Higher-order topological insulators

The striking feature of three-dimensional topological insulators is their bulk-boundary correspondence: while insulating in the bulk of the crystal, they feature robust conducting states at their surface. The appearance of these surface states can be predicted from the knowledge of the bulk electronic structure. I am going to discuss a new class of three-dimensional topological insulators, which generalize this bulk-boundary correspondence. These so-called higher-order topological insulators have gaps in the bulk and on their surfaces, but support topologically protected conducting modes on their hinges. I will present the theory for cases with chiral and helical hinge modes. The experimental realization in elementary bismuth will be discussed, where scanning-tunneling spectroscopy as well as Josephson interferometry measurements indicate the existence of hinge channels. Finally, I will comment on defect bound states in higher-order topological insulators.