  We consider a model of sub-GeV dark matter whose interaction with the
Standard Model is mediated by a new vector boson (the dark photon) which
couples kinetically to the photon. We describe the possibility of constraining
such a model using a superfluid He-4 detector, by means of an effective theory
for the description of the superfluid phonon. We find that such a detector
could provide bounds that are competitive with other direct detection
experiments only for ultralight vector mediator, in agreement with previous
studies. As a byproduct we also present, for the first time, the low-energy
effective field theory for the interaction between photons and phonons.
