Growth of silicene layers on Ag(111): unexpected effect of the substrate temperature

The deposition of one silicon monolayer on the silver (111) substrate in the temperature range 150-300${}^{\circ }$C, gives rise to a mix of (4$\times$4), ($2\sqrt{3}\times 2\sqrt{3}$)R30${}^{\circ }$ and ($\sqrt{13}\times \sqrt{13}$)R13.9${}^{\circ }$ superstructures which strongly depends on the substrate temperature. We deduced from a detailed analysis of the LEED patterns and the STM images that all these superstructures are given by a quasi identical silicon single layer with a honeycomb structure (i.e. a silicene-like layer) with different rotations relatively to the silver substrate. The STM images morphology are explained from the relative position of the silicon atoms relative to the silver atoms. A complete analysis of all possible rotations of the silicene layer predicts also a ($\sqrt{7}\times \sqrt{7}$)R19.1${}^{\circ }$ superstructure which has not been observed so far.