By performing density functional theory-based ab initio calculations, Raman-active phonon modes of single-layer two-dimensional (2D) materials and the effect of in-plane biaxial strain on the peak frequencies and corresponding activities of the Raman-active modes are calculated. Our findings confirm the Raman spectrum of the unstrained 2D crystals and provide expected variations in the Raman-active modes of the crystals under in-plane biaxial strain. The results are summarized as follows: (i) frequencies of the phonon modes soften (harden) under applied tensile (compressive) strains; (ii) the response of the Raman activities to applied strain for the in-plane and out-of-plane vibrational modes have opposite trends, thus, the built-in strains in the materials can be monitored by tracking the relative activities of those modes; (iii) in particular, the $A$ peak in single-layer Si and Ge disappears under a critical tensile strain; (iv) especially in mono- and diatomic single layers, the shift of the peak frequencies is a stronger indication of the strain rather than the change in Raman activities; (v) Raman-active modes of single-layer $\text{Re}{X}_2$ ($X=\text{S}$, Se) are almost irresponsive to the applied strain. Strain-induced modifications in the Raman spectrum of 2D materials in terms of the peak positions and the relative Raman activities of the modes could be a convenient tool for characterization.

• Received 28 December 2017

DOI:https://doi.org/10.1103/PhysRevB.97.115427