Anisotropic correlation between the piezoelectricity and anion-polarizability difference in 2D phosphorene-type ternary GaXY (X = Se, Te; Y = F, Cl, Br, I) monolayers

Inspired by the typical two-dimensional (2D) black-phosphorene-type structure with mm2 point-group symmetry, the structural stability, electronic structure, and intrinsic piezoelectricity of 2D ternary GaXY (X = Se and Te; Y = Cl, Br, and I) monolayers are systematically studied by the first-principles density functional theory. Our calculations show that these ternary monolayer compounds exhibit desirable dynamical and thermal stabilities and a large variety of bandgaps. The calculated piezoelectric coefficients d₁₁ is as large as 15.57 pm/V for GaTeF, and the largest d₁₂ reaches to 3.78 pm/V for GaSeI. It is worth noting that the e_ij and d_ij coefficients of GaXY monolayers display anisotropic periodic trends with respect to the constituent elements, which could be interpreted by a linear correlation between the piezoelectric coefficients and the differences in anionic polarizabilities \(\alpha_{X} \;{\text{or}}\;\alpha_{Y}\). It is found that d₁₁ of GaXY monolayers is directly proportional to \((\alpha_{X} - \alpha_{Y} )\), while d₁₂ is inversely proportional to \((\alpha_{X} - \alpha_{Y} )\). Such anisotropic correlation could be applicable to elucidate the origin of the piezoelectricity in other 2D ternary compounds.