Dispersion in Single-Wall Carbon Nanotube Film: An Application of Bogoliubov–Valatin Transformation for Hamiltonian Diagonalization

We present a theoretical study on the energy dispersion of an ultrathin film of periodically-aligned single-walled carbon nanotubes (SWCNTs) with the help of the Bogoliubov–Valatin transformation. The Hamiltonian of the film was derived using the many-particle green function technique in the Matsubara frequency formalism. The periodic array of SWCNTs was embedded in a dielectric with comparatively higher permittivity than the substrate and the superstrate such that the SWCNT film became independent with the axis of quantization but keeps the thickness as the variable parameter, making the film neither two-dimensional nor three-dimensional, but transdimensional. It was revealed that the energy dispersion of the SWCNT film is thickness dependent.