Van der Waals Forces in Quasi 1-D Structures

Analytical formulations of Van der Waals-Casimir forces in terms of the macroscopic response of the system have been done extensively for 2-D and 3-D systems. On the other hand, quasi 1-D materials have been studied less, in part because of the difficulty in solving the boundary conditions. In this talk, by using the RPA method, we present a formulation of the Van der Waals force in narrow infinitely long ribbons. This approach is applied in the quantum mechanical and thermal regimes to several typical systems, such as insulators, metals, and semiconductors. Novel results are found for graphene nanoribbons, for which a transition from quantum mechanical to thermal van der Waals force can be realized at room temperature by changing the chemical potential.