Probing low-mass dark matter from sub-MeV to sub-GeV with germanium-based quantum phononic spectroscopy

Abstract: We present a germanium phonon-to-charge transducer that integrates a slow-phonon phononic-crystal (PnC) region with radio-frequency quantum point-contact (RF-QPC) readout at 4 K, and we evaluate its dark-sector reach. A calibrated signal-collection model, which combines geometric guiding, propagation survival, and multiplicity-assisted primary-phonon detection, provides selection-corrected thresholds in the $10^{-3}$-$10^{-2}$~eV range and a background model informed by nanosecond timing gates and GHz-band power-spectral-density windows. Under standard halo assumptions, a 100 g module achieves projected sensitivity to DM-electron and DM-nucleon scattering at recoil energies below $10^{-2}$~eV, probing cross sections below $10^{-43}\,\mathrm{cm}^{2}$ for $m_χ\in [0.01,100]~\mathrm{MeV}/c^{2}$ (with efficiencies and thresholds folded in). We present sensitivities for both heavy-mediator ($F_{\rm DM}=1$) and light-mediator ($F_{\rm DM}\propto 1/q^{2}$) benchmarks, quantify dominant systematics (threshold, phonon quality factor $Q$, and bulk defect densities), and outline a staged program toward kg$\cdot$yr exposures that begins to test models approaching the solar CE$ν$NS background.