DM-electron scattering in materials: sum rules and heterostructures

In recent years, a growing experimental program has begun to search for sub-GeV dark matter through its scattering with electrons. An associated theoretical challenge is to compute the dark matter scattering rate in experimental targets, and to find materials with large scattering rates. In this paper we point out that, if dark matter scatters through a mediator that couples to EM charge, then electromagnetic sum rules place limits on the achievable scattering rates. These limits serve as a useful sanity check for calculations, as well as setting a theoretical target for proposed detection methods. Motivated by this analysis, we explore how conductor-dielectric heterostructures can result in enhanced scattering rates compared to bulk conductors, for dark matter masses $\lesssim$ MeV. These effects could be especially important in computing the scattering rates from thin-film targets, e.g. superconducting detectors such as SNSPDs, TESs or MKIDs, for which the scattering rate could be enhanced by orders of magnitude at low enough dark matter masses, as well as introducing or enhancing directional dependence.