Nanoscale defects as probes of time reversal symmetry breaking

Nanoscale defects such as Nitrogen Vacancy (NV) centers can serve as sensitive and non-invasive 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 conductors. We argue that the difference in relaxation rates $Γ_{\pm \hat{z}}$ of NV centers starting from $m = \pm 1$ 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. For the latter, we consider specifically the case of TRSB in stacked twisted Bismuth strontium calcium copper oxide (BSCCO) flakes, which have recently been investigated experimentally and are suggested to exhibit TRSB. We show that the average relaxation rate $\left[Γ_{+\hat{z}} + Γ_{-\hat{z}}\right]$ near such a system exhibits a Hebel-Slichter like enhancement below $T_c$. The difference $Γ_{+\hat{z}} - Γ_{-\hat{z}}$ also inherits this peak but is only non-zero for $T < T_c$ and only in a chiral d-wave superconductor. We provide concrete estimates for observing this effect.

💡 Research Summary

The authors present a comprehensive theoretical framework for using nanoscale quantum defects—specifically nitrogen‑vacancy (NV) centers in diamond—as highly sensitive, non‑invasive probes of time‑reversal symmetry breaking (TRSB) in low‑dimensional conductors. The central proposal is to initialize a single NV center in either the |m = +1⟩ or |m = −1⟩ spin sub‑level (both of which have a magnetic dipole oriented along the surface normal) and then measure the longitudinal relaxation rate 1/T₁ as the system decays to the |m = 0⟩ ground state. Because the NV transition couples to the transverse magnetic field components bₓ and b_y at the defect site, the relaxation rates can be written in terms of the spectral densities of the circularly polarized magnetic fields b₊ = bₓ + i b_y and b₋ = bₓ − i b_y evaluated at the NV transition frequency ω_NV.

In a time‑reversal invariant material the cross‑correlation Im⟨n|b_y|m⟩⟨m|bₓ|n⟩ vanishes, leaving only the symmetric bₓ² + b_y² contributions. By contrast, TRSB generates a non‑zero imaginary part of the mixed correlator N_{xy}(q, ω), which is directly proportional to the imaginary part of the Hall conductivity σ_H(q, ω) at wave‑vector q ≈ 1/z_NV (z_NV being the NV‑sample distance) and frequency ω = ω_NV. The authors derive, using the fluctuation‑dissipation theorem and a full electromagnetic Green‑function treatment of a 2D sheet sandwiched between dielectrics, that the NV relaxation rates are

Γ_{±\hat z} ∝ Re