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The graphene-graphite relationship in structural geometry is a basicprinciple to predict novel two-dimensional (2D) materials. Here, we demonstratethat this is not the case in binary metallic systems. We use the Bayesianoptimization framework combined with the density-functional theory approach todetermine the stable configuration of atomic species on a hexagonal plane. Weshow that the optimized structure of 2D Cu-Au exhibits the hexagonal lattice ofa hexagonal ring of Cu atoms containing one Au atom, where the number of the Cuatoms is larger than that of the Au atoms in the unit cell, which is difficultto speculate from the atomic distribution of CuAu in the L1$_0$ structure. Wealso show that 2D Cu-$X$ with $X=$ Be, Zn, and Pd have hexagonal or elongatedrings containing different atoms in the unit cell. Based on the binaryLennard-Jones model, we propose that such structures can appear forweakly-bonded systems located in between the phase-separated andstrongly-bonded systems with the interatomic interaction energy betweendifferent species.

Finding the stable structures of 2D hexagonal materials with Bayesian  optimization: Beyond the structural relationship with 3D crystals in  weakly-bonded binary systems