Casimir Forces Between Two Carbon Nanotubes

We compute the Casimir force between two parallel and infinitely long carbon nanotubes. The force induced by fluctuations of the electromagnetic field follows from the Maxwell stress tensor, expressed in terms of the correlators of the fields which are obtained from the Green's function and the fluctuation-dissipation theorem for the current density. We show how the force depends on the distance between the nanotubes, as well as on their chiralities and semiconducting or metallic natures. We also analyze the convergence of the approximation we use that replaces integrals in frequency by sums over complex Matsubara frequencies. The methodology presented and the results obtained can contribute to the understanding of how electromagnetic fluctuations induce Casimir forces in complex microstructured geometries.