Computing topological invariants without inversion symmetry

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.

revised version, accepted to PRB

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Cited by in corpus (6)

• Weyl semimetals from noncentrosymmetric topological insulators
• Direct measurement of topological invariants in optical lattices
• Spin texture on the Fermi surface of tensile strained HgTe
• Topological Insulator to Dirac Semimetal Transition Driven by Sign Change of Spin-Orbit Coupling in Thallium Nitride
• Three-dimensional topological insulators: A review on host materials
• Spin-orbit spillage as a measure of band inversion in insulators