Mesoscopic and many-body effects in topological phases of matter

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NONTECHNICAL SUMMARYThis award supports theoretical research and education on topological phases of electrons in materials. Electrons have an intrinsic property called spin where it appears as if the electron spins like a tiny top. The spin of the electron is also connected to its intrinsic magnetic properties; it behaves as though it was a tiny bar magnet. As an electron moves through a material it will experience a magnetic field from the atomic cores in the lattice as a consequence of the theory of relativity. The interaction of the electron with this magnetic field gives rise to the spin-orbit interaction.Topological insulators are a consequence of strong spin-orbit interaction which leads to material that is insulating in the bulk but has metallic states that cover the surface and edges and robust to defects and imperfections. The PI will investigate the conduction of electricity and the dynamics of electrons, including when a high magnetic field is applied to topological insulators and Weyl semimetals which are three dimensional materials that have electronic states analogous to those in atomically thin sheets of graphene. The PI will study new phenomena related to strong spin-orbit interaction. The main objective of the research is to provide theoretical insights into how electrons move through topological phases, how they interact with the atomic lattice and how they interact with other in topological phases. The main focus is on the electron-atomic lattice interaction and collective modes in Weyl semimetals, transport of interacting electrons on disordered surfaces of topological insulators, and thermodynamic and transport properties in low-dimensional systems. This award also supports education and outreach activities. A special focus will be given to ensuring that equal research and education opportunities exist for women and minorities, and encouraging students from underrepresented groups to participate in research. The PI aims to develop a student Olympiad program on physics. Further integration of research and educational activities will be reached through providing training and supervision to graduate and undergraduate students, and developing a graduate course sequence on modern condensed matter physics.TECHNICAL SUMMARYThis award supports theoretical research and education with the aim to understand many-body and mesoscopic phenomena in topological phases of matter. The primary objective of the study is to consider new phenomena related to topological insulators and Weyl semimetals, as well as Mott insulators with strong spin-orbit coupling and advance the basic physics of phases with nontrivial topology, beyond noninteracting electrons in ideal crystalline lattices. The PI aims to pursue research directions in the following areas: 1.) Collective modes and their interaction in gapless topological phases: Cooperative behavior of particles is often a defining property of an electronic phase. The PI will consider electron-phonon and electron-electron interactions in Weyl semimetals, and extract the experimental signatures provided by the resultant collective modes to facilitate the experimental discoveries of Weyl systems. 2.) Signatures of topological transitions in gapless systems, in particular, the theory of the magnetic breakdown - tunneling of electrons between electron orbits in momentum space in strong magnetic fields - in a system with non-trivial Fermi surface topology. This line of research will promote magneto-oscillation phenomena into a spectroscopic tool capable of discovering topological transitions in various band structures. 3.) Physics of topological surfaces: nonlinear transport, electron-electron interaction and mesoscopic physics. This direction involves considering magnetoelectric, mesoscopic and nonlinear phenomena unique to two-dimensional electron gases on topological surfaces. 4.) Mott insulators with strong spin-orbit interaction. This PI will address the question of how the physics of the Mott metal-insulator transition is modified by strong spin-orbit interaction. It will be argued that the heterostructures based on the Topological Mott insulators are useful model system for the realistic transition metal oxide heterostructures.The methods of the project will include standard tools of many-body theory, including the Keldysh diagrammatic technique, and quantum kinetic equation approach to quantum transport. The results of the program will be used to provide guidance for materials research, paying particular attention to realistic aspects of systems with nontrivial topology.