Unusual Raman dispersion for D and 2D lines in high-curvature single-walled carbon nanotubes revealed by C-13 isotope substitution

The defect-induced D line and its overtone are fundamental signatures in the Raman spectra of carbon nanomaterials. An analysis of these lines as a function of laser excitation energy is reported for double-walled carbon nanotubes where the inner tubes represent high-curvature nanotube species. From 13C substituted inner tubes it is demonstrated that the quasilinear relations between laser energy and line position (Raman dispersion) cross over unexpectedly for low-energy excitation for the inner and outer tube shells. The result is quantitatively explained by a curvature-induced phonon softening and first-principles calculations of the optical transition energies