Deep-Ultraviolet and Helicity-Dependent Raman Spectroscopy for Carbon Nanotubes and 2D Materials

Recent progress of Raman spectroscopy on carbon nanotubes and 2D materials is reviewed as a topical review. The Raman tensor with complex values is related to the chiral 1D/2D materials without mirror symmetry for the mirror in the propagating direction of light, such as chiral carbon nanotube and black phosphorus. The phenomenon of complex Raman tensor is observed by the asymmetric polar plot of helicity-dependent Raman spectroscopy using incident circularly-polarized lights. First-principles calculations of resonant Raman spectra directly give the complex Raman tensor that explains helicity-dependent Raman spectra and laser-energy-dependent relative intensities of Raman spectra. In deep-ultraviolet (DUV) Raman spectroscopy with 266 nm laser, since the energy of the photon is large compared with the energy gap, the first-order and double resonant Raman processes occur in general k points in the Brillouin zone. First-principles calculation is necessary to understand the DUV Raman spectra and the origin of double-resonance Raman spectra. Asymmetric line shapes appear for the G band of graphene for 266 nm laser and in-plane Raman mode of WS₂ for 532 nm laser, while these spectra show symmetric line shapes for other laser excitation. The interference effect on the asymmetric line shape is discussed by fitting the spectra to the Breit-Wigner-Fano line shapes.