Quantum noise spectroscopy of superconducting dynamics in thin film Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$

Abstract

Characterizing the low-energy dynamics of quantum materials is crucial to our understanding of strongly correlated electronic states. Yet, it remains experimentally challenging to investigate such dynamics with high spectroscopic resolution in both frequency and momentum space, particularly in two-dimensional correlated systems. Here, we leverage Nitrogen-Vacancy (NV) centers in diamond as a powerful and non-invasive tool to study thin-film Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ (BSCCO), revealing several distinct dynamical phenomena across the superconducting phase diagram. At zero magnetic field and low temperatures, NV depolarization ($T_1$) noise spectroscopy captures the low-frequency (GHz-scale) magnetic noise generated by nodal superconducting quasiparticle excitations, in agreement with Bardeen-Cooper-Schrieffer (BCS) mean-field theory. Near the critical temperature $T_c \approx 90$ K, supercurrent-fluctuation-induced noise leads to a sharp reduction of the NV $T_1$. By carefully analyzing the temperature-scaling of $T_1$, we observe clear deviations from the BCS prediction, reflecting the importance of order parameter fluctuations and enabling the determination of both static and dynamical critical exponents. When a small field is applied, we detect a broad and asymmetric reduction of NV $T_1$ near $T_c$; the field-induced smearing of the transition unveils the presence of a vortex liquid phase. Finally, NV decoherence ($T_2$) noise spectroscopy allows us to characterize magnetic noise at even lower MHz-scale frequencies and obtain evidence for complex vortex-solid fluctuations well below $T_c$. Our results establish quantum noise spectroscopy as a versatile platform for probing dynamical phenomena in superconductors, with frequency and length scales complementary to existing techniques.