Phonon and thermodynamic properties of goldene under external stress

We investigate the influence of external stress on the phonon and thermodynamic properties of goldene using density functional theory (DFT). Under compressive stress, the lattice constant b perpendicular to the applied stress direction increases, while the lattice constant a decreases. Conversely, under tensile stress, the lattice constant b perpendicular to the stress direction decreases, whereas lattice constant a increases. Our calculations reveal that the phonon dispersion curves remain free of imaginary frequencies under both compressive and tensile strain. With increasing stress, compressive strain induces phonon hardening in goldene, whereas tensile strain leads to phonon softening. Correspondingly, compressive strain raises the Debye temperature and lowers the heat capacity of goldene, whereas tensile strain exhibits the opposite trend. These distinct strain-dependent responses offer a practical route for tuning the thermal and vibrational properties of goldene through external stress, which holds important implications for the design of goldene-based devices.