Correlated Electron Physics in Graphene and Other Novel Quantum Materials

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NONTECHNICAL SUMMARYThis award supports theoretical research and education to further our understanding of how quantum mechanics determines the state of matter of a large collection of interacting particles at the atomic level. The stages on which such dynamics plays out are real quantum materials, designed and studied within laboratories around the world using modern experimental tools. The ultimate practical goal is to use the gained understanding for designing new materials and structures with desired properties.The discovery of superconductivity --flow of electrical current without any resistance-- in a physical system composed of two sheets of graphene, each one carbon atom thin and precisely stacked on top of each other, has started a new frontier research field aligned with the above goals. In addition, many such materials combine modern notions of topology with basic concepts of solid-state physics describing the behavior of strongly interacting electron systems, an intellectual frontier still largely unexplored. The PI will study such systems using an arsenal of modern analytical and numerical tools.The projects will involve a graduate student, who will be trained in analytical and computational methods, as well as in scientific communication, via immersion in a collaborative environment working on open problems at the frontier of condensed matter physics. It will also allow the student to travel to and participate in conferences and schools, and thus engage with the broader scientific community. The skills that will be developed are essential for many successful careers in STEM fields.TECHNICAL SUMMARYThis award supports fundamental research and education aimed at understanding properties of correlated electrons in novel quantum materials. The long-term goal is to use such understanding to design new materials and structures with desired functionalities, as well as to advance theoretical tools needed for predictive analysis. The PI's research and educational activity is centered on the theoretical description of moire materials, including twisted bilayer graphene. Such systems combine modern notions of topologically nontrivial band structure and strong electron correlations. Broadly, the main thrust of the project is to understand the underlying mechanism responsible for -- and the nature of -- the correlated insulator phases observed at commensurate fillings of the narrow bands, and the nearby superconductivity observed at generally incommensurate fillings in various moire structures. The PI will study the problem using an arsenal of analytical and numerical tools, including strong-coupling expansions, variational mean-field theory, and density-matrix renormalization group. An important part of the project is the simultaneous development of simplified models capturing the physical essence of the findings obtained within more numerically involved techniques. Such models will engender deeper understanding of the physics playing out in existing materials, and will also allow greater flexibility in further qualitative predictions not easily achieved numerically.The projects will involve a graduate student, who will be trained in analytical and computational methods, as well as in scientific communication, via immersion in a collaborative environment working on open problems at the frontier of condensed matter physics. It will also allow the student to travel to and participate in conferences and schools, and thus engage with the broader scientific community. The skills that will be developed are essential for many successful careers in STEM fields.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.