A New Spin on Topological Quantum Chemistry

Dr. Barry Bradlyn
Assistant Professor
The Grainger College of Engineering, Physics
University of Illinois, Urbana, IL

Abstract:

The discovery of topological materials is one of the most transformative recent breakthroughs in condensed matter physics, revealing new conceptual surprises in established topics such as the phases of matter and the behavior of electrons in insulators. Most work on topological insulators has focused on their metallic surface states that are present regardless of how dirty the system. In this talk, I will emphasize that topological materials feature anomalous bulk properties that can be probed by external fields even when the surfaces are gapped. I will first review the theory of topological quantum chemistry, which allows us to characterize topological materials in position space.  I will show how magnetic and nonmagnetic topological insulators protected by crystal symmetries can be characterized in the bulk. Focusing on "higher-order" topological insulators (HOTIs) protected by inversion symmetry, I will review how magnetic HOTIs have a nontrivial bulk magnetoelectric response and anomalous gapped surfaces. Then, by introducing a new notion of spin-resolved band topology, I will show how to extend this understanding to nonmagnetic helical HOTIs.