Abstract
We consider the direct detection of dark matter (DM) with polar materials, where single production of optical or acoustic phonons gives excellent reach to scattering of sub-MeV DM for both scalar and vector mediators. Using Density Functional Theory (DFT), we calculate the material-specific matrix elements, focusing on GaAs and sapphire, and show that DM scattering in an anisotropic crystal such as sapphire features a strong directional dependence. For example, for a DM candidate with mass 40 keV and relic abundance set by freeze-in, the daily modulation in the interaction rate can be established at 90\% C.L. with a gram-year of exposure. Non-thermal dark photon DM in the meV - eV mass range can also be effectively absorbed in polar materials.
Highlights
Sub-GeV dark matter (DM) has become an important direction in dark matter searches in recent years
Except for the simplest of crystals, most materials have gapped lattice vibrations with energies between 10 meV and 100 meV. This matches the typical kinetic energy of DM in the Galaxy for masses between the ∼10 keV warm DM limit and up to 1 MeV, allowing for single optical phonons to be excited in DM collisions with the crystal
We used density functional theory (DFT) methods to compute the rate for DM to create an optical phonon in GaAs or sapphire in the zero temperature limit
Summary
Sub-GeV dark matter (DM) has become an important direction in dark matter searches in recent years. A DM particle with mass less than ∼1 MeV has a de Broglie wavelength that is longer than the interparticle spacing in typical materials, implying that the DM effectively couples to the collective excitations of atoms (phonons) in the target Such DMphonon scattering processes have different kinematics and allow for a greater amount of energy to be extracted from the DM than for scattering off a single free nucleus. We study a more complex material, sapphire, which we argue is better suited for direct detection To this end we employ more advanced numerical condensed matter techniques, notably density functional theory (DFT), which allows us to accurately compute the scattering rate in sapphire and to validate the analytic treatment of GaAs used in Ref. For a brief description of the experimental setup and estimates of the backgrounds we refer the reader to Ref. [34]
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