Geometric aspects of optical and transport phenomena in gapless topological phases

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NONTECHNICAL SUMMARYThis award supports theoretical research and education on the interplay of geometry and topology with the quantum mechanics, and consequence for the optical and transport properties of materials. Unlike baseballs and other classical objects with motion described by trajectories, electrons in materials are described quantum mechanically by mathematical wave functions. The study of wave functions of systems of many electrons reveals distinct classes leading to a new classification of electronic phases of matter - one that goes beyond the usual classifications based, for example, on the states of aggregation, or on the existence of macroscopic order, like magnetization. These kinds of electronic phases are referred to as topologically, or more broadly, geometrically nontrivial. In this project, the PI aims to bridge the gap between the pure classification of electronic phases and the physical properties of the phases. The PI will focus on developing theory to describe the materials' optical and transport properties, for example, how well the material can conduct electricity or reflect light. The PI will investigate various optical and transport properties in chiral materials.The research is focused on topological phases in chiral materials. A chiral material has a "handedness", so it is distinct from its mirror image. Chirality may arise because of the way the atoms are arranged in the crystal, or induced by external perturbations, like electromagnetic fields, or strain. Regardless of its origin, chirality strongly affects the quantum mechanical behavior of electrons in a material, and so, its experimentally measurable and technologically relevant properties. Examples include magnetization induced by an electron current, and rotation of the plane of transmitted or reflected polarized light. This award also supports educational and training activities, aimed at improving the STEM education in the state of Utah. The primary effort will be directed at the supervision of summer research of high school physics teachers; creation of an extracurricular club for high school students, aimed at introducing its members to collaborative solving of research-type problems in physics; implementation of modern teaching techniques with particular focus on creating an inclusive environment for students from underrepresented groups. Further integration of the research and educational activities will be accomplished through supervision of graduate and undergraduate research, and establishing a journal club for graduate students.TECHNICAL SUMMARYThis award supports theoretical research and education on optical and transport properties of materials with nontrivial band geometry. The objective of this proposal is to provide theoretical insights into electrodynamic, hydrodynamic, and transport properties of disordered gapless topological phases, and to develop new theoretical approaches that would help reveal various geometric aspects of electron behavior in experiment. The research involves three main directions, integrated into an effort aimed at understanding optical and transport phenomena in gapless systems:1. Nonlocal electrodynamics and electron hydrodynamics of gapless topological phases, including the theory of chiral electron hydrodynamics and the chiral vortical effect in crystals. One focus will be on the study of the anomalous Hall effect in the hydrodynamic regime.2. Theory of nonlocal transport in disordered chiral metals. The activity will include a study of the extrinsic contributions to the dynamic chiral magnetic effect; investigation of nonperturbative instanton physics in disordered Dirac systems; development of nonlocal transport theory in nonuniform and strained topological systems.3. Nonlinear optical and magneto-optical phenomena in nonequilibrium states of Weyl and Dirac metals. The study will focus on the topological aspects of nonlinear phenomena in Weyl systems, including topological mechanisms of magneto-photovoltaic effect in Weyl semimetals, and building the theory of current-induced magneto-optical phenomena in metals with nontrivial band geometry.The research will be carried out using a wide spectrum of techniques: quantum kinetic equation for multi-band systems, field-theoretic approaches to itinerant disordered systems, numerical modelling, and ab initio studies. This award also supports educational and training activities, aimed at improving the STEM education in the state of Utah. The primary effort will be directed at the supervision of summer research of high school physics teachers; creation of an extracurricular club for high school students, aimed at introducing its members to collaborative solving of research-type problems in physics; implementation of modern teaching techniques with particular focus on creating an inclusive environment for students from underrepresented groups. Further integration of the research and educational activities will be accomplished through supervision of graduate and undergraduate research, and establishing a journal club for graduate students.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.