  We present a unified theoretical framework for computing spin-independent
direct detection rates via various channels relevant for sub-GeV dark matter --
nuclear recoils, electron transitions and single phonon excitations. Despite
the very different physics involved, in each case the rate factorizes into the
particle-level matrix element squared, and an integral over a target material-
and channel-specific dynamic structure factor. We show how the dynamic
structure factor can be derived in all three cases following the same
procedure, and extend previous results in the literature in several aspects.
For electron transitions, we incorporate directional dependence and point out
potential daily modulation signals in anisotropic target materials. For single
phonon excitations, we present a new derivation of the rate formula from first
principles for generic spin-independent couplings, and include the first
calculation of phonon excitation through electron couplings. We also discuss
the interplay between single phonon excitations and nuclear recoils, and
clarify the role of Umklapp processes, which can dominate the single phonon
production rate for dark matter heavier than an MeV. Our results highlight the
complementarity between various search channels in probing different kinematic
regimes of dark matter scattering, and provide a common reference to connect
dark matter theories with ongoing and future direct detection experiments.
