Directional Dark Matter Detection in Anisotropic Dirac Materials

Dirac materials, because of their small ${\cal O}(\mbox{meV})$ band gap, are a promising target for dark photon-mediated scattering and absorption of light dark matter. In this paper, we characterize the daily modulation rate of dark matter interacting with a Dirac material due to anisotropies in their crystal structure. We show that daily modulation is an ${\cal O}(1)$ fraction of the total rate for dark matter scattering in the Dirac material ZrTe$_5$. When present, the modulation is dominated by the orientation of the material's dielectric tensor with respect to the dark matter wind, and is maximized when the crystal is oriented such that the dark matter wind is completely aligned with the largest and smallest components of the dielectric tensor at two different times of the day. Because of the large modulation, any putative dark matter scattering signal could be rapidly verified or ruled out by changing the orientation of the crystal with respect to the wind and observing how the daily modulation pattern changes.