ABSTRACT
In this chapter, we successfully model the electronic dispersion relations of single-walled carbon nanotubes (SWCNTs). Whilst we use the 2D electronic dispersion relation for graphene as a starting point, the dispersion relation for SWCNTs is different in a fundamental way because it is one-dimensional (1D). The component of the electron wavevector in the axial direction (along the SWCNT) can take any value; SWCNTs which are synthesized in the laboratory are far too long for quantum confinement of electrons in the axial direction to play any role. However, in the circumferential direction (i.e. the direction circumnavigating the SWCNT), the electron wavevector can only take certain discrete values, those values for which the SWCNT circumference is an integer multiple of the electron wavelength, hence leading to the electron wave function being continuous.
