Additional curvature-induced Raman splitting in carbon nanotube ring structures

In this paper, a diameter-dependent Raman $G$ band splitting phenomenon in carbon nanotube ring structures is reported and analyzed. In Raman spectra of such structures, more modes became visible as the diameters of rings decrease, and the frequencies of these modes keep unchanged. We attribute this to the resonance condition changes caused by additional curvatures in rings. In this case, perpendicular polarized light would take more effect in rings than in straight tubes as the additional curvature increases, thus intensity enhancements for ${E}_{1}({E}_{1g})$ and ${E}_{2}({E}_{2g})$ modes are observed.