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: $\sqrt{3}\times\sqrt{3}$, $3\times3$, $\sqrt{7}\times\sqrt{7}$ 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 STM images agree well with the experimental observations. We also find the stable existence of $2\times1$ $\pi$-bonded chain and $7\times7$ 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 silicene-Ag interface and Si-Si interlayer. Instead, we find a new state near Fermi level composed of $\pi$ orbitals locating 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 $2\times1$ $\pi$-bonded chain structures, we find that the surface-related $\pi$ states of multilayer Si structures are robust on Ag surfaces.