Crossover between silicene and ultra-thin Si atomic layers on Ag(111) surfaces

We report on total-energy electronic structure calculations in the density-functional theory performed for the ultra-thin atomic layers of Si on Ag(111) surfaces. We find several distinct stable silicene structures: $\sqrt{3}\times \sqrt{3}$, 3 × 3, $\sqrt{7}\times \sqrt{7}$ with the thickness of Si increasing from monolayer to quad-layer. The structural bistability and tristability of the multilayer silicene structures on Ag surfaces are obtained, where the calculated transition barriers infer the occurrence of the flip-flop motion at low temperature. The calculated scanning tunneling microscope (STM) images agree well with the experimental observations. We also find the stable existence of 2 × 1 π-bonded chain and 7 × 7 dimer-adatom-stacking fault Si(111)-surface structures on Ag(111), which clearly shows the crossover of silicene-silicon structures for the multilayer Si on Ag surfaces. We further find the absence of the Dirac states for multilayer silicene on Ag(111) due to the covalent interactions of the silicene-Ag interface and Si-Si interlayer. Instead, we find a new state near the Fermi level composed of π orbitals located on the surface layer of $\sqrt{3}\times \sqrt{3}$ multilayer silicene, which satisfies the hexagonal symmetry and exhibits the linear energy dispersion. By examining the electronic properties of 2 × 1 π-bonded chain structures, we find that the surface-related π states of multilayer Si structures are robust on Ag surfaces. (paper)