Tetra-Germanene Study from First Principles: Structure, Electronics, Mechanics, and Vibrations

We present a theoretical investigation of the structural, electronic, and mechanical properties of tetra-germanene. Starting from a buckled rectangular unit cell, obtained via molecular dynamics simulations, the structure was optimized by employing density functional theory, yielding lattice constants (a = 4.01 Å, b = 4.17 Å), buckling height of 2.18 Å, and a cohesive energy of 5.14 eV/atom, exceeding that of hexagonal germanene. The analysis of the electronic band structure and density of states reveals metallic behavior without Dirac crossings. The orbital populations indicate minor participation of d orbitals and enhanced coordination compared to the hexagonal phase. The in-plane Young's modulus is anisotropic, with values of 53.10 N/m and 68.75 N/m along the two principal directions, while the corresponding bulk modulus is 59.16 N/m, indicating moderate stiffness and directional flexibility. Phonon dispersions are mostly free of imaginary modes, and the maximum optical frequency is ∼220 cm ^{- 1}, indicating improved thermal performance at low to moderate temperatures compared with hexagonal germanene. This combination of cohesive stability, metallic conductivity, and anisotropic elasticity suggests that tetra-germanene is a promising candidate for strain-tunable conductive channels and efficient thermal pathways in the next-generation nanoelectronic, energy efficiency, and phononic devices.