Long ranged interactions in carbon atomic chains

Based on first-principles calculations we revealed fundamental properties of infinite and finite size monatomic chains of carbon atoms in equilibrium and under an applied strain. Distributions of bond lengths and magnetic moments at atomic sites exhibit interesting even-odd disparity depending on the number of carbon atoms in the chain and on the type of saturation of carbon atoms at both ends. It was shown that, the $\pi$-bands of carbon atomic chains behave as a one dimensional free electron system. A local perturbation created by a small displacement of the single carbon atom at the center of a long chain induces oscillations of atomic forces and charge density, which are carried to long distances over the chain. These long ranged oscillations are identified as Friedel oscillations showing $1/r$ decay rate in one dimensional systems.