  A new frontier in the search for dark matter (DM) is based on the idea of
detecting the decoherence caused by DM scattering against a mesoscopic
superposition of normal matter. Such superpositions are uniquely sensitive to
very small momentum transfers from new particles and forces, especially DM with
a mass below 100 MeV. Here we investigate what sorts of dark sectors are
inaccessible with existing methods but would induce noticeable decoherence in
the next generation of matter interferometers. We show that very soft, but
medium range (0.1 nm - 1 $\mu$m) elastic interactions between nuclei and DM are
particularly suitable. We construct toy models for such interactions, discuss
existing constraints, and delineate the expected sensitivity of forthcoming
experiments. The first hints of DM in these devices would appear as small
variations in the anomalous decoherence rate with a period of one sidereal day.
This is a generic signature of interstellar sources of decoherence, clearly
distinguishing it from terrestrial backgrounds. The OTIMA experiment under
development in Vienna will begin to probe Earth-thermalizing DM once sidereal
variations in the background decoherence rate are pushed below one part in a
hundred for superposed 5-nm gold nanoparticles. The proposals by Bateman et al.
and Geraci et al. could be similarly sensitive, although they would require at
least a month of data taking. DM that is absorbed or elastically reflected by
the Earth, and so avoids a greenhouse density enhancement, would not be
detectable by those three experiments. On the other hand, the aggressive
proposals of the MAQRO collaboration and Pino et al. would immediately open up
many orders of magnitude in DM mass, interaction range, and coupling strength,
regardless of how DM behaves in bulk matter.
