D'yachkov, P. N. and Makaev, D. V. (2007) *Account of helical and rotational symmetries in the linear augmented cylindrical wave method for calculating the electronic structure of nanotubes: Towards the ab initio determination of the band structure of a (100,99) tubule.* PHYSICAL REVIEW B, 76 (19).

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Official URL: http://link.aps.org/doi/10.1103/PhysRevB.76.195411

## Abstract

Every carbon single-walled nanotube (SWNT) can be generated by first mapping only two nearest-neighbor C atoms onto a surface of a cylinder and then using the rotational and helical symmetry operators to determine the remainder of the tubule [C. T. White , Phys. Rev. B 47, 5485 (1993)]. With account of these symmetries, we developed a symmetry-adapted version of a linear augmented cylindrical wave method. In this case, the cells contain only two carbon atoms, and the ab initio theory becomes applicable to any SWNT independent of the number of atoms in a translational unit cell. The approximations are made in the sense of muffin-tin (MT) potentials and local-density-functional theory only. An electronic potential is suggested to be spherically symmetrical in the regions of atoms and constant in an interspherical region up to the two essentially impenetrable cylinder-shaped potential barriers. To construct the basis wave functions, the solutions of the Schrodinger equation for the interspherical and MT regions of the tubule were sewn together using a theorem of addition for cylindrical functions, the resulting basis functions being continuous and differentiable anywhere in the system. With account of analytical equations for these functions, the overlap and Hamiltonian integrals are calculated, which permits determination of electronic structure of nanotube. We have calculated the total band structures and densities of states of the chiral and achiral, semiconducting, semimetallic, and metallic carbon SWNTs (13, 0), (12, 2), (11, 3), (10, 5), (9, 6), (8, 7), (7, 7), (12, 4), and (100, 99) containing up to the 118 804 atoms per translational unit cell. Even for the (100, 99) system with huge unit cell, the band structure can be easily calculated and the results can be presented in the standard form of four curves for the valence band plus one curve for the low-energy states of conduction band. About 150 functions produce convergence of the band structures better then 0.01 eV independent of the number of atoms in the translational unit cell.

Item Type: | Article |
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Subjects: | Physical Science > Nanophysics Physical Science > Nano objects Material Science > Nanostructured materials |

ID Code: | 2448 |

Deposited By: | Farnush Anwar |

Deposited On: | 09 Jan 2009 13:24 |

Last Modified: | 09 Jan 2009 13:24 |

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