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

Axion and Dark Fermion Electromagnetic Form Factors in Superfluid He-4