Computing topological invariants without inversion symmetry

TL;DR

This paper introduces a new method for calculating topological invariants in noncentrosymmetric insulators using hybrid Wannier functions, applicable in 2D and 3D, and demonstrated on GeTe and HgTe.

Contribution

The authors develop a gauge-based approach to compute Z2 topological invariants without inversion symmetry, simplifying implementation in ab initio calculations.

Findings

Successfully applied to GeTe and HgTe under strain

Provides a gauge respecting time-reversal symmetry

Easier to implement in computational packages

Abstract

We consider the problem of calculating the weak and strong topological indices in noncentrosymmetric time-reversal (T) invariant insulators. In 2D we use a gauge corresponding to hybrid Wannier functions that are maximally localized in one dimension. Although this gauge is not smoothly defined on the two-torus, it respects the T symmetry of the system and allows for a definition of the Z_2 invariant in terms of time-reversal polarization. In 3D we apply the 2D approach to T-invariant planes. We illustrate the method with first-principles calculations on GeTe and on HgTe under [001] and [111] strain. Our approach differs from ones used previously for noncentrosymmetric materials and should be easier to implement in ab initio code packages.