Critical Nematic Correlations Throughout the Doping Range inBi_2−zPb_zSr_2−yLa_yCuO_6+x

Rapidly expanding experimental capabilities have led to a growing wealth of data on multiple length scales, revealing rich electronic textures at the nanoscale and mesoscale in many correlated oxides. We have defined new conceptual frameworks for interpreting and understanding the multiscale electronic textures observed at the surface of these materials 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 Bi_2−zPb_zSr_2−yLa_yCuO_6+x, we show that the locally 1D charge modulations are actually a bulk effect, since they have the kind of power law orientational correlations that only 3D models can produce.  We observe the power law behavior in underdoped, optimally doped, and slightly overdoped Bi_2−zPb_zSr_2−yLa_yCuO_6+x.