First-principles calculation of topological invariants Z2 within the FP-LAPW formalism

TL;DR

This paper presents a detailed implementation of first-principles calculations of Z2 topological invariants within the FP-LAPW formalism, enabling accurate identification of topological insulators with and without inversion symmetry.

Contribution

It introduces a systematic method for calculating Z2 invariants in FP-LAPW formalism applicable to both centrosymmetric and noncentrosymmetric materials.

Findings

Successfully applied to materials like Bi2Se3, Sb2Se3, LuPtBi, AuTlS2, and CdSnAs2

Provides a reliable way to identify topological insulators from first principles

Accelerates the discovery of new topological materials

Abstract

In this paper, we report the implementation of first-principles calculations of topological invariants Z2 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 Z2 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 Bi2Se3 and Sb2Se3 and noncentrosymmetric compounds LuPtBi, AuTlS2 and CdSnAs2. Our work provides an accurate and effective implementation of first-principles calculations to speed up the search of new topological insulators.