# Noise Magnetometry as a Probe of Correlated Electron Dynamics
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**Anchor paper:** K. Agarwal, R. Schmidt, B. Halperin, V. Oganesyan, G. Zaránd, M.D. Lukin, E. Demler, "Magnetic noise spectroscopy as a probe of local electronic correlations in two-dimensional systems," *Phys. Rev. B* 95, 155107 (2017). [arXiv:1608.03278]
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## Background
A quantum sensor (e.g. an NV center in diamond) held above a 2D conductor detects the stray magnetic field from thermal current fluctuations — a non-invasive, nanoscale local probe of electron dynamics without metallic contacts. Sweeping the sensor's stand-off distance samples the noise at different wavevectors, in principle encoding the full wavevector-dependent conductivity. Before this work, magnetic noise magnetometry had mostly detected generic current noise, with no framework connecting the noise spectrum's frequency/distance dependence to specific correlated-electron transport regimes.
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## New results
The authors built the theory connecting noise-vs-distance scaling to the electron transport regime: ballistic, diffusive, and hydrodynamic transport each produce a distinct scaling with sensor-sample distance z, reflecting the wavevector-dependence of the transverse conductivity. This lets the noise signature extract the electron fluid's viscosity or an impurity's scattering cross-section, worked out quantitatively for graphene. A companion experimental result (Andersen, Dwyer, Sanchez-Yamagishi, Rodriguez-Nieva, Agarwal, et al., *Science* 364, 154, 2019) realized a related strategy in ultraclean graphene, finding that driving graphene out of equilibrium past the sound velocity triggers a sharp electron-phonon Cerenkov instability — enhanced current fluctuations and suppressed conductivity — opening a route to tunable THz generation.
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![NV-center noise magnetometry schematic](https://ar5iv.labs.arxiv.org/html/1608.03278/assets/figmainfinal2_1.svg)
*Fig. 1 — an NV-center sensor array at varying stand-off distance above a 2D conductor, with predicted noise-vs-distance curves distinguishing ballistic, diffusive, and hydrodynamic electron transport.*
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## Related work in this direction
- J.F. Rodriguez-Nieva, K. Agarwal, T. Giamarchi, B.I. Halperin, M.D. Lukin, E. Demler, "Probing one-dimensional systems via noise magnetometry with single spin qubits," PRB 98, 195433 (2018) — extends the framework to 1D conductors, separately extracting charge and spin correlations, including Luttinger-liquid and topological-edge-state physics.
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**Two-Level-System Noise & Qubit Decoherence Theory** and **Nanoscale Probes of Symmetry-Breaking & Axion-like Response** are both nested here: the former is the microscopic noise theory underlying why the sensing qubit itself decoheres, and the latter is this same "local quantum sensor as diagnostic" methodology extended from noise/correlations to hidden symmetry breaking.
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# Parents
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* Quantum Sensing & Symmetry-Breaking Probes⏎