title: Communication: Effect of accidental mode degeneracy on Raman intensity in 2D materials: Hybrid functional study of bilayer phosphorene.
abstract: Bulk black phosphorus has two optical phonon modes labeled as Ag (2) and B2u, respectively, that are nearly degenerate in frequency. However, density functional theory calculations using local or semi-local functionals cannot reproduce this degeneracy. Here, we propose a hybrid functional approach aided by van der Waals (vdW) force fields, which can accurately describe the lattice dynamic and electronic properties of both bulk and few-layer black phosphorus (phosphorene). Using this approach we show that in bilayer phosphorene, the two Raman modes derived from the B2u and Ag (2) modes could exhibit strong resonance as a result of the accidental degeneracy so that both modes could be observed in Raman experiment. Without the mode degeneracy, however, the Raman intensity of the B2u-derived mode would be too weak to be observed. We further show that the accidental degeneracy is correlated to the applied strain, which enables Raman spectroscopy to be a powerful tool for characterizing built-in strains in 2D materials, e.g., due to the interaction with substrates, which has emerged as an important issue in vdW epitaxy.
authors.affiliation: Department of Physics, Applied Physics and Astronomy, Rensselaer Polytechnic Institute, Troy, New York 12180, USA.
authors.forename: Yi-Yang
authors.initials: YY
authors.lastname: Sun
authors.affiliation: Department of Physics, Applied Physics and Astronomy, Rensselaer Polytechnic Institute, Troy, New York 12180, USA.
authors.forename: Shengbai
authors.initials: S
authors.lastname: Zhang