Universal Features of Emergent Electronic Fractals in Quantum Materials*

Electrons inside of many quantum materials spontaneously form clumpy patterns on multiple length scales. By importing techniques from disordered statistical mechanics into the field of quantum materials, we have defined new conceptual frameworks for understanding and controlling this electronic inhomogeneity. This allows us to use the rich information available from spatially resolved probes 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. For instance, scanning tunneling microscopy on BSCO reveals that the orientations of electronic stripes in that material form fractal, self similar patterns displaying power law behavior throughout the superconducting doping range [1], leading to a connected scaffolding on which superconductivity can arise. Surprisingly similar structures are also found in antiferromagnetic domains in NdNiO3 and the Mott metal-insulator transition in VO2. In NdNiO3, scanning resonant magnetic X-ray scattering reveals a highly textured magnetic fabric, establishing a self-similar network of antiferromagnetic domains [2]. In VO2, both scanning near-field optical microscopy and far-field optical microscopy have revealed that as opposed to transitioning from insulator to metal all at once, VO2 forms an intricate, fractal network of metallic puddles that extend like filigree over a wide range of temperatures [3]. This identification opens the door to using hysteresis effects to sculpt the filigree, in order to improve the function of VO2 in novel electronic applications such as neuromorphic devices and quantum sensing. The universal features of these fractal electronic textures across a disparate collection of quantum materials hints at a common origin. We show that this emergent electronic complexity is the result of proximity to a critical point arising from the combined effects of quenched disorder and interactions.