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This study investigates the strain-induced structural transitions of $\eta\leftrightarrow \theta$ and the changes in electronic band structures ofAu$_2$X (X=S, Se, Te, Si, Ge) and Au$_4$SSe. We focus on Au$_2$S monolayers,which can form multiple meta-stable monolayers theoretically, including$\eta$-Au$_2$S, a buckled penta-monolayer composed of a square Au lattice and Sadatoms. The $\theta$-Au$_2$S is regarded as a distorted structure of$\eta$-Au$_2$S. Based on density functional theory (DFT) calculations using ageneralized gradient approximation, the conduction and the valence bands of$\theta$-Au$_2$S intersect at the $\Gamma$ point, leading to linear dispersion,whereas $\eta$-Au$_2$S has a band gap of 1.02 eV. The conduction band minimumdepends on the specific Au-Au bond distance, while the valence band maximumdepends on both Au-S and Au-Au interactions. The band gap undergoes significantchanges during the $\eta \leftrightarrow \theta$ phase transition of Au$_2$Sinduced by applying tensile or compressive in-plane biaxial strain to thelattice. Moreover, substituting S atoms with other elements alters theelectronic band structures, resulting in a variety of physical propertieswithout disrupting the fundamental Au lattice network. Therefore, the family ofAu$_2$X monolayers holds potential as materials for atomic scale networkdevices.

Electronic band structure change with structural transition of buckled Au$_2$X monolayers induced by strain