First-principles calculation of Z ₂ topological invariants within the FP-LAPW formalism

In this paper, we report the implementation of first-principles calculations of Z ₂ topological invariants within the full-potential linearized augmented plane-wave (FP-LAPW) formalism. In systems with both time-reversal and spatial inversion symmetry (centrosymmetric), one can use the parity analysis of Bloch functions at time-reversal invariant momenta to determine the Z ₂ invariants. In systems without spatial inversion symmetry (noncentrosymmetric), however, a more complex and systematic method in terms of the Berry gauge potential and the Berry curvature is required to identify the band topology. We show in detail how both methods are implemented in FP-LAPW formalism and applied to several classes of materials including centrosymmetric compounds Bi ₂Se ₃ and Sb ₂Se ₃ and noncentrosymmetric compounds LuPtBi, AuTlS ₂ and CdSnAs ₂. Our work provides an accurate and effective implementation of first-principles calculations to speed up the search of new topological insulators.