Electrodynamics of carbon nanotubes: Dynamic conductivity, impedance boundary conditions, and surface wave propagation

Effective boundary conditions, in the form of two-sided impedance boundary conditions, are formulated for the linear electrodynamics of single- and multishell carbon nanotubes (CN's). The impedance is derived using the dynamic conductivity of CN's, which is obtained for different CN's (zigzag, armchair, and chiral) in the frame of the semiclassical as well as quantum-mechanical treatments. Propagation of surface waves in CN's is considered. The phase velocities and the slow-wave coefficients of surface waves are explored for a wide frequency range, from the microwave to the ultraviolet regimes. Relaxation is shown to qualitatively change the dispersion characteristics in the low-frequency limit, thereby rendering the existence of weakly retarded plasmons impossible. A dispersionless propagation regime is shown possible for the surface waves in the infrared regime. Attenuation and retardation in metallic and semiconductor CN's are compared.