Topology on a new facet of bismuth*

Bismuth-based materials have been instrumental in the development of topological physics, even though bulk bismuth itself has been long thought to be topologically trivial. A recent study has, however, shown that bismuth is in fact a higher-order topological insulator featuring one-dimensional (1D) topological hinge states protected by three-fold rotational and inversion symmetries. In this talk, we uncover another hidden facet of the band topology of bismuth by showing that bismuth is also a first-order topological crystalline insulator protected by a two-fold rotational symmetry. As a result, its $(1\bar{1}0)$ surface exhibits a pair of gapless Dirac surface states. Remarkably, these surface Dirac cones are unpinned in the sense that they are not restricted to locate at specific $k$ points in the $(1\bar{1}0)$ surface Brillouin zone. These unpinned 2D Dirac surface states could be probed directly via various spectroscopic techniques. Our analysis also reveals the presence of a distinct, previously uncharacterized set of 1D topological hinge states protected by the two-fold rotational symmetry. Our study thus provides a comprehensive understanding of the topological band structure of bismuth.