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Directional Detectability of Dark Matter With Single Phonon Excitations: Target Comparison

Single phonon excitations are sensitive probes of light dark matter in the keV-GeV mass window. For anisotropic target materials, the signal depends on the direction of the incoming dark matter wind and exhibits a daily modulation. We discuss in detail the various sources of anisotropy, and carry out a comparative study of 26 crystal targets, focused on sub-MeV dark matter benchmarks. We compute the modulation reach for the most promising targets, corresponding to the cross section where the daily modulation can be observed for a given exposure, which allows us to combine the strength of DM-phonon couplings and the amplitude of daily modulation. We highlight Al$_2$O$_3$ (sapphire), CaWO$_4$ and h-BN (hexagonal boron nitride) as the best polar materials for recovering a daily modulation signal, which feature $\mathcal{O}(1 - 100)\%$ variations of detection rates throughout the day, depending on the dark matter mass and interaction. The directional nature of single phonon excitations offers a useful handle to mitigate backgrounds, which is crucial for fully realizing the discovery potential of near future experiments.