Two-Dimensional Noble Metal Chalcogenides in the Frustrated Snub-Square Lattice

We study two-dimensional noble metal chalcogenides, with composition {Cu, Ag, Au}2{S, Se, Te}, crystallizing in a snub-square lattice. This is a semi-regular two-dimensional tesselation formed by triangles and squares that exhibits geometrical frustration. We use for comparison a square lattice, from which the snub-square tiling can be derived by a simple rotation of the squares. The mono-layer snub-square chalcogenides are very close to thermodynamic stability, with the most stable system (Ag2Se) a mere 7 meV/atom above the convex hull of stability. All compounds studied in the square and snub-square lattice are semiconductors, with band gaps ranging from 0.1 to more than 2.5 eV. Excitonic effects are strong, with an exciton binding energy of around 0.3 eV. We propose the Cu (001) surface as a possible substrate to synthesize Cu2Se, although many other metal and semiconducting surfaces can be found with very good lattice matching.