  The search for sub-GeV dark matter (DM) particles via electronic transitions
in underground detectors attracted much theoretical and experimental interest
in the past few years. A still open question in this field is whether
experimental results can in general be interpreted in a framework where the
response of detector materials to an external DM probe is described by a single
ionisation or crystal form factor, as expected for the so-called dark photon
model. Here, ionisation and crystal form factors are examples of material
response functions: interaction-specific integrals of the initial and final
state electron wave functions. In this work, we address this question through a
systematic classification of the material response functions induced by a wide
range of models for spin-0, spin-1/2 and spin-1 DM. We find several examples
for which an accurate description of the electronic transition rate at DM
direct detection experiments requires material response functions that go
beyond those expected for the dark photon model. This concretely illustrates
the limitations of a framework that is entirely based on the standard
ionisation and crystal form factors, and points towards the need for the
general response-function-based formalism we pushed forward recently [1,2]. For
the models that require non-standard atomic and crystal response functions, we
use the response functions of [1,2] to calculate the DM-induced electronic
transition rate in atomic and crystal detectors, and to present 90% confidence
level exclusion limits on the strength of the DM-electron interaction from the
null results reported by XENON10, XENON1T, EDELWEISS and SENSEI.
