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

This study investigates the strain-induced structural transitions of $\eta \leftrightarrow \theta$ and the changes in electronic band structures of Au$_2$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 S adatoms. The $\theta$-Au$_2$S is regarded as a distorted structure of $\eta$-Au$_2$S. Based on density functional theory (DFT) calculations using a generalized 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 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 $\eta \leftrightarrow \theta$ phase transition of Au$_2$S 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 Au$_2$X monolayers holds potential as materials for atomic scale network devices.