Effective masses of the optical transitions of single-walled carbon nanotubes (SWNTs)

 

effmass

Fig. 1. Effective masses of the optical transitions of the groups Mod0, Mod1, Mod2 SWNTs versus tube radius, chiral angle and transition energy.

 

The electronic density of states (DOS) enters many summations/integrations over the Brillouin zone of periodic systems. In the vicinity of a minimum/maximum of an electronic band, the parabolic approximation for the band is often used and the DOS has a very simple analytic form. In this form, the specific system is characterized by its effective mass, which is the inverse of the second derivative of the band energy with respect to the wavevector at the band minimum/maximum. In the case of optical transitions, it is the joint DOS, i.e., the DOS of the difference of the band energies that is the relevant quantity.

 

The effective masses of 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 effective masses 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.

 

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Valentin Popov

July 22, 2005