Electromagnetic properties of a composite medium comprising chains of tunnel-coupled carbon nanotubes

When creating a model of a composite medium based on carbon nanotubes in the gigahertz and subterahertz ranges, it is necessary to take into account the tunnel coupling between nanoparticles. To simplify the consideration, we present a model of a composite medium consisting of the same randomly oriented linear chains of parallel single walled metallic carbon nanotubes connected by tunnel contacts. The problem of scattering of electromagnetic radiation by the chains was solved through the application of the integral equation technique of classical electrodynamics and the Landauer – Buttiker formalism for quantum transport. It is shown that electron tunnelling between the nanotubes leads to the electromagnetic size effects in chains of finite length. In this case, in the gigahertz frequency range, there is a regime in which the comparable in magnitude real and imaginary parts of the effective permittivity of the composite medium decrease with increasing frequency that is often observed in experiments. It has been found that size effects can manifest themselves within small sections of the chain limited by contacts of low conductivity. The obtained results provide an understanding of the physical mechanisms responsible for the frequency dispersion of the permittivity of composite materials based on carbon nanotubes.