Emergent Relativity in topological materials: Weyl physics in micro and macro

Topological band theory is an extension of conventional band theory to include the characterization of crystalline materials according to the topological properties of their band structure. It extends the simple classification of electronic behavior of insulators and metals to include novel phases such as topological insulators and semimetals (and many more). While topologically insulating states have been around since the early days of the quantum Hall effect, only within the past few years, due to a combination of theoretical experimental and material science breakthroughs, topological semimetals have been realized and explored. These materials feature magnetic monopoles in momentum space and realize old concepts from relativistic QFT such as anomalies of Weyl Fermions. I will describe the connection between the topological nature of band crossings, Weyl Fermions, Chiral anomalies and transport, and how some textbook effects can be realized via lattice defamation in systems ranging from solid state to classical macroscopic metamaterials.