Casimir Interactions Between Scatterers in Metallic Carbon Nanotubes

Abstract

We study interactions between localized scatterers on metallic carbon nanotubes by a mapping onto a one-dimensional Casimir problem. Backscattering of electrons between localized scattering potentials mediates long range forces between them. We model spatially localized scatterers by local and non-local potentials and treat simultaneously the effects of intravalley and intervalley backscattering. We find that the long range forces between scatterers exhibit the universal power law decay of the Casimir force in one dimension, with prefactors that control the sign and strength of the interaction. These prefactors are nonuniversal and depend on the symmetry and degree of localization of the scattering potentials. We find that local potentials inevitably lead to a coupled valley scattering problem, though by contrast non-local potentials lead to two decoupled single-valley problems in a physically realized regime. The Casimir effect due to two-valley scattering potentials is characterized by the appearance of spatially periodic modulations of the force.

19 pages, 12 figures

References in corpus (6)

• Control of graphene's properties by reversible hydrogenation
• Long-Range Interaction Between Adatoms in Graphene
• Oscillating Casimir force between impurities in one-dimensional Fermi liquids
• Indirect forces between impurities in one-dimensional quantum liquids
• Casimir Effect for Massless Fermions in One Dimension: A Force Operator Approach
• Degeneracy breaking and intervalley scattering due to short-ranged impurities in finite single-wall carbon nanotubes

Cited by in corpus (5)

• Sign Flip in the Casimir Force for Interacting Fermion Systems
• Lattice-fermionic Casimir effect and topological insulators
• Casimir force variability in one-dimensional QED systems
• Dual chiral density wave induced oscillating Casimir effect
• Lifshitz formulas for finite-density Casimir effect