Anisotropic Adatom Interactions on Black Phosphorus: A Simulation Study Based on First-Principles Calculations

Liquid metals exhibit a unique electronic signature (a pseudogap and a backward-bending band) absent in conventional crystalline materials. Recent studies have explored these effects by depositing alkali adatoms on black phosphorus. The spatial arrangement of adatoms is influenced not only by well-known interactions, such as dipole–dipole forces and Friedel oscillations, but also by a previously uncharacterized, attractive interaction potential along the armchair direction. This directional potential, which cannot be adequately explained by existing models, affects the global distribution of adatoms. To capture this behavior, we develop a simulation framework that incorporates all relevant interaction mechanisms. We apply simulated annealing to an effective interaction potential that combines theoretical Friedel oscillation contributions with dipole–dipole interactions. Additionally, we perform density functional theory (DFT) calculations to evaluate total energies as functions of interatomic distance, to extract the directional interaction potential from first principles. This study provides insight into electronic interactions in dopant self-organization on anisotropic two-dimensional materials and establishes a framework for modeling disorder in quasi-2D systems.