Dynamical stability of two-dimensional metals in the periodic table

We study the dynamical stability of two-dimensional (2D) metals from Li to Pb in the periodic table. Using a first-principles approach, we calculate the phonon band structure of 2D metals that have planar hexagonal (HX), buckled honeycomb (bHC), and buckled square (bSQ) lattice structures. The bHC and bSQ are dynamically stable structures for most transition metals, whereas the HX and bHC are dynamically stable structures for alkali earth and noble metals. Thin films thicker than bHC and bSQ are dynamically stable for group 5 elements and indium. We demonstrate that the trend in the dynamical stability of 2D metals is correlated with that of three-dimensional (3D) metals. This provides design principles of ordered alloys: 2D metals are building blocks for constructing 3D alloys, where the similarity regarding the dynamical stability of different 2D metals is important for creating dynamically stable alloys.