  Aromatic organic compounds, because of their small excitation energies ~
O(few eV) and scintillating properties, are promising targets for detecting
dark matter of mass ~ O(few MeV). Additionally, their planar molecular
structures lead to large anisotropies in the electronic wavefunctions, yielding
a significant daily modulation in the event rate expected to be observed in
crystals of these molecules. We characterize the daily modulation rate of dark
matter interacting with an anisotropic scintillating organic crystal such as
trans-stilbene, and show that daily modulation is an ~ O(1) fraction of the
total rate for small DM masses and comparable to, or larger than, the ~ 10%
annual modulation fraction at large DM masses. As we discuss in detail, this
modulation provides significant leverage for detecting or excluding dark matter
scattering, even in the presence of a non-negligible background rate. Assuming
a non-modulating background rate of 1/min/kg that scales with total exposure,
we find that a 100 kg yr experiment is sensitive to the cross section
corresponding to the correct relic density for dark matter masses between
1.3-14 MeV (1.5-1000 MeV) if dark matter interacts via a heavy (light)
mediator. This modulation can be understood using an effective velocity scale
v* = Delta E/q*, where Delta E is the electronic transition energy and q* is a
characteristic momentum scale of the electronic orbitals. We also characterize
promising future directions for development of scintillating organic crystals
as dark matter detectors.
