Linear response theory for light dark matter-electron scattering in materials

TL;DR

This paper develops a comprehensive formalism combining non-relativistic dark matter-electron interaction theory with linear response to accurately predict electronic transition rates in materials, accounting for screening and collective effects.

Contribution

It introduces a novel formalism that relates dark matter interactions with electronic responses in materials using generalized susceptibilities, extending previous models to include collective effects and screening.

Findings

In-medium effects significantly influence detector sensitivity for DM coupling to electron density.

The formalism can be extended to spin-polarised materials.

The approach provides a more accurate prediction of electronic transition rates in DM detection experiments.

Abstract

We combine the non-relativistic effective theory of dark matter (DM) - electron interactions with linear response theory to obtain a formalism that fully accounts for screening and collective excitations in DM-induced electronic transition rate calculations for general DM-electron interactions. In the same way that the response of a dielectric material to an external electric field in electrodynamics is described by the dielectric function, so in our formalism the response of a detector material to a DM perturbation is described by a set of generalised susceptibilities which can be directly related to densities and currents arising from the non-relativistic expansion of the Dirac Hamiltonian. We apply our formalism to assess the sensitivity of non-spin-polarised detectors, and find that in-medium effects significantly affect the experimental sensitivity if DM couples to the detector's electron density, while being decoupled from other densities and currents. Our formalism can be straightforwardly extended to the case of spin-polarised materials.