Probing the Berezinskii-Kosterlitz-Thouless transition in two-dimensional superconductors using noise magnetometry

The Berezinskii-Kosterlitz-Thouless (BKT) transition is an exotic phase transition which occurs in two-dimensional systems and is characterized by the spontaneous proliferation of topological defects (vortices) above a critical temperature. While two-dimensional superconductors, including moirė and high-Tc superconductors, should in principle undergo such a BKT transition, it is often hard to conclusively demonstrate the presence of BKT physics using bulk DC transport alone. Here we will show how, using diamond nitrogen-vacancy (NV) center noise magnetometry, the precise details and dynamics of the BKT transition in superconductors could be fully characterized by studying the magnetic noise scaling with temperature, sample-depth, and frequency. A key prediction is that the magnetic noise will exhibit a nonmonotonic temperature and sample-depth dependence just above the BKT transition, providing a clear experimental signature. We also find that there is a clear qualitative difference between the magnetic noise produced by moving vortices and that which would result from Gaussian superconducting fluctuations, further demonstrating the power of noise magnetometry for probing two-dimensional superconductivity. We conclude by showing a wide variety of two-dimensional superconductors for which this technique is experimentally feasible given current constraints.