Moir\'e pattern of a single layer MoS$_2$ grown on Cu(111)

We present results of first principles calculations of the geometric and electronic structures of a single layer of Molybdenum disulfide (MoS$_2$) on Cu(111) utilizing the van der Waals density functional [1]. The lowest energy Moir\'e structure consists of $(4\times 4)$ MoS$_2$ on $(5\times 5)$ Cu(111), in agreement with experimental observation [2]. Examination of the local density of electronic states and charge redistribution shows that the layer is not purely physisorbed on the surface, rather there exists a chemical interaction between it and the Cu surface atoms. Interestingly the MoS$_2$ film is found to be not appreciably buckled, while the atoms in the top Cu layer gets reorganized and vertically disordered. The sizes of Moir\'e patterns for a single layer of MoS$_2$ adsorbed on several other close packed metal surfaces are estimated by minimizing the lattice mismatch between the film and the substrate. \\[4pt] [1] M. Dion \textit{et al}, Phys. Rev. Lett. \textbf{92}, 246401 (2004) \\[0pt] [2] D. Kim \textit{et al}, Langmuir \textbf{27}, 11650 (2011)