Comprehensive First-Principles Investigation of the Structural, Mechanical, Electronic, and Optical Properties of Homoelemental Phase T-GaN Monolayer

Abstract

The exploration of non-hexagonal two-dimensional topologies has opened new possibilities for tailoring the properties of group III-V monolayers beyond those accessible through conventional honeycomb phases. In this context, we have investigated the structural, mechanical, electronic, and optical properties of T-GaN, a two-dimensional tetragonal gallium nitride monolayer composed of alternating four- and eight-membered rings featuring coexisting homoelemental (Ga-Ga, N-N) and heteropolar (Ga-N) bonds, using density functional theory (DFT) within the generalized gradient approximation (GGA/PBE) and the hybrid HSE06 functional. The dynamical stability of T-GaN was confirmed by phonon dispersion calculations, which revealed the absence of imaginary frequencies throughout the Brillouin zone, and was further supported by \textit{ab initio} molecular dynamics (AIMD) simulations. The mechanical characterization reveals a pronounced in-plane anisotropy, with critical strains of approximately 16.5\% and 7.0\% along the $x$- and $y$-directions, respectively. The electronic band structure analysis indicates that T-GaN is a nonmagnetic semiconductor with an indirect band gap of 0.35~eV (PBE) and 1.15~eV (HSE06), with the valence band maximum dominated by nitrogen 2\textit{p} orbitals and the conduction band minimum governed by gallium 4\textit{s} and 4\textit{p} states. The optical response was evaluated along three crystallographic directions, exhibiting considerable anisotropy in the absorption coefficient, refractive index, and reflectivity. These findings provide new insights into the physical properties of tetragonal group III-V monolayers and suggest that T-GaN may serve as a promising candidate for anisotropic nanoelectronic and optoelectronic applications.