Electron-photon matrix element for the optical transitions of single-walled carbon nanotubes (SWNTs)

Fig. 1.Momentum matrix elements (squared modulus) of the groups Mod0, Mod1, Mod2 SWNTs versus tube radius, chiral angle and transition energy.

The optical transitions in solids are absorptions/emissions of photons with excitation/annihilation of electron-hole pairs. These processes are determined by the electron-photon interaction. Most important are the dipole-allowed transitions, where the probability of the transitions is determined by the matrix element of the momentum[1,2]. The momentum matrix element 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 follow family patterns for L1+2L2=const and 2L1+L2=const (Ref. [3,4]). 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.

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Valentin Popov

July 22, 2005