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Register a new userChirality dependent frequency shift of radial breathing mode in metallic carbon nanotubes
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A phonon frequency shift of the radial breathing mode for metallic single wall carbon nanotubes is predicted as a function of Fermi energy. Armchair nanotubes do not show any frequency shift while zigzag nanotubes exhibit phonon softening, but this softening is not associated with the broadening. This chirality dependence originates from a curvature-induced energy gap and a special electron-phonon coupling mechanism for radial breathing modes. Because of the particle-hole symmetry, only the off-site deformation potential contributes to the frequency shift. On the other hand, the on-site potential contributes to the Raman intensity, and the radial breathing mode intensity is stronger than that of the $G$ band. The relationship between the chirality dependence of the frequency shift of the radial breathing mode and the $Gamma$ point optical phonon frequency shift is discussed.
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The quantum corrections to the frequencies of the $Gamma$ point longitudinal optical (LO) and transverse optical (TO) phonon modes in carbon nanotubes are investigated theoretically. The frequency shift and broadening of the TO phonon mode strongly depend on the curvature effect due to a special electron-phonon coupling in carbon nanotubes, which is shown by the Fermi energy dependence of the frequency shift for different nanotube chiralities. It is also shown that the TO mode near the $Gamma$ point decouples from electrons due to local gauge symmetry and that a phonon mixing between LO and TO modes is absent due to time-reversal symmetry. Some comparison between theory and experiment is presented.
The radial-breathing-like phonon modes (RBLMs) of the double-walled carbon nanotubes are studied in a simple analytical model, in which the interaction force constants (FCs) can be obtained analytically from the continuous model. The RBLMs frequencies are obtained by solving the dynamical matrix, and their relationship with the tube radii can be obtained analytically, offering a powerful experimental tool for determining precisely the radii of the multi-walled carbon nanotubes.
Using the first principles calculations we have studied the vibrational modes and Raman spectra of a (10, 10) single-walled carbon nanotube (SWNT) bundle under hydrostatic pressure. Detailed analysis shows that the original radial breathing mode (RBM) of the SWNT bundle disappears after the structural phase transition (SPT). And significantly a RBM-like mode appears at about 509 cm^{-1}, which could be considered as a fingerprint of the SPT happened in the SWNT bundle, and further used to determine the microscopic structure of the bundle after the SPT.
In terms of lattice dynamics theory, we study the vibrational properties of the oxygen-functionalized single wall carbon nanotubes (O-SWCNs). Due to the C-O and O-O interactions, many degenerate phonon modes are split and even some new phonon modes are obtained, different from the bare SWCNs. A distinct Raman shift is found in both the radial breathing mode and G modes, depending not only on the tube diameter and chirality but also on oxygen coverage and adsorption configurations. With the oxygen coverage increasing, interesting, a nonmonotonic up- and down-shift is observed in G modes, which is contributed to the competition between the bond expansion and contraction, there coexisting in the functionalized carbon nanotube.
Through magnetic linear dichroism spectroscopy, the magnetic susceptibility anisotropy of metallic single-walled carbon nanotubes has been extracted and found to be 2-4 times greater than values for semiconducting single-walled carbon nanotubes. This large anisotropy is consistent with our calculations and can be understood in terms of large orbital paramagnetism of electrons in metallic nanotubes arising from the Aharonov-Bohm-phase-induced gap opening in a parallel field. We also compare our values with previous work for semiconducting nanotubes, which confirm a break from the prediction that the magnetic susceptibility anisotropy increases linearly with the diameter.
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