Effective masses of the
optical transitions of single-walled carbon nanotubes (SWNTs)
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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. |
Valentin Popov