Scanning tunneling microscopy observation of the hinge states of bismuth nanocrystals

The recent application of topological quantum chemistry to rhombohedral bismuth established the nontrivial band structure of this material. This is a second-order topological insulator characterized by the presence of topology-imposed hinge states. The spatial distribution of hinge states and the possible presence of additional symmetry-protected surface states is expected to depend on the crystal shape and symmetries. To explore this issue, we have grown bismuth nanocrystals in the tens of nanometers on the (110) surface of InAs. By scanning tunneling spectroscopy, we mapped the local density of states on all facets and identified the presence of the hinge states at the intersection of all facets. Our paper confirms the classification of bulk bismuth as a second-order topological insulator. We propose that the ubiquitous presence of the hinge states result from their tunnel coupling across the nanometer-sized facets.