Shear Modes in a 2D Polar Metal

Low-frequency shear and breathing modes are important Raman signatures of two-dimensional (2D) materials, providing information on the number of layers and insights into interlayer interactions. We elucidate the nature of low-frequency modes in a 2D polar metal-2D Ga covalently bonded to a SiC substrate, using a first-principles Green's function-based approach. The low-frequency Raman modes are dominated by surface resonance modes, consisting primarily of out-of-phase shear modes in Ga, coupled to SiC phonons. Breathing modes are strongly coupled to the substrate and do not give rise to peaks in the phonon spectra. The highest-frequency shear mode blue-shifts significantly with increasing thickness, reflecting both an increase in the number of Ga layers and an increase in the effective interlayer force constant. The surface resonance modes evolve into localized 2D Ga modes as the phonon momentum increases. The predicted low-frequency modes are consistent with Raman measurements on 2D polar Ga.