Optical spatial dispersion via Wannier interpolation

We present a numerical implementation, based on Wannier interpolation, of a Kubo-Greenwood formalism for computing the spatially dispersive optical conductivity in crystals at first order in the wave vector of light. This approach is more efficient than direct $\textit{ab initio}$ methods because, with less computational cost, it allows for a much finer sampling of reciprocal space, resulting in better resolved spectra. Moreover, Wannier interpolation avoids errors arising from truncation of the sums over conduction bands when evaluating the spatially dispersive optical matrix elements. We validate our method by computing the optical activity spectrum of selected crystals, both polar (GaN) and chiral (trigonal Te, trigonal Se, and $\alpha$-quartz), and comparing with existing literature.