CAREER: Anomalous Quantum Transport - Interactions, Disorder, Topology

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NONTECHNICAL SUMMARYThis award supports theoretical research and education to advance understanding of quantum mechanical effects involving electrons on mesoscopic length scales which lie between the scale of an atom and the macroscopic scales of the world around us. The discovery and understanding of electronic phenomena on the mesoscale can in principle lead to the development of novel miniature electronic devices and technologies. Fundamental understanding of the fundamental limits set by nature on the transfer of electromagnetic, thermal and optical signals in mesostructures, together with the emerging capability to quantitatively describe how interactions among electrons, design, interplay of novel materials, and material imperfections converge to affect or optimize electronic phenomena are foundational to future device operation and associated technologies. This project aims to investigate electronic conduction through nanoscale circuits where dominant effects require quantum mechanics for their description, and to study properties of novel materials systems discovered that display many remarkable quantum mechanical effects. These materials include graphene, classes of superconductors which can conduct electricity without loss, and topological materials. Topological materials include topological insulators which are insulators in the bulk of the material but can conduct electricity on the surfaces or edges, and Weyl semimetals which have electrons that appear to be massless and have a "handedness" derived from the direction of their motion relative to the direction of intrinsic magnetism of the electron. The PI will also investigate topological materials that can be engineered from ordinary superconductor and semiconductor materials. Engineered topological materials may enable the realization of topological quantum computing. The PI will engage public and high-school student audiences through a multifaceted outreach science program that includes coaching high-school students for Science Olympiad interscholastic competitions, and organizing Wisconsin Science Experience, an open house in which the public can come to learn about the research and teaching at the Physics Department. The Physics Fair will include laboratory tours, hands-on demonstrations, activities for kids and families, and informal conversations with scientists.TECHNICAL SUMMARY This award supports theoretical research and education to advance understanding of the interplay of quantum coherence and electron interactions in mesoscopic systems, a fundamental problem at the heart of condensed matter physics. Decisively the most important concepts of the present day are related to topological symmetries, orders and emergent quantum states of strongly correlated electrons. The central goal of this project is to investigate how the interplay of interactions, disorder and band topology manifest in anomalous quantum transport specific to novel multiband materials and multilayered heterostructures. The first research objective of this project is to develop a hydrodynamic theory of charge, spin and energy transport in modern nanoelectronic devices. The second thrust of the project is to develop theory of optical response in unconventional superconductors, and photogalvanic phenomena in Weyl semimetals and two-dimensional transition metal dichalcogenides. The third area of work is devoted to revealing peculiarities of anomalous Josephson and proximity effects in quantum circuits of topological insulators and superconductors. The final objective is to develop a nonequilibrium theory of superconducting states with competing orders and extend Keldysh field theoretic approach to describe unconventional classes of topological insulators and superconductors. The proposed work will advance our understanding of electron transport in an actively studied class of topologically nontrivial conductors, Weyl semimetals, superconductors and hybrid nanosystems based upon them. The work on hydrodynamic transport is motivated by recent experiments in graphene, and may be useful to graphene device applications. The research on competing phases in correlated materials and the discovery of novel ways of tuning and controlling them may be impactful for the development of new superconductor based technologies. Apart from the fundamental interest and importance, research devoted to topological states of matter may have transformative implications for the realization of novel quantum computation capabilities. The research will have a broad impact on science students, and public audience through an extensive public science engagement program and outreach activities that include a interscholastic Science Olympiad for high-school students.