Title: Band inversion and quasi-nodal spheres

Abstract: Band inversion is a known feature in a wide range of topological insulators characterized by a change of orbital type around a high symmetry point close to the Fermi level. In some cases of band inversion which are due to the hybridization of the Hamiltonian, the presence of quasi-nodal spheres has been detected. In order to understand this phenomenon, we develop a local effective four-fold Hamiltonian which models the band inversion and reproduces the quasi-nodal sphere. This model shows that the change of orbital type along the quasi-nodal sphere characterizes the topological nature of the material. Using K-theoretical methods we show that the parametrized change of orbital type is equivalent to the strong Fu-Kane-Mele invariant. We corroborate these results with ab-initio calculations for the materials YH3 and CaTe where in both cases the signal of the spin Hall conductivity is localized on the quasi-nodal spheres in momentum space. We conclude that the existence of the quasi-nodal spheres is enforced in systems with band inversion due to orbital hybridization.