NSF/DMR-BSF: Theory of Quantum Materials

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NONTECHNICAL SUMMARYThis award supports theoretical research on atomic scale models of interacting electrons and ions in so-called "quantum materials". Some examples of quantum materials include high-temperature superconductors, two layers of carbon atom sheets on top of each other with a relative twist angle, and materials in which the electron-electron interaction energies are much larger compared to their kinetic energies. These systems typically have many scientifically interesting and technologically important properties that emerge collectively from the complex interactions of their constituent entities as a whole. While the specific properties of quantum materials depend sensitively on their structure and quantum chemistry, certain emergent properties, such as high-temperature superconductivity, can be understood from a more general quantum statistical mechanical perspective. The advantage of such a perspective is its generality, and ideally the promise that it could lead to mathematically well-controlled solutions to paradigmatic models that can serve as the framework for a qualitative understanding of the properties of interesting materials. In this project, the principle investigator will study an array of such atomic scale models on material systems and topics that are at the heart of contemporary condensed matter physics.Recent advances in the theory of quantum materials have had, and will continue to have, both practical and conceptual implications beyond physics. The issues involved in this project are central across a broad range of subfields of physics including the traditional study of quantum materials in a condensed matter context, studies of strongly interacting matter in a string theory and quantum gravity context, studies of cold atom condensates in atomic-molecular-and-optical physics context, and as a venue for exploring and exploiting new ideas in quantum information theory. More generally, quantum materials play an important role in a range of more applied sciences, and hence, increased understanding of the problems to be investigated in this project has the potential to influence broader developments in science and technology as well. Students and postdocs, who will be involved in this research, are likely to develop into future leaders of the field, while those who do not continue in physics will nonetheless develop skills which will allow them to make contributions to society in a broader context.TECHNICAL SUMMARYThis award supports theoretical research on atomic scale models of interacting electrons and ions in quantum materials on several fronts. One focus is on the microscopic mechanisms that give rise to the various broken symmetry phases that populate the low temperature reaches of the phase diagrams of such materials, especially superconductivity and charge density waves. The research will focus on the significant non-universal, but robust, properties that determine the basic energy and temperature scales which characterize these phases, including transition temperatures. Another focus of interest are transport properties of strongly interacting systems in regimes of temperature and interaction strengths in which the quasiparticle paradigm breaks down. While the breakdown of the Fermi liquid paradigm is apparent in a variety of experimentally interesting material systems, it is likely that not all non-Fermi-liquid metals are the same. An important goal is to identify basic features that allow such states to be identified more by what they are than by what they are not, and to make progress on understanding these behaviors by identifying solvable model problems that exhibit similar properties. Finally, an important component of the research will be a continuation and extension of earlier studies of the universal properties of systems near a quantum critical point at which the nature of the ground-state order changes qualitatively, such as in quantum critical phenomena in metallic systems. Recent advances in the theory of quantum materials have had, and will continue to have, both practical and conceptual implications beyond physics. The issues involved in this project are central across a broad range of subfields of physics including the traditional study of quantum materials in a condensed matter context, studies of strongly interacting matter in a string theory and quantum gravity context, studies of cold atom condensates in atomic-molecular-and-optical physics context, and as a venue for exploring and exploiting new ideas in quantum information theory. More generally, quantum materials play an important role in a range of more applied sciences, and hence, increased understanding of the problems to be investigated in this project has the potential to influence broader developments in science and technology as well. Students and postdocs, who will be involved in this research, are likely to develop into future leaders of the field, while those who do not continue in physics will nonetheless develop skills which will allow them to make contributions to society in a broader context.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.