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

Abstract

Physical properties of graphene nanotubes may strongly depend on external fields. In a recent paper 8 , 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 non-trivial 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 that is more efficient than others proposed. 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.

Confinement of Dirac electrons in graphene magnetic quantum dots

“…This type of magnetic interacting systems in graphene [16] as well as in fullerenes and nanotubes [31][32][33] has the formal structure of supersymmetric quantum mechanics (susy-qm) [34][35][36][37]. The symmetry of the field and the supersymmetric algebraic structure allow us to get simple and clear expressions for different properties of these magnetic systems.…”

Coherent states in the symmetric gauge for graphene under a constant perpendicular magnetic field

“…The interaction of conducting electrons of graphene with magnetic or electric fields, as a way of controlling or confining them, has attracted growing interest. In particular, many authors have addressed the magnetic confinement of electrons in many different configurations, like square well magnetic barriers [32,33], radial magnetic fields [34], magnetic fields corresponding to solvable potentials [35,36], smooth inhomogeneous magnetic fields [37][38][39][40][41][42][43], etc. In this context, following Malkin and Man'ko's ideas [10], one can try to build the coherent states for such a kind of systems considering, in principle, homogeneous perpendicular magnetic fields.…”