Abstract
We report the observation of four Raman modes in individual, aligned single-walled carbon nanotubes, with frequencies between the RBM and D modes, and above the G± modes. By studying the diameter and excitation-energy dependence, we find that these strongly dispersive and comparatively intense modes share the lowest-frequency helical phonon branch as the origin, which can be derived from the out-of-plane acoustic (ZA) phonon branch of graphene. This ZA phonon is observed due to a defect-assisted, double-resonant process, similar to the D mode; its two-phonon overtones and combinations with transverse optical (TO) phonons do not require defects. Our assignment is supported by a theoretical model based on sixth-nearest neighbour tight-binding and a force-constant approach. We present a complete theoretical evaluation of the diameter and excitation-energy dependence of the ZA, 2ZA, and TO±ZA modes, which fits very well to our experimental results and previous studies of the so-called region of intermediate frequency modes.
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