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

The stability and electronic structure of competing silicene phases under in-plane compressive stress, either free-standing or on the ZrB2(0001) surface, has been studied by first-principles calculations. A particular (root 3 x root 3)-reconstructed structural modification was found to be stable on the ZrB2(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 ZrB2(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.