Higher-order topology of Bismuth

Recently, several theoretical and experimental works have proposed bismuth as a solid-state realization of higher-order topological insulators. However, the topological classification of bismuth has been performed based on various symmetry indicators. We show the symmetry indicators are insufficient for defining the bulk topological invariants of sixteen-band, Liu-Allen model. In this work, we perform homotopy classification of non-Abelian Berry’s connections for the Liu-Allen model of bismuth, and compute bulk invariants from the windings of gauge-invariant eigenvalues of straight Wilson lines and planar Wilson loops. We identify a set of topological invariants for the hexagonal planes of bismuth and antimony from the quantized non-Abelian flux, which are crucial for addressing the higher-order topology of such materials.