  We consider the absorption by bound electrons of dark matter in the form of
dark photons and axion-like particles, as well as of dark photons from the Sun,
in current and next-generation direct detection experiments. Experiments
sensitive to electron recoils can detect such particles with masses between a
few eV to more than 10 keV. For dark photon dark matter, we update a previous
bound based on XENON10 data and derive new bounds based on data from XENON100
and CDMSlite. We find these experiments to disfavor previously allowed
parameter space. Moreover, we derive sensitivity projections for SuperCDMS at
SNOLAB for silicon and germanium targets, as well as for various possible
experiments with scintillating targets (cesium iodide, sodium iodide, and
gallium arsenide). The projected sensitivity can probe large new regions of
parameter space. For axion-like particles, the same current direction detection
data improves on previously known direct-detection constraints but does not
bound new parameter space beyond known stellar cooling bounds. However,
projected sensitivities of the upcoming SuperCDMS SNOLAB using germanium can go
beyond these and even probe parameter space consistent with possible hints from
the white dwarf luminosity function. We find similar results for dark photons
from the sun. For all cases, direct-detection experiments can have
unprecedented sensitivity to dark-sector particles.
