Spatial complexity due to bulk electronic nematicity in a superconducting underdoped cuprate

Surface probes such as scanning tunnelling microscopy have detected complex electronic patterns at the nanoscale in many high-temperature superconductors. In cuprates, the pattern formation is associated with the pseudogap phase, a precursor to the high-temperature superconducting state. Rotational symmetry breaking of the host crystal in the form of electronic nematicity has recently been proposed as a unifying theme of the pseudogap phase. However, the fundamental physics governing the nanoscale pattern formation has not yet been identifed. Here we introduce a new set of methods for analysing strongly correlated electronic systems, including the effects of both disorder and broken symmetry. We use universal cluster properties extracted from scanning tunnelling microscopy studies of cuprate superconductors to identify the fundamental physics controlling the complex pattern formation. Because of a delicate balance between disorder, interactions, and material anisotropy, we find that the electron nematic is fractal in nature, and that it extends throughout the bulk of the material.