Quantum noise spectroscopy of dynamical critical phenomena and vortex dynamics in layered cuprate superconductor -- Part I

Characterizing the critical behavior in quantum materials across distinct phases fundamentally advances our understanding of the underlying electronic correlations. Probing critical phenomena requires excellent resolution at both low energy and long length-scales, which is often challenging to achieve simultaneously with existing techniques. In this work, we use nitrogen-vacancy (NV) centers in diamond as a table-top quantum sensor to diagnose critical fluctuations in the metal-to-superconducting transition of layered high-T_c superconductor Bi₂Sr₂CaCu₂O_8+δ (BSCCO). In the absence of an external magnetic field, we reveal a pronounced dip in NV center relaxation time (T₁) near the critical temperature T_c ~ 90 K, attributed to Cooper-pair fluctuation-induced magnetic noise. Crucially, the scaling of magnetic noise with temperature near criticality deviates from BCS mean-field predictions and reflects critical order parameter fluctuations. When a small magnetic field is applied, we observe a significant asymmetric T₁ spectrum, indicating the presence of vortex liquid states below T_c. Additionally, NV decoherence (T₂) spectroscopy reveals a broad two-peak noise spectrum deep within the superconducting phase, potentially linked to complex vortex dynamics. Our results provide a simple but powerful new tool for probing dynamical critical phenomena in unconventional superconductivity.