A qualitative study of a nanotube model using an iterative Taylor method

M. Gadella, L. P. Lara () and J. Negro ()
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M. Gadella: Departamento de Física Teórica, Atómica y Óptica and IMUVA, Universidad de Valladolid, Paseo Belén 7, Valladolid 47011, Spain
L. P. Lara: Departamento de Física, FCEIA, UNR, Av. Pellegini 250, 2000 Rosario, Argentina
J. Negro: Departamento de Física Teórica, Atómica y Óptica and IMUVA, Universidad de Valladolid, Paseo Belén 7, Valladolid 47011, Spain

International Journal of Modern Physics C (IJMPC), 2017, vol. 28, issue 03, 1-22

Abstract: Physical properties of graphene nanotubes may strongly depend on external fields. In a recent paper V. Jakubský, S. Kuru, J. Negro, J. Phys. A: Math. Theor. 47, 115307 (2014), the authors have studied a model of carbon nanotubes under the presence of an external magnetic field, chosen for some symmetry properties. The model admits an exact solution, provided that the value of a parameter, here denoted as kz, be equal to zero. This parameter is the eigenvalue of the component of the momentum in the direction of the nanotube axis. However, it seems that this parameter cannot be discarded for physical reasons. The choice of nontrivial values for this parameter produces an equation of motion for electrons in the nanotube (a Dirac–Weyl equation), which cannot be exactly solvable. Then, we proposed some iterative approximate methods to solve this equation and obtaining its eigenvalues. Some tests have shown that an iterative Taylor method is more efficient than some others we have used. For kz≠0, we have found that, excluding the minimal energy eigenvalue, the lowest energy values obtained for kz=0 split into two different ones and, therefore, producing gaps in the energy spectrum.

Keywords: Graphene nanotubes; Dirac–Weyl equation; iterative methods for ODE; iterative Taylor method; band structures (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1142/S012918311750036X

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