Machine-learned search for the stable structures of silicene on Ag(111)

The honeycomb lattice of silicene exhibits a variety of nontrivial reconstructions on the Ag(111) surface, whose diversity hampers the theoretical prediction of experimentally unidentified structures using computationally expensive density functional theory (DFT) calculations. We here apply an efficient method based on an evolutionary algorithm and a Gaussian process, which is trained on the fly with DFT calculations, to the search for the stable structures of silicene on Ag(111). We demonstrate that the structure search method can not only reproduce the well-known structures, but also predict the existence of metastable structures that are close in stability to the most stable ones. Detailed analyses of the obtained results reveal that such metastable structures play crucial roles in the stabilization of less ordered phases often observed experimentally. The present method can replace the conventional manual search based on intuition and is widely applicable to the investigations of new systems such as emerging two-dimensional materials.