Electronic and optical properties of computationally predicted Na-K-Sb crystals

Thanks to their favorable electronic and optical properties, sodium-potassium-antimonides are an emerging class of crystals used as photocathodes in particle accelerators. The persisting challenges related to the synthesis and characterization of these materials demand support from theory and make the study of computationally predicted polymorphs particularly relevant to identifying the structure and composition of the samples. Using first-principles methods based on density-functional theory and many-body perturbation theory, the electronic and optical properties of cubic NaK$_{2}$Sb and hexagonal Na$_{2}$KSb are studied. Both systems, most commonly found in the hexagonal and cubic phase, respectively, exhibit an indirect fundamental gap that is energetically very close to the direct band gap at $\Gamma$ of magnitude 0.81 eV for NaK$_{2}$Sb and 0.70 eV for Na$_{2}$KSb. In the band structure of both materials, Sb $p$-states dominate the valence region with minor contributions from the alkali $p$-states, while the alkali $s$-states mainly contribute at lower energies. The optical spectra of both crystals are not subject to sizeable excitonic effects, except for a redshift of the excitation energies of the 50-100 meV and some redistribution of the oscillator strength beyond the lowest-energy peak in the near-infrared region. Our results indicate that computationally predicted cubic NaK$_{2}$Sb and hexagonal Na$_{2}$KSb have favorable characteristics as photocathodes and, as such, their presence in polycrystalline samples is not detrimental for these applications.