Novel two-dimensional silicon and germanium allotropes: a first-principles study

Graphene has been extensively studied but its integration into Si-based device technologies is difficult. It has been recently predicted by first-principles calculations that freestanding silicene and germanene, the counterparts of graphene made of Si and Ge atoms respectively, have graphene-like electronic structure with a low buckled structure [1]. So far, the models predicted by first-principles calculations were not able to describe completely the experimental results. These difficulties tend to suggest a more complex phase diagram for freestanding silicene or for silicene on a substrate than the simple buckled phase. We report for the first time a novel two-dimensional silicon and germanium allotropes, with a structure similar of that of MoS$_2$ layer [2]. After investigating a large range of lattice constants by first-principles calculations with OpenMX code, we show that this structure is the ground state for freestanding two-dimensional silicon and germanium layers instead of the usually considered low buckled silicene and germanene. \\[4pt] [1] S. Cahangirov et \textit{al.}, Phys. Rev. Lett. \textbf{102}, 236804 (2007). \newline [2] B. Radisavljevic et \textit{al.}, Nature Nano. \textbf{6}, 147 (2011).