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arXiv:2607.24906

Probing nonlocal superconducting fluctuations with covariance noise magnetometry

Gustav Romare, Ilya Esterlis, Shimon Kolkowitz, Alex Levchenko

cond-mat.supr-conquant-phSubmitted Jul 27, 2026• Announced Jul 29, 2026
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Abstract

The nonlocal superconducting fluctuation corrections to the conductivity tensor $σ_{ij}(\mathbf{q},ω)$ are calculated within the time-dependent Ginzburg-Landau framework, and their observable consequences for quantum noise magnetometry are worked out. For a single nitrogen-vacancy (NV) sensor we obtain the relaxation rate $1/T_1$ as a function of temperature, sample-sensor distance, and probe frequency, identifying the scales at which the nonlocality and the dynamics of the pair fluctuations cut off the critical enhancement near $T_c$. For two-sensor covariance magnetometry we show that the two-point field correlator develops additional spatial structure whose range directly measures the fluctuation correlation length $ξ(T)$. We further analyze two channels that accompany the paraconductivity: the Maki-Thompson correction to the spin susceptibility, and the fluctuation diamagnetism. Finally, we solve exactly, to all orders in a dc electric field and at all wave vectors, for the nonequilibrium current noise of the fluctuating film: the noise decouples from the nonlinear paraconductivity, violating the fluctuation-dissipation theorem by universal factors at criticality and acquiring a bias-induced spatial anisotropy directly measurable by covariance magnetometry. The results are connected to a recent experiment measuring current noise near a thin film of BSCCO.

