Electronic Fractals in Strongly Correlated Quantum Materials

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NONTECHNICAL SUMMARYThis award supports theoretical research on refining and extending techniques aimed at maximizing the information that can be extracted from experiments performed on strongly correlated electronic materials. The fragility and complexity of ice crystals and trees have found their counterparts in strongly correlated electronic materials. Inside conventional metals and semiconductors, electrons are typically evenly spread out, like liquid filling a container. But in correlated quantum materials, where electrons interact strongly with each other and with the atomic nuclei of the material, electrons act more like an exotic gumbo. Nanoscale images of the surfaces of these materials show that the electrons clump into complicated shapes, at least at the surface. Understanding the formation of these patterns is vital to our understanding of the electronic properties and to our eventual technological control of these materials. The PI has defined new paradigms for interpreting and understanding nanoscale electronic textures observed at the surface of these materials. These new analysis methods allow conclusions to be drawn about the inside of a material, based on observations that are made only on the outside of the material. The key insight is that the geometric structure of fractals reveals the dimension in which they reside: Fractals have different shapes when they form only on the surface of a material (like frost on a window), from when the fractals extend deep inside the material (like a tree whose roots reach deep underground). This new field of analysis has revealed universal behavior across several families of strongly correlated electronic materials. The PI proposes to uncover why these patterns are so ubiquitous at the surface of correlated materials. This award also supports the PI's educational and outreach activities. The PI continues to be a popularizer of science. She has already produced the YouTube channel www.youtube.com/profcarlson (with over 65,000 views) which has made her lectures on introductory electricity and magnetism freely available, as well as the popular video series, “Understanding the Quantum World,” with The Great Courses. The PI will start a YouTube channel for the Purdue Quantum Science and Engineering Instutite, and also produce a second video series with The Great Courses, on Quantum Materials. TECHNICAL SUMMARYThis award supports theoretical research that is aimed at refining and extending the geometric cluster analysis technique pioneered by the PI in the field of strongly correlated electronic systems, in order to maximize the information that can be extracted from experiments using the PI's new methods, and to facilitate the broad application of these techniques to various materials and image probes. In order to do this, the PI will advance the theory of geometric criticality in clean and random Ising models, via numerical simulations. At the successful completion of these calculations, several conventional (and widely available) experimental techniques will have at their disposal new modes of datataking and analysis and new methods enabling the detection and characterization of novel phases of matter.These studies are transformational in that the PI is importing concepts and techniques from fractal mathematics and disordered statistical mechanics into the field of correlated quantum materials in order to better understand fractal electronic pattern formation and its impact on these materials. The successful implementation of these ideas is expected to continue to have potentially important impact in several correlated quantum materials, including cuprate and iron pnictide superconductors, manganites, nickelates, cobaltates, and vanadium oxides.This award also supports the PI's educational and outreach activities. The PI continues to be a popularizer of science. She has already produced the YouTube channel www.youtube.com/profcarlson (with over 65,000 views) which has made her lectures on introductory electricity and magnetism freely available, as well as the popular video series, “Understanding the Quantum World,” with The Great Courses. The PI will start a YouTube channel for the Purdue Quantum Science and Engineering Instutite, and also produce a second video series with The Great Courses, on Quantum Materials.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.