First-principles study on competing phases of silicene: Effect of substrate and strain

Abstract

The stability and electronic structure of competing silicene phases under in-plane compressive stress, either free-standing or on the ZrB${}_{2}$(0001) surface, has been studied by first-principles calculations. A particular ($\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}$)-reconstructed structural modification was found to be stable on the ZrB${}_{2}$(0001) surface under epitaxial conditions. In contrast to the planar and buckled forms of free-standing silicene, in this ``planar-like'' phase, all but one of the Si atoms per hexagon reside in a single plane. While without substrate, for a wide range of strain, this phase is energetically less favorable than the buckled one, it is calculated to represent the ground state on the ZrB${}_{2}$(0001) surface. The atomic positions are found to be determined by the interactions with the nearest-neighbor Zr atoms competing with Si-Si bonding interactions provided by the constraint of the honeycomb lattice.