Thickness dependence of wavenumbers and optical-activity selection rule of zone-center phonons in two-dimensional gallium sulfide metal monochalcogenide

Gallium sulfide (GaS) stands out as a versatile nonlinear optical material for green-blue optoelectronic and photocatalytic nano-devices. In addition, the in-plane breaking strain and mechanical strength of layered GaS make it a promising candidate for next-generation flexible nanodevices. The fast and reliable assessment of the number of layers, without sample loss, is key for these applications. Here we unveil the influence of dimensionality in the structural, mechanical, and vibrational properties of GaS by applying density-functional theory-based quantum-simulations and group-theory analysis. We find its intralayer structure and interlayer distances are essentially independent of the number of layers, in agreement with the van der Waals forces as dominant interlayer interactions. The translational symmetry breaking along the stacking direction results in different structural symmetries for monolayers, N-odd layers, N-even layers, and bulk geometries. Its force constants against rigid-layer shear, KLSM = 1.35 x 1019 N m-3, and breathing, KLBM = 5.00 x 1019 N m-3, displacements remain the same from bulk to bilayer structures. The related stiffness coefficients in bulk are C44 = 10.2 GPa and C33 = 37.7 GPa, respectively. This insight into GaS interlayer interactions and elastic coefficients reveals it as a promising lubricant for nano-mechanic applications and it is easy to cleave for thickness engineering, even in comparison with layered graphite, MoS2 and other transition metal dichalcogenides and group-IIIA metal monochalcogenides. We present the GaS Raman and infrared spectra dependence on the layer number as strategies for sample thickness characterization and derive formulas for distinguishing the number of layers in both high and low-frequency regimes. In addition, our analysis of their optical-activity selection rules and polarization dependencies is applicable to isostructural group-IIIA metal monochalcogenides with 2H-layer stacking, such as gallium/indium sulphide/selenide. These results contribute to rapid and non-destructive characterization of the material's structure, which is of paramount importance for the manufacturing of devices and the utilization of its diverse properties. The phonon wavenumber dependency on the thickness of two-dimensional materials may be used for their thickness assessment and to probe their interlayer interactions. Here we investigate these properties in beta-gallium sulfide.