The structural behavior of physisorbed metallenes.

Atomically thin metallenes have properties attractive for applications, but they are intrinsically unstable and require delicate stabilization in pores or other nano-constrictions. Substrates provide solid support, but metallenes' essential properties can only be retained in weak physisorption. Here, we study 45 physisorbed, atomically thin metallene structures in flat and buckled lattices using a sequential multi-scale model based on density-functional theory calculations. The lattices are mostly buckled but flat for a handful of elements such as Na, K, Rb, Ag, Au, and Cd, depending on physisorption strength. Moreover, under certain conditions, the structure can be controlled by applying biaxial tensile stress parallel or an electric field normal to the surface. The stress reduces the threshold of adhesion strength required to flatten a buckled lattice, and the electric field can be used to increase that threshold controllably. Our results help provide fundamental information about the structures of physisorbed metallenes and suggest means to control them at will by suitable substrate choice or tuning of experimental parameters.