  We consider the direct detection of dark matter (DM) with polar materials,
where single production of optical or acoustic phonons gives excellent reach to
scattering of sub-MeV DM for both scalar and vector mediators. Using Density
Functional Theory (DFT), we calculate the material-specific matrix elements,
focusing on GaAs and sapphire, and show that DM scattering in an anisotropic
crystal such as sapphire features a strong directional dependence. For example,
for a DM candidate with mass 40 keV and relic abundance set by freeze-in, the
daily modulation in the interaction rate can be established at 90\% C.L. with a
gram-year of exposure. Non-thermal dark photon DM in the meV - eV mass range
can also be effectively absorbed in polar materials.
