One-electron states and interband optical absorption in single-wall carbon nanotubes

Abstract

Explicit expressions for the wavefunctions and dispersion equation for the band π-electrons in single-wall carbon nanotubes are obtained within the method of zero-range potentials. They are then used to investigate the absorption spectrum of polarized light caused by direct interband transitions in isolated nanotubes. It is shown that, at least, under the above approximations, circular dichroism is absent in chiral nanotubes for a light wave propagating along the tube axis. The results obtained are compared with those calculated in a similar way for a graphite plane.

Linear diatomic crystal: single-electron states and large-radius excitons

“…Thus, all calculations made on the base of solvable zero-range potentials model indicate the instability of the single-electron states in the vicinity of the energy gap with respect to the formation of excitons. This might be a shortage of this model, but it is worth mentioning that results obtained on one-particle states in real 1D systems, like SWCNTs [13], [14], within its framework agree with existing experimental data in limits of accuracy of the latter.…”

“…The matter is that results on the band structure and single-electron states, obtained by this method for SWCNTs in [13], [14], appeared to be in good accordance with the experimental data and results of ab initio calculations related to the band states. For certainty we use the linear crystal parameters (the electron bare mass, lattice parameters) taken from works on nanotubes [13], [14]. In section 3 we obtain the e-h bare interaction potential and that screened by the crystal band electrons, and then the large-radius exciton spectrum for the linear crystal in vacuum.…”

Mass-jump and mass-bump boundary conditions for singular self-adjoint extensions of the Schrödinger operator in one dimension

“…Singular interactions are widely used as theoretical models in quantum physics [1,2,3] and nanotechnology for creation and control of electronic devices [4,5,6]. The localized structure defects or additional interaction atoms in materials can be modeled by such interactions [7].…”

Environment Effects on Excitons in Semiconducting Carbon Nanotubes

“…[41][42][43][44][45][46][47][48][49][50][51][52][53][54][55] Environmental effects were theoretically discussed by assuming a dielectric constant 25,26,29,30,56) or using more elaborate models. [57][58][59][60][61] In this paper, we study environmental effects based on a k Á p scheme by exactly taking account of the image effect within a continuum model. The paper is organized as follows: In §2 a brief review is given on the k Á p description of electronic states, the Coulomb potential in the presence of cylindrical dielectric medium, and a method of calculation of exciton states.…”