  First-principles methods have recently established themselves in the field of
photocathode research to provide microscopic, quantum-mechanical
characterization of relevant materials for electron sources. While most of the
existing studies are focused on bulk crystals, the knowledge of surface
properties is essential to assess the photoemission performance of the samples.
In the framework of density-functional theory, we investigate stability and
electronic properties of surface slabs of CsK$_2$Sb, an emerging semiconducting
photocathode material for particle accelerators. Considering surfaces with
Miller indices 0 and 1, and accounting for all possible terminations, we find
that, at the interface with vacuum, the atomic layers may rearrange
considerably to minimize the electrostatic repulsion between neighboring alkali
species. From the analysis of the surface energy as a function of the chemical
potential, we find a striking preference for surfaces oriented along the (111)
direction. Yet, at large and intermediate concentrations of Cs and K,
respectively, (100) and (110) slabs are energetically most favorable. The
considered surfaces exhibit either semiconducting or metallic character. Of the
former kind is the most stable (111) slab which has a band gap of about 1.3 eV,
in excellent agreement with experimental values for CsK$_2$Sb samples. Metallic
surfaces have lower work function, on the order of 2.5 eV, in line with the
emission threshold measured for CsK$_2$Sb photocathodes. All in all these
results contribute to the fundamental understanding of the microscopic
properties of CsK$_2$Sb in particular and of multi-alkali antimonides in
general, and represent an useful complement to the ongoing experimental efforts
in the characterization of this emerging class of photocathode materials.
