High-throughput computational search for two-dimensional binary compounds: Energetic stability versus synthesizability of three-dimensional counterparts

Using first principles calculations, the energetic stability of two-dimensional (2D) binary alloys $XY$ is investigated, where $X$ and $Y$ indicate the metallic element from Li to Pb in the periodic table, i.e., the total number of 1081 alloys. The formation energy of 2D alloys in the buckled honeycomb (bHC) lattice structure is correlated to that of three-dimensional alloys in the B$_h$ structure. By performing phonon dispersion calculations, we show that if an alloy in the B$_h$ structure has been synthesized experimentally, that in the bHC structure is dynamically stable. In contrast, an alloy in the bHC structure is unstable, that in the B$_h$ structure has not been synthesized yet. The negatively large formation energy is not a necessary and sufficient condition for yielding the dynamical stability of alloys.