Grand-canonical evolutionary algorithm for the prediction of two-dimensional materials

Single-layer materials represent a new materials class with properties that are potentially transformative for applications in nanoelectronics and solar-energy harvesting. With the goal of discovering novel two-dimensional (2D) materials with unusual compositions and structures, we have developed a grand-canonical evolutionary algorithm that searches the structure and composition space while constraining the thickness of the structures. Coupling the algorithm to first-principles total-energy methods, we show that this approach can successfully identify known 2D materials and find low-energy ones. We present the details of the algorithm, including suitable objective functions, and illustrate its potential with a study of the Sn-S and C-Si binary materials systems. The algorithm identifies several 2D structures of InP, recovers known 2D structures in the binary Sn-S and C-Si systems, and finds two 1D Si defects in graphene with formation energies below that of isolated substitutional Si atoms.