SFB Colloquium

The mathematical field of topology has become a framework for the low-energy electronic structure of crystalline solids. Typical of a bulk insulating three-dimensional topological crystal are conducting two-dimensional surface states. In my talk I will establish that the electronic structure of bismuth, an element consistently described as bulk topologically trivial, is in fact topological and follows a generalized bulk–boundary correspondence of higher-order: not the surfaces of the crystal, but its hinges host topologically protected conducting modes.
I will then move on to discuss the consequences of higher-order topology for materials with crystalline defects. Defects in topological insulators are known to bind anomalous electronic states with two fewer dimensions than the bulk; the most commonly cited examples are the one-dimensional helical modes bound to screw dislocations in weak topological insulators. I will explain how to extend the classification of topological defect states to zero-dimensional modes at defect terminations in higher-order phases.