Crystal responses to general dark matter-electron interactions
  We develop a formalism to describe the scattering of dark matter (DM)
particles by electrons bound in crystals for a general form of the underlying
DM-electron interaction. Such a description is relevant for direct-detection
experiments of DM particles lighter than a nucleon, which might be observed in
operating DM experiments via electron excitations in semiconductor crystal
detectors. Our formalism is based on an effective theory approach to general
non-relativistic DM-electron interactions, including the anapole, and magnetic
and electric dipole couplings, combined with crystal response functions defined
in terms of electron wave function overlap integrals. Our main finding is that,
for the usual simplification of the velocity integral, the rate of DM-induced
electronic transitions in a semiconductor material depends on at most five
independent crystal response functions, four of which were not known
previously. We identify these crystal responses, and evaluate them using
density functional theory for crystalline silicon and germanium, which are used
in operating DM direct detection experiments. Our calculations allow us to set
90% confidence level limits on the strength of DM-electron interactions from
data reported by the SENSEI and EDELWEISS experiments. The novel crystal
response functions discovered in this work encode properties of crystalline
solids that do not interact with conventional experimental probes, suggesting
the use of the DM wind as a probe to reveal new kinds of hidden order in
materials.
