Dynamical stability of two-dimensional metals in the periodic table

We study the dynamical stability of elemental two-dimensional (2D) metals from Li to Pb by calculating the phonon band structure from first principles, where 2D structures are assumed to be planer hexagonal, buckled honeycomb, and buckled square lattice structures. We show the relationship between the stability of 2D structures and that of three-dimensional structures. This provides a material design concept for alloys, where the similarity with regard to the stable 2D structures, rather than the energetic stability of alloy, is important to yield dynamically stable alloys.