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

D. -M. Mei, N. Budhathoki, S. A. Panamaldeniya, K. -M. Dong, S. Bhattarai, A. Warren, A. Prem, S. Chhetri

TL;DR

This work proposes GeQuLEP, a germanium-based phonon-to-charge sensor that marries a near-surface slow-phonon phononic crystal with RF-QPC readout at 4 K to reach sub-eV thresholds for low-mass dark matter. The authors develop a calibrated efficiency pipeline linking phonon generation, geometric collection, propagation survival, and local capture, enabling selection-corrected thresholds in the $10^{-3}$–$10^{-2}$ eV range and background models informed by timing and GHz PSD windows. Projected sensitivities for DM–electron and DM–nucleon scattering span sub-MeV to sub-GeV DM masses under heavy- and light-mediator benchmarks, with a staged kg·yr plan to approach the solar CEνNS background floor. The work also identifies dominant systematics (threshold, phonon $Q$, and bulk defect densities) and outlines a practical roadmap from cm-scale coupons to kg-scale arrays, highlighting the potential for sub-eV DM discovery and novel solar CEνNS measurements using phonon 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.

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

TL;DR

This work proposes GeQuLEP, a germanium-based phonon-to-charge sensor that marries a near-surface slow-phonon phononic crystal with RF-QPC readout at 4 K to reach sub-eV thresholds for low-mass dark matter. The authors develop a calibrated efficiency pipeline linking phonon generation, geometric collection, propagation survival, and local capture, enabling selection-corrected thresholds in the – eV range and background models informed by timing and GHz PSD windows. Projected sensitivities for DM–electron and DM–nucleon scattering span sub-MeV to sub-GeV DM masses under heavy- and light-mediator benchmarks, with a staged kg·yr plan to approach the solar CEνNS background floor. The work also identifies dominant systematics (threshold, phonon , and bulk defect densities) and outlines a practical roadmap from cm-scale coupons to kg-scale arrays, highlighting the potential for sub-eV DM discovery and novel solar CEνNS measurements using phonon 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 -~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 ~eV, probing cross sections below for (with efficiencies and thresholds folded in). We present sensitivities for both heavy-mediator () and light-mediator () benchmarks, quantify dominant systematics (threshold, phonon quality factor , and bulk defect densities), and outline a staged program toward kgyr exposures that begins to test models approaching the solar CENS background.

Paper Structure

This paper contains 73 sections, 43 equations, 12 figures, 1 table.

Table of Contents

  1. Introduction
  2. Contributions
  3. Organization
  4. Concept and Design
  5. Localized charge states in Ge: gate-defined and impurity-bound
  6. Gate-defined dots
  7. Impurity-bound dots and dipole states below 10 K
  8. Deformation potential coupling and strain tensor
  9. Phononic crystal for slow-phonon guiding and thermal filtering
  10. Phonon-to-charge transduction with RF-QPC
  11. Integrated design priorities
  12. Phonon Generation and Propagation in Ge
  13. Microscopic picture and spectral scales
  14. Anharmonic down–conversion and ballistic regime
  15. Implications for the GeQuLEP design
  16. ...and 58 more sections

Figures (12)

  • Figure 1: Comparison of DPs in Ge: a gate-defined Gaussian well (solid blue) and an impurity-induced, dipole-bound Gaussian well at 4K (dashed orange). The Gaussian widths are $\sigma=\mathbf{16.2}\,\mathrm{nm}$ (gate-defined) and $\sigma'=\mathbf{12.4}\,\mathrm{nm}$ (impurity-induced). These values were chosen to reproduce the level spacing and localization length expected for our lithographic gate geometry at $\mathbf{4}\,\mathrm{K}$ and acceptor densities in the range $\mathbf{\sim10^{10}}\ \mathrm{cm^{-3}}$. Despite different origins, both yield localized confinement suitable for strong DP coupling and phonon transduction Mei2024Mei2022sanmath.
  • Figure 2: Top: Schematic of the GeQuLEP detector architecture. A high-purity Ge crystal hosts spatially separated p-type (acceptor) and n-type (donor) dipole-bound regions, each co–located with a $\sim\!1µ m$ PnC cavity that traps target GHz phonons and filters thermal backgrounds. Bottom: RF-QPC reflectometry. Phonon–induced charge motion modulates the QPC conductance and is read out as a change in the reflected RF carrier after cryogenic amplification and demodulation.
  • Figure 3: Top: Schematic energy spectrum of primary (LA/TA) phonons produced by a localized recoil in Ge. The initial primary-phonon energy distribution is represented by a log-normal function parameterized by a median energy $E_0$ and logarithmic width $\sigma_{\ln E}$; this empirical fit seeds the cascade model and aids visualization. Bottom: Athermal spectrum after anharmonic down–conversion, with weight shifted to lower–frequency modes that propagate ballistically at cryogenic temperature.
  • Figure 4: Effective refractive index $n_{\mathrm{eff}}$ as a function of phonon frequency $\omega$ based on a synthetic dispersion relation in a SiGe PnC cavity.
  • Figure 5: Phonon absorption cross section $\sigma$ as a function of phonon frequency in the quantum well region. The enhanced absorption at higher frequencies corresponds to the regime where phonons are strongly confined and slowed, increasing the likelihood of interaction with dipole states.
  • ...and 7 more figures