Crystal responses to general dark matter-electron interactions

TL;DR

This paper develops a comprehensive formalism for modeling dark matter-electron interactions in crystals, identifying new crystal response functions and applying them to interpret experimental data from silicon and germanium detectors.

Contribution

It introduces a novel formalism incorporating general non-relativistic DM-electron interactions and identifies five key crystal response functions, four of which are newly characterized.

Findings

Identified five key crystal response functions affecting DM-electron scattering rates.

Evaluated these functions for silicon and germanium using density functional theory.

Set new limits on DM-electron interaction strengths based on existing experimental data.

Abstract

We develop a formalism to describe the scattering of dark matter (DM) particles by electrons bound in crystals for a general form of the underlying DM-electron interaction. Such a description is relevant for direct-detection experiments of DM particles lighter than a nucleon, which might be observed in operating DM experiments via electron excitations in semiconductor crystal detectors. Our formalism is based on an effective theory approach to general non-relativistic DM-electron interactions, including the anapole, and magnetic and electric dipole couplings, combined with crystal response functions defined in terms of electron wave function overlap integrals. Our main finding is that, for the usual simplification of the velocity integral, the rate of DM-induced electronic transitions in a semiconductor material depends on at most five independent crystal response functions, four of which were not known previously. We identify these crystal responses, and evaluate them using density functional theory for crystalline silicon and germanium, which are used in operating DM direct detection experiments. Our calculations allow us to set 90% confidence level limits on the strength of DM-electron interactions from data reported by the SENSEI and EDELWEISS experiments. The novel crystal response functions discovered in this work encode properties of crystalline solids that do not interact with conventional experimental probes, suggesting the use of the DM wind as a probe to reveal new kinds of hidden order in materials.