The Role of Symmetries in Dark Matter Detector Design

Abstract

Anisotropic materials have emerged as promising candidates for the next generation of sub-GeV dark matter direct detection experiments, because their intrinsic directionality gives rise to a daily modulation signal as the detector rotates with respect to a dark matter wind. Predicting the shape of the modulation signal requires knowledge of the electronic excited states: however, we show that the amplitude of the modulation can be estimated using only the symmetries of the material. By decomposing the finite momentum dark matter--electron scattering form factor into spherical harmonics, we show that the 230 crystallographic space groups collapse to just 5 classes, distinguished by their suppression of the quadrupole modes of the squared form factor. We apply our symmetry-projection framework to the special case of molecular crystals, and derive an accurate group-theoretic estimator for the loss of daily modulation signal due to crystallisation, which depends only on the symmetries and relative orientations of the molecules within the crystal. Finally, we demonstrate that these estimates are linearly proportional to the absolute magnitude of the modulation signal, allowing us to rank molecular crystals without the need for expensive electronic structure calculations. Together, these results provide a fast and interpretable route to large-scale screening of anisotropic materials for directional dark matter detection.