Theories of Transport and Optical Phenomena in Topological and Correlated Materials

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NONTECHNICAL SUMMARYThis award supports research and education towards understanding fundamental electronic and optical properties of materials. The electronic and optical properties of materials form the basis of much of modern information technology. Newly discovered materials that go under the classification "topological materials" respond in unique ways to applied electric and magnetic fields, and their properties in some cases can be unusually robust to impurities. The first area of the research portion of this project involves developing theoretical methods to predict and understand properties of topological materials, extending previous work in this area. A particular focus is on improving our understanding of the optical properties that appear when materials are studied with intense laser light. The electrons in these materials appear effectively massless, which creates exciting opportunities for basic science and technology.The other main area of research involves understanding how interactions between electrons in a very clean material lead to fluid-like collective motion of electrons, but with interesting differences compared to the flow of a normal fluid, like water. Understanding these hydrodynamical flows of electrons, or of atoms in an atomic gas, could help in the design of future generations of electronic devices.Educational work in this project includes several activities beyond standard professorial classroom teaching and mentoring of graduate students. The PI is working on a textbook that will be a broad introduction to topological materials, building on his previously published lecture notes. He will pursue outreach activities with local science teachers and with the general public, to give them a sense of recent developments in quantum materials. Undergraduates will be involved in introductory research problems to give them a sense of modern research in the above areas.TECHNICAL SUMMARYThis project combines research in two areas of quantum condensed matter physics with related education and outreach activities. One area of research is concerned with gapless topological states of electrons, building on discoveries of new classes of materials and new phenomena that they enable. The other area involves transport in interacting electron metals including hydrodynamic effects that arise in very clean materials. The main broader impacts of the work to be conducted are on education, primarily of the PI's graduate students but also of scientists and non-scientists more generally, and on understanding the physical underpinnings of future quantum technologies.The PI seeks to understand new kinds of electronic behavior in two areas of quantum condensed matter physics. One area involves topological behavior in metallic or gapless materials. Two recently discovered examples with a long history as theoretical possibilities are the topological bulk semimetals of Weyl or Dirac type. These, and more complicated states such as gapless spin liquids, are subjects of active experimental and theoretical study, but what unique properties they might have is not well understood, compared to the insulating case. This research direction builds on promising recent results on how nonlinear optics and other properties not usually thought of as having a topological origin can become unexpectedly strong and even quantized in topological phases. The supported work will advance the understanding of these kinds of materials more systematically, including interaction effects, and find new examples of topological behavior beyond linear response.Hydrodynamics of simple fluids was arguably the first simplified or "effective" theory of an interacting condensed matter system. The second area of research involves how the modified forms of hydrodynamics arising in the long-time, long-distance dynamics of electrons differ from conventional classical hydrodynamics, which describes a simple fluid like ordinary water. Theoretical work in recent years has given several examples of how electron hydrodynamics in materials can differ from ordinary classical single-component hydrodynamics, whether from extra conserved quantities, the long-ranged nature of Coulomb repulsion, or broken symmetries such as time-reversal or inversion. The behavior of quantum fluids is both experimentally important, for actual transport in practical devices made from very clean materials at small length scales, and is connected to deep questions about thermalization and relaxation rates.Educational activities include undergraduate and graduate student supervision and classroom teaching, lecturing at advanced schools and co-authorship of an introductory textbook on topological matter, and outreach to schools and teachers. One goal of the educational work is to bring some of the magic of recent discoveries in quantum condensed matter physics to a broader audience.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.