All-electron dark matter-electron scattering with random-phase approximation dielectric screening and local field effects

Abstract

Accurate predictions for dark matter-electron scattering in solids require an all-electron treatment together with a faithful description of dielectric screening beyond simple approximations. In particular, local field effects, arising from microscopic inhomogeneities of the electronic response, can significantly modify scattering rates across relevant momentum and energy scales. We present an all-electron framework for computing dark matter-electron scattering rates that incorporates dielectric screening at the random-phase approximation (RPA) level, including local field effects. Using crystalline silicon as a benchmark, we show that local field effects play an important role both at large momentum transfers, spanning multiple Brillouin zones, and at low momentum near the plasmon resonance. We compute electron recoil spectra and projected sensitivities for non-relativistic halo dark matter and for boosted dark matter or other dark-sector particles, which are sensitive to the impact of local field effects in these high and low momentum regimes, respectively. We further present RPA dielectric functions including local field effects for Ge, GaAs, SiC, and diamond, enabling a systematic comparison across target materials. These developments are implemented in the open source code QCDark2.

Figures (18)

• Figure 1: Comparison of the dynamic structure factor (eq. (\ref{['eq:dynamic_structure_factor']}) averaged over angular $\vec{q}$ coordinates) for silicon calculated without local field effects (LFEs) on the left and with LFEs on the right. The red boxes at low momentum transfer and the cyan boxes at intermediate momentum transfer highlight the two areas where LFEs have the largest effect, as discussed further in the text.
• Figure 2: The dielectric function and loss function for Si calculated with QCDark2 in the $q \rightarrow 0$ limit compared to experimental data from Palik. Gaussian smoothing with $\sigma_{\omega} = 0.2$ eV has been applied to the QCDark2 curves for visual clarity. We see excellent agreement in the location of the plasmon peak at 16.6 eV between the RPA calculation and experiment. The inclusion of LFEs broaden the plasmon peak, in better agreement with the data.
• Figure 3: The left plot shows the loss function for all materials we consider, including Si, Ge, GaAs, SiC, and diamond (C), calculated with QCDark2 in the $q \rightarrow 0$ limit. The dotted vertical lines correspond to the locations of the plasmon peak for each material taken from experimental data (Si: Palik, Ge: Marton1967, GaAs: Brockt2000, SiC: Costantini2023, diamond: Serin1998EELS_database). The lighter dashed curves do not include LFEs, while the darker solid curves do include them. The right plot shows the ratio of the dynamic structure factor, $S$, with LFEs to $S$ without LFEs at $q_{\mathrm{diff}}$, the momentum where they differ the most for each material (which is the momentum indicated in the legend). Gaussian smoothing with $\sigma_{\omega} = 0.4$ eV has been applied to all curves for better visual clarity.
• Figure 4: The top row shows the dynamic structure factor of Si with and without LFEs at intermediate momenta compared to experimental data from Weissker2010. The bottom row shows the dynamic structure taken at momentum slices below, inside, and above the cyan box in figure \ref{['fig:S_LFEs']}, where we see significant differences between $S^{\mathrm{noLFE}}$ and $S^{\mathrm{LFE}}$. Above 3 $\alpha m_e$, LFEs greatly suppress the dynamic structure factor until $\sim$ 8 $\alpha m_e$.
• Figure 5: Kinematic limits on $(\omega, q)$ (white dashed curves) for three DM fluxes. The limits are overlaid on the dynamic structure factor (with LFEs) of Si from figure \ref{['fig:S_LFEs']}, showing the two regions most affected by LFEs in the red and cyan boxes. The regions excluded by the kinematic limits are shaded. The left plot shows the lower kinematic limit on halo DM for a DM mass of $m_{\chi} = 1$ GeV, which excludes the low-momentum plasmon region but does include the intermediate-momentum region. The middle and right plots show the lower and upper kinematic bounds on SRDM with masses of $m_{\chi} = 0.5$ MeV and $m_{\chi} = 50$ keV, respectively. The $m_{\chi} = 0.5$ MeV case includes contributions from both regions affected by LFEs, while the $m_{\chi} = 50$ keV case is only impacted by the plasmon region. The maximum velocities of $v = 0.02$ and $v = 0.06$ for the two SRDM examples are determined by the fluxes simulated in Emken2024 for a massless dark mediator.