Anomalous slow dynamics across multiple superconducting transitions in inhomogeneous YBa2Cu3O6 + δ crystals

The interplay between lattice dynamics, nanoscale granularity, and electronic coherence is a key aspect of high‑temperature superconductivity. Here we have investigated the slow lattice dynamics in an inhomogeneous YBa2Cu3O6+δ single crystal exhibiting two distinct superconducting transitions at TC1 ≈ 86 K and TC2 ≈ 55 K, due to spatial variations in oxygen content. We have used a combination of X ray Photon Correlation Spectroscopy (XPCS) to resolve the temperature dependent speckle dynamics and Auto-Correlation (AC) imaging to identify characteristic spatial fluctuation scales. A sharp, critical like enhancement of lattice fluctuations at TC1, together with a broader fluctuation dominated crossover at TC2 in the underdoped regions, closely mirrors the temperature dependence of the dissipative magnetic susceptibility. AC imaging reveals a hierarchical organization of structural correlations: short range (20–90 nm) nanoscale modulations associated with oxygen/charge ordering, and long range (≈ 2 μm) correlations that intensify at the superconducting transition temperatures. These results demonstrate that superconducting coherence in intrinsically inhomogeneous granular YBCO emerges from the coupled evolution of nanoscale lattice fluctuations and micro to mesoscale structural networks, providing a multiscale framework for understanding how disorder and competing orders govern the superconducting state.