Computing topological invariants without inversion symmetry

We consider the problem of calculating the weak and strong topological indices in noncentrosymmetric time-reversal ($\mathcal{T}$) 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 $\mathcal{T}$ symmetry of the system and allows for a definition of the ${\mathbb{Z}}_{2}$ invariant in terms of time-reversal polarization. In 3D we apply the 2D approach to $\mathcal{T}$-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.