Topology of ${\mathrm{SmB}}_{6}$ revisited by means of topological quantum chemistry

The mixed-valence compound with partially filled samarium flat bands hybridizing with conduction bands is a paramount example of a correlated topological heavy-fermion system. In this study, we revisit the topology of within the formalism of topological quantum chemistry and symmetry-based indicators. Based on this approach, we reach a detailed classification of the material's topology, and we reformulate the origin of topology in terms of band representations. We corroborate these aspects by constructing a minimal TB model that is consistent with all the symmetries of the system and is able to reproduce the topology of the material. We finally unveil the previously overlooked formation of multiple topological gaps, and we discuss its implications for experiments.