  Condensed matter materials have shown great potential in searching for light
dark matter (DM) via detecting the phonon or magnon signals induced by the
scattering of DMs off the materials. In this paper, we study the possibility of
detecting electromagnetic form factors of fermionic DM and axion-like particles
(ALPs) using superfluid Helium-4. The phonon induced by a sub-GeV fermionic DM
scattering off the superfluid can be described using the effective field theory
with the interaction between DM and the bulk ${}^4$He. Signals arising from the
electromagnetic form factors of light DM in the presence of an external
electric field are calculated. Projected constraints on the charge radius, the
anapole moment, and the magnetic moment of the DM are derived with 1
kg$\cdot$year exposure. The phonon signal induced by the scattering of ALPs off
the superfluid is also calculated, which can put competitive and the first
direct detection bounds on ALP-photon-dark photon couplings in the projected
experiments.
