Halo-dependent Anharmonic Effects in Collective Excitation for Light Dark Matter Direct Detection

Phonon, the collective excitation of lattice vibration in the crystal, has been put forward as a means to search for light dark matter. However, the accurate modeling of the multi-phonon production process is challenging in theory. The anharmonicity of the crystal must be taken into account, as it has a significant impact on dark matter-nucleus scattering cross section in the low dark matter mass region. Notably, such an effect is sensitive to the velocity distribution of the dark matter halo. In this work, we consider the potential dark matter substructures indicated by the recent Gaia satellite observation and investigate their impact on the anharmonicity of the silicon crystal. By employing the likelihood analysis with the Asimov dataset, we present the expected sensitivity of dark matter-nucleus interactions, which can differ from the standard halo model by a factor of 2-3.