First-principle studies of surface phonon modes in GeSe Multi-Layers

Abstract

The surface phonon dispersion spectra of GeSe layered crystals were investigated by first-principles calculations within the density functional perturbation theory (DFPT). We model the GeSe surface as an arrangement of periodically placed slabs with a varying number of layers. To minimize the artificial interaction between the periodic images of the slabs, large enough vacuum space is taken in the perpendicular direction, and the slabs extend to infinity in the other directions. Detailed first-principles analysis of modes revealed surface phonons outside the bulk frequency zones in addition to vibrations in the bulk frequency range. To obtain the phonon states, the derivative of the forces with respect to the atomic coordinates were calculated at equilibrium positions in DFPT. In the phonon spectra, vibrational modes localized at the surface appear above the bulk phonon bands and inside the bulk phonon gap. The lowest frequency modes are reminiscent of Rayleigh surface waves. The thickness dependence of the phonon spectra was explored by comparing the results of the slabs with 1-8 layers. A few suggestions are provided to verify our findings in future experiments.