Computing topological invariants without inversion symmetry

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 Z₂ 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.