Beyond ideal two-dimensional metals : Edges, vacancies, and polarizabilities

Recent experimental discoveries of graphene-stabilized patches of two-dimensional (2D) metals have motivated also their computational studies. However, so far the studies have been restricted to ideal and infinite 2D metallic monolayers, which is insufficient because in reality the properties of such metallic patches are governed by microstructures pervaded by edges, defects, and several types of perturbations. Here we use density-functional theory to calculate edge and vacancy formation energies of hexagonal and square lattices of 45 elemental 2D metals. We find that the edge and vacancy formation energies are strongly correlated and decrease with increasing Wigner-Seitz radii, analogously to surface energies. Despite a radical reduction in atomic coordination numbers, the 2D and three-dimensional (3D) vacancy formation energies and work functions are nearly the same for each metal. Finally, static polarizabilities reveal a clear cubic dependence on bond length. These trends provide useful insights when moving towards reality with elemental 2D metals.