Fractal stripe structures throughout the superconducting dome in a cuprate superconductor

Scanning surface probes have recently revealed rich electronic textures at the nanoscale and mesoscale in many quantum materials. We have defined new conceptual frameworks for interpreting and understanding these multiscale electronic textures by employing theoretical tools from fractal mathematics and disordered statistical mechanics. This allows us to use the rich spatial information available from scanning probes in order to diagnose criticality from the spatial structure alone, without the need of a sweep of temperature or external field. These new methods have enabled the discovery of universal, fractal electronic textures across a variety of quantum materials. [Nat. Commun. 10, 4568 (2019); PRL 116, 036401 (2016); Nat. Commun. 3, 915 (2012)] Applying these cluster techniques to scanning tunneling microscopy on Bi2−zPbzSr2−yLayCuO6+x, we show that fractal nematic clusters pervade the bulk of the material, throughout the superconducting doping range.