Superconductivity-enhanced magnetic field noise

We consider the stray magnetic field noise outside a two-dimensional superconductor. Our considerations are motivated by recent experiments, which observed an enhancement in the magnetic field noise below the superconducting critical temperature based on the relaxation of diamond nitrogen-vacancy centers. Such enhancement is not captured by the standard two-fluid model for the superconducting state, recently proposed to explain such NV relaxometry experiments. Instead, we show that a microscopic BCS theory captures such an enhancement, and we compare with a similar theory and phenomenon, known as the Hebel-Schlicter peak (or coherence peak), observed in the relaxation of nuclear spins in the material. The primary difference is that the NV probes long-wavelength magnetic noise outside the sample, while the nuclear spin probes local hyperfine noise inside the sample. Accordingly, the noise probed by the NV depends on its height and can probe, in pristine samples, the superfluid coherence length. Finally, we discuss potential avenues for NVs to probe unconventional superconductivity via deviations from the above BCS theory.