Untangling Electrons in Crystals

The fundamental goal of condensed matter physics is to understand, classify, and discover phases of matter. In every day life, we encounter phases such as solids, liquids and gases. These describe the arrangement of atoms. But more exotic phases result from the behavior of electrons. A fascinating example is the topological insulator, which has the unusual property of being an insulator on its inside, and a metal on its surface. Though we do not encounter topological insulators every day, they may enable energy-efficient technologies.

Yet, while over 200,000 crystalline solids are known, only a few hundred have been identified as topological insulators. This begs the question: are these materials just rare, or do we not know where to look for them? This talk presents a new theory—topological quantum chemistry—that unifies traditional concepts in physics and chemistry with mathematical tools such as symmetry and topology, enabling a deeper understanding of topological insulators and the prediction of yet-undiscovered topological materials.