Long-range 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 π 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.