Electron-phonon coupling
for the radial-breathing mode (RBM) of single-walled carbon nanotubes (SWNTs)
|
|
The resonant Raman scattering from solids is
accompanied by creation of virtual electron-hole pairs, emission/absorption
of a phonon, and annihilation of the virtual electron-hole pairs. Therefore,
the electron-phonon coupling plays an important role in the scattering
process. The matrix element of this coupling is determined by the scalar
product of the derivative of the optical transition energies[1,2]
with respect to the atomic displacement vector and the phonon
eigenvector[3,4]. The electron-phonon coupling matrix elements
for all optical transitions up to 3.5 eV for all 300 SWNTs with radii from 2 Ǻ
to 12 Ǻ were calculated within a symmetry-adapted non-orthogonal
tight-binding model[1,2]. The obtained matrix
elements can be positive or negative. They decrease with the increase of the
radius and chiral angle and increase with the increase of the transition energy[3,4] (Fig. 1). The points follow family patterns
for L1+2L2=const and 2L1+L2=const. References: 1. V. N. Popov, New J. Phys. 6 (2004) 1-17. 2. V. N. Popov and L. Henrard, Phys. Rev. B 70 (2004) 115407. 3. V. N. Popov, L. Henrard, and Ph. Lambin, Nano Letters 4 (2004) 1795-1799. 4. V. N. Popov, L. Henrard, and Ph. Lambin, Phys. Rev. B 72 (2005) 035436. |
Valentin Popov