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 novel 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 new 2D structures of InP, recovers known 2D structures in the binary Sn-S and C-Si systems, and finds two new 1D Si defects in graphene with formation energies below that of isolated substitutional Si atoms.

Crystal structure prediction is a long-standing challenge in the physical sciences. In recent years, much practical success has been had by framing it as a global optimization problem, leveraging the existence of increasingly robust and accurate free energy calculations. This optimization problem has often been solved using evolutionary algorithms (EAs). However, many choices are possible when designing an EA for structure prediction, and innovation in the field is ongoing. We review the current state of evolutionary algorithms for crystal structure and composition prediction and discuss the details of methodological and algorithmic choices. Finally, we review the application of these algorithms to many systems of practical and fundamental scientific interest.

Two-dimensional (2D) materials present a new class of materials whose structures and properties can differ from their bulk counterparts. We perform a genetic algorithm structure search using density-functional theory to identify low-energy structures of 2D group-IV dioxides AO2 (A=Si, Ge, Sn, Pb). We find that 2D SiO2 is most stable in the experimentally determined bi-tetrahedral structure, while 2D SnO2 and PbO2 are most stable in the 1T structure. For 2D GeO2, the genetic algorithm finds a new low-energy 2D structure with monoclinic symmetry. Each system exhibits 2D structures with formation energies ranging from 26 to 151 meV/atom, below those of certain already synthesized 2D materials. The phonon spectra confirm their dynamic stability. Using the HSE06 hybrid functional, we determine that the 2D dioxides are insulators or semiconductors, with a direct band gap of 7.2 eV at Γ for 2D SiO2, and indirect band gaps of 4.8 -2.7 eV for the other dioxides. To guide future applications of these 2D materials in nano-electronic devices, we determine their band-edge alignment with graphene, phosphorene, and single-layer BN and MoS2. An assessment of the dielectric properties and electrochemical stability of the 2D group-IV dioxides shows that 2D GeO2 and SnO2 are particularly promising candidates for gate oxides and SnO2 also as a protective layer in heterostructure nanoelectronic devices.