Machine learning-driven global optimization reveals nanometre-scale mixed phases of borophene on Ag(100)

Abstract

Metal-supported borophene exhibits significant polymorphism and an inherently complex potential energy landscape, posing challenges to exploring its structural diversity. In this study, we integrate a neural network-driven machine learning potential with stochastic surface walking global optimization and an active learning framework to comprehensively map the potential energy surface (PES) of large-size borophene on an Ag(100) substrate. Our exhaustive search identifies 59 857 local minima across 556 distinct supercells, revealing a PES segmented into multiple energy basins and three major funnels. Among the low-energy configurations, 1391 low-energy structures extend to the nanometre scale, showcasing a diverse array of mixed-phase borophene architectures, including monolayer ribbons (β₁₂ and χ₃) and bilayer fragments (BL-α₅, BL-α₇, BL-α₁, BL-α₆, and BL-α₁α₆). Notably, the global minimum structures feature monolayers composed of alternating χ₃ and β₁₂ ribbons and bilayers formed from BL-α₅, BL-α₁α₆, and BL-α₁ fragments. All mixed-phase borophenes exhibit metallic properties, and their simulated scanning tunneling microscopy (STM) images are provided to facilitate future experimental validation. These findings highlight the extraordinary structural complexity and rich polymorphism of borophene on extended metal surfaces, offering valuable insight into their formation, stability, and potential for tunable electronic properties.