Coherence from Randomness: Sub-keV Dark Matter Scattering off Random, Heterogeneous Materials

The sub-keV mass range has long posed a challenge for the direct detection of dark matter via elastic scattering. In this Letter, we propose a new mechanism in which dark matter, assumed to be quadratically coupled to SM particles, scatters from random heterogeneous materials with intrinsic density fluctuations, yielding an enhanced coherent response. This effect can substantially increase the total scattering rate and induce measurable accelerations of the target. Using this idea, we derive new constraints from the MICROSCOPE mission that extend into previously unexplored parameter space for sub-keV dark matter, probing cross sections down to $\sim 4\times {10}^{-38}\mathrm{c}{\mathrm{m}}^2$.