We develop a new quantum-mechanical method for calculating the electronic structure of the chiral nanotubes, both perfect and having impurities [1-6]. This is the linear augmented cylindrical wave (LACW) method. The main argument for using cylindrical waves is to account for the cylindrical geometry of the nanotubes in an explicit form that offers the obvious advantages. In this model, the electronic spectrum of the single-wall nanotubes is governed by movement of electrons in the interatomic space of cylindrical layer and by scattering of electrons on the atomic spheres. Each tubule can be generated by first mapping of only the two nearest-neighbor C atoms onto a surface of a cylinder and the remainder of the tubule can be determined using the rotational and helical symmetry operators. In the symmetry-adapted version of this method, the cells contain only two carbon atoms, and the theory becomes applicable to any tubule irrespectively on the number of atoms in the translational unit cell. The method is implemented as a program package and can be applied to determine the total band structures and densities of states of the chiral semiconducting and metallic single-wall carbon tubules, both pure and intercalated. Based on a Green’s function technique, the first-principles numerical method for calculations on the electronic structure of the point impurities in the chiral tubules is elaborated. The electron Green’s function for a host tubule is calculated using the LACW theory. The Green’s function for the impurities is calculated in the terms of Dyson’s matrix equation.
References
1. P.N. D’yachkov, D.Z. Kutlubaev, and D.V. Makaev. Linear augmented cylindrical wave Green’s function method for electronic structure of nanotubes with substitutional impurities. Phys. Rev. B, 82, 035426 (2010).
2. P. N. D’yachkov and D. V. Makaev, Electronic structure of BN nanotubes with intrinsic defects NB and BN and isoelectronic substitutional impurities PN, AsN, SbN, InB, GaB, and AlB, J. Phys. Chem. Solids, 70, 180-185 (2009)
3. P.N. D'yachkov and D.V. Makaev, Account of helical and rotational symmetries in the linear augmented cylindrical wave method for calculating the electronic structure of nanotubes: towards ab initio determination of band structure of (100, 99) tubule, Phys. Rev. B, 76, 195411 (2007).
4. P.N. D'yachkov and D.V. Makaev. Linear augmented cylindrical wave method for calculating the electronic structure of double-wall carbon nanotubes. Phys. Rev. B, 74, 155442 (2006).
5. P.N. D'yachkov and D.V. Makaev. Electronic structure of embedded carbon nanotubes. Phys. Rev. B, 71, 081101 (2005).
6. P.N. D'yachkov, “Augmented waves for nanomaterials”, in Encyclopedia of Nanoscience and Nanotechnology (Ed. N.S. Nalwa, American Scientific Publishers, Vol. 1, p. 191-212, 2004).
1. P.N. D’yachkov, D.Z. Kutlubaev, and D.V. Makaev. Linear augmented cylindrical wave Green’s function method for electronic structure of nanotubes with substitutional impurities. Phys. Rev. B, 82, 035426 (2010).
2. P. N. D’yachkov and D. V. Makaev, Electronic structure of BN nanotubes with intrinsic defects NB and BN and isoelectronic substitutional impurities PN, AsN, SbN, InB, GaB, and AlB, J. Phys. Chem. Solids, 70, 180-185 (2009)
3. P.N. D'yachkov and D.V. Makaev, Account of helical and rotational symmetries in the linear augmented cylindrical wave method for calculating the electronic structure of nanotubes: towards ab initio determination of band structure of (100, 99) tubule, Phys. Rev. B, 76, 195411 (2007).
4. P.N. D'yachkov and D.V. Makaev. Linear augmented cylindrical wave method for calculating the electronic structure of double-wall carbon nanotubes. Phys. Rev. B, 74, 155442 (2006).
5. P.N. D'yachkov and D.V. Makaev. Electronic structure of embedded carbon nanotubes. Phys. Rev. B, 71, 081101 (2005).
6. P.N. D'yachkov, “Augmented waves for nanomaterials”, in Encyclopedia of Nanoscience and Nanotechnology (Ed. N.S. Nalwa, American Scientific Publishers, Vol. 1, p. 191-212, 2004).