Electrodynamics of Carbon Nanotubes with Non-Local Surface Conductivity

A new framework that can be utilized for the electrodynamics of carbon nanotubes (CNTs) with non-local surface conductivity (spatial dispersion) is presented. The model of non-local conductivity is developed on the basis of the Kubo technique applied to the Dirac equation for pseudospins. As a result, the effective boundary conditions for the electromagnetic (EM) field on a CNT surface are formulated. The dispersion relation for the eigenmodes of an infinitely long CNT is obtained and analyzed. It is shown that due to nonlocality, a new type of eigenmode is created that disappears in the local conductivity limit. These eigenmodes should be properly accounted for in the correct formulation of the CNT end conditions for the surface current, which are manifested in the EM-field scattering problem. Additional boundary conditions that consider nonlocality effects are also formulated based on the exact solution obtained for the surface current by means of using the Wiener–Hopf (WH) technique for a semi-infinite CNT. The scattering pattern of the EM-field is simulated by a finite-length model of a CNT, using a numerically solved integral equation for the surface current density and its approximate analytical solution. Thus, the scattering field of a CNT, prevailing in a wide frequency range from THz to infrared light, is analytically solved and analyzed. Potential applications for the design of nanoantennas and other electronic devices, including pointing out some future directions, are also discussed.