  Direct-detection experiments sensitive to low-energy electron recoils from
sub-GeV dark matter (DM) interactions will also be sensitive to solar neutrinos
via coherent neutrino-nucleus scattering (CNS), since the recoiling nucleus can
produce a small ionization signal. Solar neutrinos constitute both an
interesting signal in their own right and a potential background to a DM search
that cannot be controlled or reduced by improved shielding, material
purification and handling, or improved detector design. We explore these two
possibilities in detail for semiconductor (Si and Ge) and Xe targets,
considering several possibilities for the unmeasured ionization efficiency at
low energies. For DM-electron-scattering searches, neutrinos start being an
important background for exposures larger than ~1-10 kg-years in Si and Ge, and
for exposures larger than ~0.1-1 kg-year in Xe. For the absorption of bosonic
DM (dark photons and axion-like particles) by electrons, neutrinos are most
relevant for masses below ~1 keV and again slightly more important in Xe.
Treating the neutrinos as a signal, we find that the CNS of B-8 neutrinos can
be observed with ~2 sigma significance with exposures of ~2, 7, and 20 kg-years
in Xe, Ge, and Si, respectively, assuming there are no other backgrounds. We
give an example for how this would constrain non-standard neutrino
interactions. Neutrino components at lower energy can only be detected if the
ionization efficiency is sufficiently large. In this case, observing pep
neutrinos via CNS requires exposures ~10-100 kg-years in Si or Ge (~1000
kg-years in Xe), and observing CNO neutrinos would require an order of
magnitude more exposure. Only Si could potentially detect Be-7 neutrinos. These
measurements would allow for a direct measurement of the electron-neutrino
survival probability over a wide energy range.
