This study investigates the strain-induced structural transitions of η ↔ θ and the changes in electronic band structures of Au2X (X = S, Se, Te, Si, Ge) and Au4SSe. We focus on Au2S monolayers, which can form multiple meta-stable monolayers theoretically, including η-Au2S, a buckled penta-monolayer composed of a square Au lattice and S adatoms. The θ-Au2S is regarded as a distorted structure of η-Au2S. Based on density functional theory (DFT) calculations using a generalized gradient approximation, the conduction and the valence bands of θ-Au2S intersect at the Γ point, leading to linear dispersion, whereas η-Au2S has a band gap of 1.02 eV. The conduction band minimum depends on the specific Au-Au bond distance, while the valence band maximum depends on both Au-S and Au-Au interactions. The band gap undergoes significant changes during the η ↔ θ phase transition of Au2S induced by applying tensile or compressive in-plane biaxial strain to the lattice. Moreover, substituting S atoms with other elements alters the electronic band structures, resulting in a variety of physical properties without disrupting the fundamental Au lattice network. Therefore, the family of Au2X monolayers holds potential as materials for atomic scale network devices.
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