Raman Activity of Multilayer Phosphorene under Strain

Using computational tools, we study the behavior of activities of lattice vibrational Raman modes in few-layered phosphorene of up to four layers subjected to a uniaxial strain of −2 to +6% applied in the armchair and zigzag directions. We study both high- and low-frequency modes and find very appreciable frequency shifts in response to the applied strain of up to ≈20 cm–1. The Raman activities are characterized by Ag2/Ag1 activity ratios, which provide very meaningful characteristics of functionalization via layer- and strain-engineering. The ratios exhibit a pronounced vibrational anisotropy, namely a linear increase with the applied armchair strain and a highly nonlinear behavior with a strong drop of the ratio with the strain applied along the zigzag direction. For the low-frequency modes, which are Raman active exclusively in few-layered systems, we find the breathing interlayer modes of primary importance due to their strong activities. For few-layered structures with a thickness ≥4, a splitting of the breathing modes into a pair of modes with complementary activities is found, with the lower frequency mode being strain activated. Our calculated database of results contains full angular information on activities of both low- and high-frequency Raman modes. These results, free of experimental complexities, such as dielectric embedding, defects, and size and orientation of the flakes, provide a convenient benchmark for experiments. Combined with high-spatial-resolution Raman scattering experiments, our calculated results will aid in the understanding of the complicated inhomogeneous strain distributions in few-layered phosphorene or the manufacture of materials with desired electronic properties via strain- or layer-engineering.