Beyond-DFT $\textit{ab initio}$ Calculations for Accurate Prediction of Sub-GeV Dark Matter Experimental Reach

Abstract: As the search space for light dark matter (DM) has shifted to sub-GeV DM candidate particles, increasing attention has turned to solid state detectors built from quantum materials. While traditional solid state detector targets (e.g. Si or Ge) have been utilized in searches for dark matter (DM) for decades, more complex, anisotropic materials with narrow band gaps are desirable for detecting sub-MeV dark matter through DM-electron scattering and absorption channels. In order to determine if a novel target material can expand the search space for light DM it is necessary to determine the projected reach of a dark matter search conducted with that material in the DM mass - DM-electron scattering cross-section parameter space. The DM-electron scattering rate can be calculated from first-principles with knowledge of the loss function, however the accuracy of these predictions is limited by the first-principles level of theory used to calculate the dielectric function. Here we perform a case study on silicon, a well-studied semiconducting material, to demonstrate that traditional Kohn-Sham density functional theory (DFT) calculations erroneously overestimate projected experimental reach. We show that for silicon this can be remedied by the incorporation of self-energy corrections as implemented in the GW approximation. Moreover, we emphasize the care that must taken in selecting the appropriate level of theory for predicting experimental reach of next-generation complex DM detector materials.