Silicene-derived phases on Ag(111) substrate versus coverage:Ab initiostudies

Abstract

Silicene is systematically investigated as an epitaxial overlayer on an Ag(111) substrate based on the ab initio density functional theory. The geometry and stability of five silicene-silver adsorbate systems with four coincidence lattices, $\sqrt{7}\ifmmode\times\else\texttimes\fi{}\sqrt{7}$ on $\sqrt{13}\ifmmode\times\else\texttimes\fi{}\sqrt{13}$, $3\ifmmode\times\else\texttimes\fi{}3$ on $4\ifmmode\times\else\texttimes\fi{}4$, $2\ifmmode\times\else\texttimes\fi{}2$ on $\sqrt{7}\ifmmode\times\else\texttimes\fi{}\sqrt{7}$, and $\sqrt{7}\ifmmode\times\else\texttimes\fi{}\sqrt{7}$ on $2\sqrt{3}\ifmmode\times\else\texttimes\fi{}2\sqrt{3}$, are related to the Si coverage, biaxial strain, and preparation conditions. Their phase diagram is calculated for varying chemical potential of the Si reservoir. The scanning tunneling microscopy images calculated for the optimized atomic geometries agree with those observed experimentally. The destruction of the original honeycomb symmetry and the strong adsorbate-substrate interaction significantly influence the electronic structure. Four peeled-off silicene sheets show conical linear bands, with small gaps. However, the band edges of the $3\ifmmode\times\else\texttimes\fi{}3$ on $4\ifmmode\times\else\texttimes\fi{}4$ geometry cannot be explained in terms of gap opening between Dirac cones for symmetry reasons. We confirm the conclusion that the linear bands observed by ARPES are due to folded Ag bands.