Higher-Order Topological Phases

Frank Schindler (UZH)

The mathematical field of topology has become a framework to describe the low-energy electronic structure of crystalline solids. A typical feature of a bulk insulating three-dimensional topological crystal are conducting two-dimensional surface states. This constitutes the topological bulk-boundary correspondence. In my talk, I will explain how one can extend the notion of three-dimensional topological insulators to systems that host no gapless surface states, but exhibit topologically protected gapless hinge states. I furthermore present experimental evidence establishing that the electronic structure of bismuth, an element consistently described as topologically trivial, is in fact topological and follows this generalized bulk-boundary correspondence of higher-order. The type of hinge states discussed here may be used for lossless electronic transport, spintronics, or — when proximitized with superconductivity — for topological quantum computation.