The atomic structure of the $\sqrt{3} \times \sqrt{3}$ phase of silicene   on Ag(111)
  The growth of the $\sqrt{3} \times \sqrt{3}$ reconstructed silicene on Ag substrate has been frequently observed in experiments while its atomic structure and formation mechanism is poorly understood. Here by first-principles calculations we show that $\sqrt{3} \times \sqrt{3}$ reconstructed silicene is constituted by dumbbell units of Si atoms arranged in a honeycomb pattern. Our model shows excellent agreement with the experimentally reported lattice constant and STM image. We propose a new mechanism for explaining the spontaneous and consequential formation of $\sqrt{3} \times \sqrt{3}$ structures from $3 \times 3$ structures on Ag substrate. We show that the $\sqrt{3} \times \sqrt{3}$ reconstruction is mainly determined by the interaction between Si atoms and have weak influence from Ag substrate. The proposed mechanism opens the path to understanding of multilayer silicon. 
Seymur Cahangirov, Veli Ongun \"Oz\c{c}elik, Lede Xian, Jose Avila,   Suyeon Cho, Mar\'ia C. Asensio, Salim Ciraci, and Ange...
cond-mat.mes-hall physics.comp-ph