Extended Calculation of Dark Matter-Electron Scattering in Crystal Targets

TL;DR

This paper enhances the calculation of dark matter-electron scattering in crystal detectors by incorporating detailed electronic wave functions and additional states, significantly impacting detection rate predictions especially for heavy mediators.

Contribution

It introduces an advanced computational framework combining density functional theory and semi-analytic methods, implemented in the open-source program EXCEED-DM, for more accurate dark matter detection predictions.

Findings

All-electron reconstruction significantly affects wave function components.

Including additional electronic states alters detection rate estimates.

Extended calculations modify the detection prospects for silicon and germanium.

Abstract

We extend the calculation of dark matter direct detection rates via electronic transitions in general dielectric crystal targets, combining state-of-the-art density functional theory calculations of electronic band structures and wave functions near the band gap, with semi-analytic approximations to include additional states farther away from the band gap. We show, in particular, the importance of all-electron reconstruction for recovering large momentum components of electronic wave functions, which, together with the inclusion of additional states, has a significant impact on direct detection rates, especially for heavy mediator models and at $\mathcal{O}(10\,\text{eV})$ and higher energy depositions. Applying our framework to silicon and germanium (that have been established already as sensitive dark matter detectors), we find that our extended calculations can appreciably change the detection prospects. Our calculational framework is implemented in an open-source program $\texttt{EXCEED-DM}$ (EXtended Calculation of Electronic Excitations for Direct detection of Dark Matter), to be released in an upcoming publication.