Mechanical Properties of Carbon Nanotubes in a Chiral Model of Graphene

Taking into account the SP2-hybridization effect for valence electrons in carbon atoms, we introduce a unitary matrix (U) as an order parameter and suggest a scalar chiral model of graphene for the description of carbon nanotubes. We consider both single-walled and two-walled carbon nanotubes, analyze corresponding solutions to the model equations and estimate the Young's modulus. We discuss also the possible extension of the model in question to describe fullerenes as three-dimensional hedgehog structures (skyrmions). We find the corresponding Lagrangian density for the spherirically-symmetric chiral angle. The other extension of the model concerns spin and magnetic excitations of graphene-based configurations. To this end, the 8-spinor field should be introduced as a new order parameter (Rybakov, 2015).