First-principles upper bounds on dark matter-electron scattering rates from condensed matter sum rules

Abstract

A wide variety of condensed matter systems are used or proposed as detectors to search for dark matter-electron scattering. In general, the scattering rate depends on detailed knowledge of the electronic properties of these systems. However, when dark matter couples to electron density, the dark matter-electron scattering rate can be related to the electron energy loss function, whose integrals are bounded by first-principles sum rules that rely on only a few macroscopic target properties. In this paper, we use these first-principles sum rules to derive upper bounds on the dark matter-electron scattering rate depending on only a few material properties: the plasma frequency ${\omega }_{\text{p}}$, the target mass density ${\rho }_T$, and the static (longitudinal) dielectric function at finite momentum transfer, $\epsilon (q,0)$. The bulk material properties ${\omega }_{\text{p}}$ and ${\rho }_T$ vary only over a limited range across a wide variety of materials, and to a good approximation, the generic large-$q$ dependence of $\epsilon (q,0)$ can be understood from a simple scaling law depending only on ${\omega }_{\text{p}}$ which we verify with analytic and numerical examples. Thus, our upper bounds are largely material-agnostic, and place a fundamental limit on the sensitivity of any dark matter-electron direct detection experiment probing the coupling to electron density.

9 + 3 pages, 4 figures