We formulated a hydrodynamic model in order to describe the dynamical behavior of the π- electrons in single carbon nanotube shells of arbitrary chirality, either metallic or semiconducting, below terahertz frequencies, as long as only intraband transitions of the π- electrons are allowed. The hydrodynamic equations were derived in a self-consistent way from the semiclassical Boltzmann equation. The electron fluid was taken to comprise many electron species, each characterized by a different effective mass, which takes into account the interaction with the nanotube ion lattice. A linear transport model for the π- electrons was derived from the hydrodynamic equations. A transmission line model was eventually formulated to describe the propagation of an electric signal along a single-wall carbon nanotube of arbitrary chirality. The transport model formulated can be also used for analyzing electromagnetic propagation in complex structures composed of single carbon-nanotube shells with different chirality, such as bundles of single wall carbon nanotubes and multi-wall carbon nanotubes, provided that the tunneling between adjacent shells may be disregarded.
"Hydrodynamic model for the signal propagation along carbon nanotubes," Journal of Nanophotonics 4(1), 041695 (1 April 2010). https://doi.org/10.1117/1.3424968