Topological order in quantum materials

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The goal of condensed matter physics is to discover and describe new states of macroscopic matter. The traditional classification of phases of matter is largely based on the idea of broken symmetry: for example crystalline order of atoms in solids breaks translational symmetry of empty space and macroscopic magnetization in ferromagnets breaks rotational symmetry of space. In recent years a new paradigm for classification of phases has been emerging, which emphasizes topological (meaning insensitive to smooth changes in material parameters) properties of the electronic structure of materials, rather than broken symmetries. In this proposal I will outline a research program, aimed towards developing a complete theoretical understanding of the physics of quantum materials with nontrivial topological properties of the electronic structure. The focus of the proposal will be on materials, which are not insulators, and yet possess topologically-nontrivial electronic structure.