Directional detection of light dark matter with polar materials

We consider the direct detection of dark matter (DM) with polar materials, where single production of optical or acoustic phonons gives an excellent reach to the scattering of sub-MeV DM for both scalar and vector mediators. Using density functional theory, 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. Nonthermal dark photon DM in the meV--eV mass range can also be effectively absorbed in polar materials.