Comments
16 pages, 9 figures

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The nonlocal superconducting fluctuation corrections to the conductivity tensor σij(q,ω)σ_{ij}(\mathbf{q},ω)σij​(q,ω) are calculated within the time-dependent Ginzburg-Landau framework, and their observable consequences for quantum noise magnetometry are worked out. For a single nitrogen-vacancy (NV) sensor we obtain the relaxation rate 1/T11/T_11/T1​ as a function of temperature, sample-sensor distance, and probe frequency, identifying the scales at which the nonlocality and the dynamics of the pair fluctuations cut off the critical enhancement near TcT_cTc​. For two-sensor covariance magnetometry we show that the two-point field correlator develops additional spatial structure whose range directly measures the fluctuation correlation length ξ(T)ξ(T)ξ(T). We further analyze two channels that accompany the paraconductivity: the Maki-Thompson correction to the spin susceptibility, and the fluctuation diamagnetism. Finally, we solve exactly, to all orders in a dc electric field and at all wave vectors, for the nonequilibrium current noise of the fluctuating film: the noise decouples from the nonlinear paraconductivity, violating the fluctuation-dissipation theorem by universal factors at criticality and acquiring a bias-induced spatial anisotropy directly measurable by covariance magnetometry. The results are connected to a recent experiment measuring current noise near a thin film of BSCCO.
We calculate the two-point magnetic noise spectrum arising from Gaussian superconducting fluctuations, a quantity directly measurable by spin qubit pairs such as nitrogen vacancy centers in diamond. The analysis utilizes the time-dependent Ginzburg-Landau theory, reflecting the direct contribution of fluctuating Cooper pairs to the current correlations and consequent magnetic noise. We treat both two-dimensional systems and wires, considering them in equilibrium and under a uniform electric field. The signal is expected to be strongest in high-temperature superconductors, and we contrast our findings with the predicted signatures of a vortex liquid to offer an additional route to elucidate the nature of fluctuations in these systems.
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We compute the evanescent-wave Johnson noise (EWJN) in the vacuum half-space above a superconductor, and the resulting relaxation time (T1T_1T1​) of spin and charge qubits placed at nanometer distances from the surface. The electromagnetic response is described by a single microscopic transverse current-response kernel Q(q,ω)Q(q, ω)Q(q,ω) for a BCS superconductor. This is computed for varying densities of both non-magnetic impurities and magnetic impurities, for arbitrary frequency and temperature and for wave vectors q≪kFq \ll k_Fq≪kF​ (the Fermi wavevector). When combined with the fluctuation-dissipation theorem and the nonlocal surface impedances of the half-space, this yields the magnetic and electric field noise at any distance z≫kF−1z \gg k_F^{-1}z≫kF−1​ from the surface, from which we obtain T1T_1T1​. Just below TcT_cTc​ the magnetic noise is enhanced relative to the normal state by the coherence (Hebel-Slichter-type) peak of the dissipative conductivity and drops exponentially at lower temperatures; the electric noise shows no coherence peak. The theory predicts that there is a zero-temperature noise floor induced by magnetic impurities. In the gapless regime produced by pair breaking, the finite subgap density of states ν(0)ν(0)ν(0) yields a temperature-independent noise spectral density and a relaxation rate bounded by T1−1(T)≤[ν(0)/νF]2 T1,N−1(T)T_1^{-1}(T)\le[ν(0)/ν_F]^{2}\,T_{1,N}^{-1}(T)T1−1​(T)≤[ν(0)/νF​]2T1,N−1​(T) for T≪TcT\ll T_cT≪Tc​, with equality in the extreme nonlocal regime. Here ν(0)ν(0)ν(0) and νFν_FνF​ are the superconducting and normal-state densities of states at the Fermi energy, and T1,N(T)T_{1,N}(T)T1,N​(T) is the relaxation time the same electrode would produce in its normal state at the same temperature.
A single-spin qubit placed near the surface of a conductor acquires an additional contribution to its 1/T 1 relaxation rate due to magnetic noise created by electric current fluctuations in the material.We analyze this technique as a wireless probe of superconductivity in atomically thin two-dimensional materials.At temperatures T T c , the dominant contribution to the qubit relaxation rate is due to transverse electric current fluctuations arising from quasiparticle excitations.We demonstrate that this method enables detection of metal-to-superconductor transitions, as well as investigation of the symmetry of the superconducting gap function, through the noise scaling with temperature.We show that scaling of the noise with sample-probe distance provides a window into the nonlocal quasistatic conductivity of superconductors, both clean and disordered.At low temperatures the quasiparticle fluctuations get suppressed, yet the noise can be substantial due to resonant contributions from collective longitudinal modes, such as plasmons in monolayers and Josephson plasmons in bilayers.Potential experimental implications are discussed.
Resistive transport near a superconducting phase can arise from the motion of normal-state quasiparticles or that of vortices. The conductivity alone does not distinguish between these mechanisms. We propose an unambiguous method for telling them apart, using the recently developed experimental tool of covariance magnetometry, which uses nitrogen-vacancy centers in diamond to probe real-time spatiotemporal correlations in magnetic noise. Our key insight is that, under an applied current, the underlying charge carriers leave a directional fingerprint in the spatially correlated magnetic noise above the sample: ordinary electric carriers drift parallel to the current, whereas vortices, owing to the Magnus force, drift perpendicular to it. The noise covariance detects this anisotropy and identifies the vortex-driven nature of transport. We compute the noise correlations expected for a representative thin-film superconductor and demonstrate that the anisotropic signal is well within the reach of current experimental capabilities.
Superparamagnetism in nanoscale magnetic layers is a critical property for a wide range of spintronic-based sensor and computing applications. While conventional magnetization measurements can detect superparamagnetic signatures, they often require the application of high perturbative fields and are difficult to implement for magnetic layers integrated within functional devices. In this study, we non-invasively investigate the superparamagnetic spin dynamics of a nanoscale CoFeB layer of thickness 1.1 nm, deposited on a diamond substrate, by probing its low-frequency near-field electromagnetic (EM) fluctuations using nitrogen-vacancy (NV) centers-based quantum dephasometry. Our measurements reveal an unconventional, non-monotonic temperature dependence of the dephasing time of NV centers, which we attribute to EM fluctuations produced by thermally driven superparamagnetic domain flipping in CoFeB. Our findings are further supported by the theoretical interpretation of the dephasing dynamics of NV centers and the complementary SQUID-based magnetization characterizations of the CoFeB layer. Additionally, exploiting the technique of NV dephasometry, we extract the spectral density of the EM fluctuations in CoFeB, which is used to isolate different components of the EM fluctuations acting on NV centers. We also measure the CoFeB-to-NV distance-dependent coherence times of NV centers to investigate the effect of the dimensionality of the CoFeB layer on the generated near-field EM fluctuations. These results provide critical insight into the magnetization dynamics and near-field EM environment of nanoscale magnetic layers. It also has significant implications for the development of hybrid quantum spintronic devices and applications involving nanoscale opto-magnetic materials.