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Nanoscale Defects as Probes of Time-Reversal Symmetry Breaking

Suman Jyoti De1, T. Pereg-Barnea1,2, and Kartiek Agarwal3,1

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Phys. Rev. X 16, 011001 – Published 2 January, 2026

DOI: https://doi.org/10.1103/9h4l-21mt

Abstract

Nanoscale defects such as nitrogen-vacancy (NV) centers can serve as sensitive and noninvasive probes of electromagnetic fields and fluctuations from materials, which in turn can be used to characterize these systems. Here we specifically discuss how NV centers can probe time-reversal symmetry breaking (TRSB) phenomena in low-dimensional electronic systems. We argue that the difference in relaxation rates Γ±z^ of NV centers starting from m=±1 spin states to the ground state with m=0 directly probes TRSB. The effect arises from the difference in the fluctuation spectrum of left- and right-polarized electromagnetic fields emanating from such materials. In the quantum Hall setting, the NV center experiences (nearly zero) large additional contribution to its relaxation due to the presence of the material when its magnetic dipole (anti)aligns with the external field. More generally, the difference in the relaxation rates is sensitive to the imaginary part of the wave-vector-dependent Hall conductivity. We argue that this can be used to determine the Hall viscosity, which can potentially distinguish candidate fractional quantum Hall states and be used to infer the pairing angular momentum in TRSB superconductors. We compute the average relaxation rate [Γ+z^+Γ−z^] near thin film superconductors and find that it exhibits a Hebel-Slichter-like enhancement below Tc. The difference Γ+z^−Γ−z^ also inherits this peak but is only nonzero for T<Tc and only if the superconductivity is chiral. We provide concrete estimates for observing this effect in stacked twisted bismuth strontium calcium copper oxide flakes.

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Determining when a material breaks time-reversal symmetry—a property that distinguishes between the forward and backward flow of time—is especially challenging in low-dimensional systems. Conventional experimental methods often disturb the material or fail to detect such effects on very small scales. We introduce a noninvasive way to probe time-reversal symmetry breaking using nanoscale defects called nitrogen-vacancy (NV) centers in diamond. When placed near a material that breaks time-reversal symmetry, these atomic-scale sensors respond differently to left- and right-circularly polarized magnetic fields, allowing us to detect this subtle property through precise spin-relaxation measurements.

To establish this approach, we calculate how the spin-relaxation rate of an NV center depends on magnetic field fluctuations above a material’s surface. When the NV center’s magnetic dipole is oriented perpendicular to the surface, the relaxation rates for its two spin states differ only if the material itself breaks time-reversal symmetry. Subtracting these rates isolates a signal that directly reflects the asymmetric electromagnetic behavior of the material. In particular, this differential signal reveals information about a key property known as the Hall conductivity, which characterizes how electric currents deflect sideways under a magnetic field.

This method provides a window into the local electromagnetic behavior of 2D materials that break time-reversal symmetry. It offers a route to measure elusive quantities such as the Hall viscosity—a special, nondissipative type of viscosity that arises in quantum Hall fluids and chiral superconductors. With further development, this NV-based technique could distinguish between competing fractional quantum Hall states and reveal the internal angular momentum of exotic superconducting phases.

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Phys. Rev. X 16, 011001– Published 2 January, 2026
  • Received 7 August 2024
  • Revised 11 July 2025
  • Accepted 7 October 2025
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