For direct detection of sub-MeV dark matter, a promising strategy is to search for individual phonon excitations in a crystal. We perform an analytic calculation of the rate for light dark matter ($\mathrm{keV}<m_{\mathrm{DM}}<\mathrm{MeV}$) to produce two acoustic phonons through scattering in cubic crystals such as GaAs, Ge, Si, and diamond. The multiphonon rate is always smaller than the rate to produce a single optical phonon, whenever the latter is kinematically accessible. In Si and diamond, there is a dark matter mass range for which multiphonon production can be the most promising process, depending on the experimental threshold.

• Received 22 November 2019
• Accepted 19 January 2020

DOI:https://doi.org/10.1103/PhysRevD.101.036006

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Published by the American Physical Society