Quantum and Thermal Dispersion Forces: Application to Graphene Nanoribbons

The van der Waals dispersion force between graphene nanoribbons is investigated. For this purpose, a nonretarded Lifshitz-like formula for parallel 1D systems is presented within the random phase approximation. Using the response properties of the ribbons from a tight binding model, it is found that the qualitative behavior of the force is similar to the one between two insulating 1D systems. On the other hand, the quantum mechanical van der Waals force can become thermal in nature when the nanoribbons have sufficiently strong chemical potential. It is found that this tuning capability is due to the unique dielectric properties of graphene nanoribbons. Results for other typical 1D materials are also presented, which enable building a better understanding of this ubiquitous force at reduced dimensions.