Multiple topological facets of Bismuth

Bismuth, due to its large spin-orbit coupling, plays a fundamental role in many topological materials. Yet the topological classification of pure Bismuth has remained, thus far, rather ambiguous. While some theoretical models indicate its trivial topological nature, other theoretical and experimental studies suggest non-trivial topological classifications, such as a strong or a higher order topological insulator. I will explain the origin for this ambiguity and present scanning tunneling microscopy data in which we resolve the topological classification of Bismuth, as a strong topological insulator with weak indices, by spectroscopically mapping the response of its boundary modes to a topological defect in the form of a screw dislocation [1]. Next, I will present our work on Bi₂TeI, which consists of a stack of Bi-bilayers. Our data shows that in this form the topological nature is of a dual topological insulator [2]. Bi₂TeI hosts a weak topological insulator surface state on its ‘side’ facets and a topological crystalline insulator surface state protected by mirror symmetry on its top and bottom facets. We visualize the topological crystalline surface states and show their sensitivity to mirror symmetry-breaking as well as the one dimensional channels, derived from the 2D weak topological insulator states, which run along step-edges. We studied the coexistence of the two types of states on step-edges, where both facets join. Our measurements reveal that the two types of states remain well decoupled from one another due to separation in momentum space and in energy. We show, however, that this protection is susceptible to strong disorder.

[1] Nayak et. al., Sci. Adv., 5, eaax6996 (2019)
[2] Avraham et. al. Nature Materials 19, 610 (2020)