# 2017 · Magnetic Noise Spectroscopy of Local Correlations in 2D Systems
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**Paper focus:** Agarwal, Schmidt, Halperin, Oganesyan, Zaránd, Lukin, and Demler, *Magnetic Noise Spectroscopy as a Probe of Local Electronic Correlations in Two-Dimensional Systems* (2017). The paper develops a quantitative bridge between the relaxation of a nearby spin sensor and the nonlocal transport of a conducting sheet. Its importance is the response calculation: it specifies what the sensor measures, how geometry filters the material's fluctuations, and which transport regimes could become distinguishable. [1](https://doi.org/10.1103/PhysRevB.95.155107)
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### Figure to read
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Sensor-height dependence as a guide to electronic transport regimes. [Figure 1 in the source paper](https://arxiv.org/pdf/1608.03278#page=2). Agarwal, Kartiek; Schmidt, Richard; Halperin, Bertrand; Oganesyan, Vadim; Zaránd, Gergely; Lukin, Mikhail D.; Demler, Eugene. *Magnetic noise spectroscopy as a probe of local electronic correlations in two-dimensional systems*, Phys. Rev. B 95, 155107 (2017). Figure linked rather than reproduced; the archived manuscript does not provide an explicit open reproduction license.
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Read the relative positions of the electron-electron and momentum-relaxing mean free paths before identifying a regime. The curves are schematic and require the full response kernel for quantitative fitting.
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### Start with the field at the sensor
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A current fluctuation at one point in a sheet produces a magnetic field throughout the surrounding space. Fourier components with large in-plane wavevector decay strongly with distance from the sheet. A sensor at height $z$ therefore detects a weighted sum of current fluctuations, with a characteristic momentum scale of order $1/z$. The electromagnetic relation is the first stage of the inference problem; the sensor's spin response is the second. [1](https://doi.org/10.1103/PhysRevB.95.155107)
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Under the equilibrium and screening assumptions examined in the paper, the noise can be related to the dissipative transverse conductivity through fluctuation-dissipation reasoning. In an appropriate low-frequency regime, a schematic estimate resembles temperature times transverse conductivity divided by a geometric power of height. The complete expressions retain the momentum integral, tensor components, and material assumptions. A simple height estimate should be used for intuition, not substituted for the full kernel in a precision fit.
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### What is new compared with ordinary transport?
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A conventional terminal measurement often emphasizes a long-wavelength response together with contacts and geometry. The local noise measurement can probe shorter spatial scales without driving a large net current through the material. This creates access to crossovers among ballistic motion, interaction-dominated flow, and momentum-relaxing diffusion. The relevant regime depends on the relative sizes of sensor height and electron-electron or momentum-relaxing mean free paths. [1](https://doi.org/10.1103/PhysRevB.95.155107)
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The original figure organizes those scales and predicts qualitatively distinct distance dependences. It is a schematic experimental guide, not a claim that every sample exhibits all the regimes. To make the comparison quantitative, one needs material parameters and a distance range wide enough to resolve the predicted crossovers. Sensor-height uncertainty can otherwise imitate changes in a power law or obscure a narrow hydrodynamic interval.
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### A local impurity as another test
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The paper also considers how a localized impurity can modify nearby current noise, including a treatment of a correlated impurity within its stated approximations. This extends the method beyond a spatially uniform conductor. The scientific opportunity is to ask how a localized change in electronic correlations perturbs a nonlocal current response. Interpreting that perturbation requires a model of both the impurity and the surrounding material; a dip in noise is not a model-free measurement of a many-body energy scale. [1](https://doi.org/10.1103/PhysRevB.95.155107)
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The wider NV-magnetometry literature supplies complementary experimental constraints, including shallow-sensor coherence, spatial resolution, optical readout, and environmental backgrounds. General quantum-sensing theory further distinguishes relaxation spectroscopy from coherent phase measurements. These references are important because the proposed material response must be translated into an actual pulse and readout sequence with a quantified uncertainty. [2](https://doi.org/10.1038/natrevmats.2017.88) [3](https://doi.org/10.1103/RevModPhys.89.035002)
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### How the program has developed
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The one-dimensional extension by Rodriguez-Nieva and collaborators analyzes charge and spin correlations in wires and edge systems, with different geometry and response functions. More recent work by De, Pereg-Barnea, and Agarwal uses differences between circularly polarized fluctuations to access time-reversal-breaking response. These developments add information channels rather than merely improving the amplitude sensitivity of the original proposal. [4](https://doi.org/10.1103/PhysRevB.98.195433) [5](https://doi.org/10.1103/9h4l-21mt)
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An effective experiment should vary several controls—height, temperature, frequency, or sensor polarization—and test whether one response model explains them consistently. It should also separate equilibrium inference from strongly driven noise, where a standard fluctuation-dissipation relation may no longer apply. The [materials-probes page](https://knowen.org/nodes/33551) gives concrete transport examples, while [local magnetometry](https://knowen.org/nodes/33550) explains the newer symmetry-sensitive direction. The remaining challenge is robust inversion: converting a filtered field spectrum into credible, discriminating information about electronic correlations.
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### References
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1. Agarwal, Kartiek; Schmidt, Richard; Halperin, Bertrand; Oganesyan, Vadim; Zaránd, Gergely; Lukin, Mikhail D.; Demler, Eugene. [Magnetic noise spectroscopy as a probe of local electronic correlations in two-dimensional systems](https://doi.org/10.1103/PhysRevB.95.155107). Phys. Rev. B 95, 155107 (2017). [Open manuscript](https://arxiv.org/abs/1608.03278).
2. Casola, Francesco; van der Sar, Toeno; Yacoby, Amir. [Probing condensed matter physics with magnetometry based on nitrogen-vacancy centres in diamond](https://doi.org/10.1038/natrevmats.2017.88). Nature Reviews Materials 3, 17088 (2018). [Open manuscript](https://arxiv.org/abs/1804.08742).
3. Degen, C. L.; Reinhard, F.; Cappellaro, P.. [Quantum sensing](https://doi.org/10.1103/RevModPhys.89.035002). Reviews of Modern Physics 89, 035002 (2017). [Open manuscript](https://arxiv.org/abs/1611.02427).
4. Rodriguez-Nieva, Joaquin F.; Agarwal, Kartiek; Giamarchi, Thierry; Halperin, Bertrand I.; Lukin, Mikhail D.; Demler, Eugene. [Probing one-dimensional systems via noise magnetometry with single spin qubits](https://doi.org/10.1103/PhysRevB.98.195433). Phys. Rev. B 98, 195433 (2018). [Open manuscript](https://arxiv.org/abs/1803.01521).
5. De, Suman Jyoti; Pereg-Barnea, Tami; Agarwal, Kartiek. [Nanoscale Defects as Probes of Time-Reversal Symmetry Breaking](https://doi.org/10.1103/9h4l-21mt). Physical Review X 16, 011001 (2026). [Open manuscript](https://arxiv.org/abs/2406.14648).
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*Independent research synthesis. Literature checked 5 September 2026; preprints are identified in the references.*
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# Parents
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* Local Noise Magnetometry
* Fluctuation Probes of Quantum Materials⏎