Low-Energy Signals from the Formation of Dark Matter-Nuclear Bound States

Dark matter particles may bind with nuclei if there exists an attractive force of sufficient strength. We show that a dark photon mediator of mass $\sim (10 - 100)$ MeV that kinetically mixes with Standard Model electromagnetism at the level of $\sim 10^{-3}$ generates keV-scale binding energies between dark matter and heavy elements, while forbidding the ability to bind with light elements. In underground direct detection experiments, the formation of such bound states liberates keV-scale energy in the form of electrons and photons, giving rise to mono-energetic electronic signals with a time-structure that may contain daily and seasonal modulations. We show that data from liquid-xenon detectors provides exquisite sensitivity to this scenario, constraining the galactic abundance of such dark particles to be at most $\sim 10^{-18} - 10^{-12}$ of the galactic dark matter density for masses spanning $\sim (1 - 10^5)$ GeV. However, an exponentially small fractional abundance of these dark particles is enough to explain the observed electron recoil excess at XENON1T.