Raman spectra of few-layer phosphorene studied from first-principles calculations

Raman spectra of few-layer phosphorene have been systematically studied using density functional theory calculations. We find that due to the interlayer van der Waals interactions, the low-frequency rigid layer A_g breathing mode and B_1g shear mode can shift by as much as 45.1cm^-1 and 38.5cm^-1, respectively, as the layer numbers increase from 2L to 5L. In addition, a typical characteristic for the experimentally observable mode (∼460cm^-1 in bulk) is identified. Interestingly, this mode changes from coupled in-plane and out-of-plane vibrations in single layer to pure in-plane vibrations in a few layers and the corresponding frequencies vary by as much as over 10cm^-1. We argue that this Raman frequency variation might be used to experimentally characterize the thickness of this intriguing 2D layered material.