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In the search for novel materials for vacuum electron sources, multi-alkaliantimonides and in particular sodium-potassium-antimonides have been recentlyregarded as especially promising due to their favorable electronic and opticalproperties. In the framework of density-functional theory and many-bodyperturbation theory, we investigate the electronic structure and the dielectricresponse of two representative members of this family, namely Na$_2$KSb andNaK$_2$Sb. We find that both materials have a direct gap, which is on the orderof 1.5 eV in Na$_2$KSb and 1.0 eV in NaK$_2$Sb. In either system, valence andconduction bands are dominated by Sb states with p- and s-character,respectively. The imaginary part of the dielectric function, computed uponexplicit inclusion of electron-hole interactions to characterize the opticalresponse of the materials, exhibits maxima starting from the near-infraredregion, extending up to the visible and the ultraviolet band. With ouranalysis, we clarify that the lowest-energy excitations are non-excitonic innature and that their binding energy is on the order of 100 meV. Our resultsconfirm the potential of Na$_2$KSb and NaK$_2$Sb as photoemissive materials forvacuum electron sources, photomultipliers, and imaging devices.

Electronic structure and optical properties of Na$_2$KSb and NaK$_2$Sb from first-principles many-body theory