Modulation signals of solar reflected dark matter in crystal-based detectors

The scattering of light dark matter (DM) off thermal electrons within the Sun generates a ``fast'' sub-component of the DM flux that can be detected in underground direct detection experiments. This ``fast'' sub-component has a specific origin-namely, from the Sun. In this study, we demonstrate that in detectors composed of single crystals, like in Bragg scattering, the collision rate and energy deposition are influenced by the angle between the momentum of the incoming DM and the orientations of the crystallographic axes. This results in a directional modulation of the signal. We calculate the magnitude of directional modulations for both germanium and silicon crystals, considering both the contact interaction and light mediator scenarios. Our findings indicate that for the contact interaction case, the daily modulation of the collision rate is approximately 0.1% of the total, while in the light mediator case, it can reach as high as 30%. Additionally, our analysis suggests that future ton-scale crystal detectors will be able to explore the freeze-in DM regime with $m_{\rm{DM}} \sim 0.1 \rm{MeV}$.