prediction $\\Gamma_1 \\propto |T-T_c|^{-1/2}$ whose observed deviation ($x \\approx 1$) is the central critical-fluctuation claim.","marker":"[55]"},{"why":"Supplies the vortex liquid and vortex solid phenomenology used to interpret the in-field broadening of $\\Gamma_1$ and the low-frequency $\\Gamma_2$ noise.","marker":"[12]"},{"why":"Provides the dynamic critical phenomena classification ($\\nu = 1/2$, $z = 2$, Langevin model A) that underlies the order-parameter dynamics model.","marker":"[37]"},{"why":"Gives the analytical weak-coupling ratios $\\tau_{\\rm M}/\\tau_{\\rm GL} = 1$ and $\\tau_{\\rm SC}/\\tau_{\\rm GL} = 0.5$ used as comparison values for the fitted ratios.","marker":"[59]"}],"fun_headline_variants":["NV diamonds capture cuprate's critical slowdown near Tc","Cuprate film's vortex phases mapped by NV noise spectroscopy","NV sensors reveal sharper-than-BCS critical peak in BSCCO","Diamond qubits probe superconducting fluctuations with precision","Quantum noise spectroscopy exposes vortex dynamics in cuprates"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The quantitative claims assume the superconductor's order parameter relaxes exactly as a Gaussian-noise Langevin equation with mean-field exponents predicts, and that the NV sensors sit at an assumed average distance of 25 nm from 240 independent copper-oxide layers; if the real distance or interlayer coupling differs, the fitted relaxation times and the apparent critical exponent change substantially.","fun_headline_variants_meta":{"raw":{"variants":["NV diamonds capture cuprate's critical slowdown near Tc","Cuprate film's vortex phases mapped by NV noise spectroscopy","NV sensors reveal sharper-than-BCS critical peak in BSCCO","Diamond qubits probe superconducting fluctuations with precision","Quantum noise spectroscopy exposes vortex dynamics in cuprates"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000287,"raw_usage":{"total_tokens":1816,"prompt_tokens":1207,"completion_tokens":609,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":823,"completion_tokens_details":{"reasoning_tokens":528}},"tokens_in":823,"tokens_out":609,"duration_ms":6869,"temperature":1.0,"reasoning_tokens":528,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-08T22:42:57.011864+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure $\\Gamma_1(T)$ near $T_c$ with a single NV whose distance from the BSCCO surface is known by construction, rather than an ensemble with an assumed 25 nm average standoff; if the extracted divergence exponent moves from $x \\approx 1$ toward the BCS value $1/2$, or if the fitted ratios $\\tau_{\\rm M}/\\tau_{\\rm GL}$ and $\\tau_{\\rm SC}/\\tau_{\\rm GL}$ shift substantially when $z_0$ is varied within the model, the central quantitative claim would be overturned. A complementary check is to measure the same critical current fluctuations via paraconductivity or THz conductivity on the same film and compare exponents.","supporting_citations":[{"cited_title":"A., Yao, N","cited_arxiv_id":null,"evidence_quote":"Establishes the quantum noise spectroscopy formalism whose filter functions map NV $T_1$ and $T_2$ data onto magnetic noise spectra."},{"cited_title":"V., Geshkenbein, V","cited_arxiv_id":null,"evidence_quote":"Supplies the vortex liquid and vortex solid phenomenology used to interpret the in-field broadening of $\\Gamma_1$ and the low-frequency $\\Gamma_2$ noise."}],"review_version":1}