2017 · Magnetic Noise Spectroscopy of Local Correlations in 2D Systems

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

Figure to read

Sensor-height dependence as a guide to electronic transport regimes. Figure 1 in the source paper. 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.

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.

Start with the field at the sensor

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

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.

What is new compared with ordinary transport?

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

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.

A local impurity as another test

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

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 3

How the program has developed

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 5

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 gives concrete transport examples, while local magnetometry explains the newer symmetry-sensitive direction. The remaining challenge is robust inversion: converting a filtered field spectrum into credible, discriminating information about electronic correlations.

References

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. Phys. Rev. B 95, 155107 (2017). Open manuscript.
2. Casola, Francesco; van der Sar, Toeno; Yacoby, Amir. Probing condensed matter physics with magnetometry based on nitrogen-vacancy centres in diamond. Nature Reviews Materials 3, 17088 (2018). Open manuscript.
3. Degen, C. L.; Reinhard, F.; Cappellaro, P.. Quantum sensing. Reviews of Modern Physics 89, 035002 (2017). Open manuscript.
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. Phys. Rev. B 98, 195433 (2018). Open manuscript.
5. De, Suman Jyoti; Pereg-Barnea, Tami; Agarwal, Kartiek. Nanoscale Defects as Probes of Time-Reversal Symmetry Breaking. Physical Review X 16, 011001 (2026). Open manuscript.

Independent research synthesis. Literature checked 5 September 2026; preprints are identified in the references.