A new spin on topological material modeling from topological quantum chemistry

The past several years have seen a flurry of activity in the prediction, modeling, and discovery of new topological materials. Much of this activity has been enabled by symmetry-based approaches to band theory such as the theory of topological quantum chemistry and symmetry-based indicators of band topology, allowing for the discovery of multifold nodal semimetals, higher-order topological insulators, and fragile topology. More than just a classification tool, however, symmetry-based approaches can also be used to model observables in topological materials. In this talk, I will show how topological quantum chemistry allows us to predict new phenomena in topological insulators and semimetals. Focusing first on magnetic materials, I will show how magnetic space group theory leads us to predict a novel non-dissipative viscosity coefficient in magnetic topological semimetals and allows us to compute its value in simple tight-binding models. Next, I will show how we can gain new insights into dynamical axion electrodynamics in Weyl charge-density wave systems using simple models built from magnetic band representations. Turning to time-reversal invariant systems, I will apply position space tools to the study of bulk signatures of higher order topological insulators and topological semimetals. For centrosymmetric systems I will show how higher order topology manifests in the bulk spin texture. Finally, for non-centrosymmetric semimetals I will show how topological quantum chemistry sheds light on the interplay between spin, chirality, and band topology.