Communication: Effect of accidental mode degeneracy on Raman intensity in 2D materials: Hybrid functional study of bilayer phosphorene
- Department of Physics, Applied Physics and Astronomy, Rensselaer Polytechnic Institute, Troy, New York 12180 (United States)
Bulk black phosphorus has two optical phonon modes labeled as A{sub g}{sup 2} and B{sub 2u}, 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 B{sub 2u} and A{sub g}{sup 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 B{sub 2u}-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.
- OSTI ID:
- 22675960
- Journal Information:
- Journal of Chemical Physics, Journal Name: Journal of Chemical Physics Journal Issue: 2 Vol. 145; ISSN JCPSA6; ISSN 0021-9606
- Country of Publication:
- United States
- Language:
- English
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