On quasi-nodal spheres and the spin Hall effect: the case of YH3 and CaTe

TL;DR

This paper links the localization of spin Hall conductivity on quasinodal spheres to topological insulator properties, using models and ab initio calculations for YH3 and CaTe to demonstrate this relationship.

Contribution

It introduces a local effective Hamiltonian modeling band inversion and quasinodal spheres, connecting spin Hall signals and orbital changes to topological invariants.

Findings

Spin Hall conductivity is localized on quasinodal spheres.

Orbital type change is concentrated along quasinodal spheres.

Localization of spin Hall signals indicates topological insulator behavior.

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 in topological insulators, the existence of quasinodal spheres has been detected, and the change of orbital type is shown to be concentrated along these spheres in momentum space. To understand this phenomenon, we develop a local effective fourfold Hamiltonian that models the band inversion and reproduces the quasinodal sphere. This model shows that the signal of the spin Hall conductivity, as well as the change of orbital type, are both localized on the quasinodal sphere, and moreover, that these two indicators characterize the topological nature of the material. Using K-theoretical methods, we show that the change of orbital type parametrized by an odd clutching function 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 quasinodal spheres in momentum space. We conclude that a nontrivial spin Hall conductivity localized on the points of change of orbital type is a good indicator for topological insulation.