Spatially dispersive optical effects in solids via Wannier interpolation

The response of materials to light is described by the optical conductivity, which, in spatially dispersive media, depends on the wave vector q of the incident electromagnetic wave. The first-order term in q, which requires broken inversion symmetry, describes natural optical activity and magneto-optical effects. In this work, we implement a Wannier-interpolation scheme for computing the spatially dispersive optical conductivity within the Kubo formalism, with special attention to  phenomena that also require broken time-reversal symmetry. This method is particularly well suited for accurately treating interband optical transitions in small-gap semiconductors, where dense sampling in reciprocal space — difficult to achieve with direct ab initio methods — is essential for resolving the features of the response spectrum. After testing our implementation by computing the polar optical activity of GaN, we present preliminary results on the magneto-optical spatial-dispersive effects in the linear magnetoelectric Cr₂O₃.