Electron mean-free path in metal-coated nanowires

The mean-free path Leff is calculated for a circular shell geometry under the assumptions of (i) billiard scattering and (ii) diffusive scattering. Similarly to a spherical shell geometry, Leff displays qualitatively different behavior on the shell thickness D for the two models. Whereas, for the billiard model Leff=πD/2, the mean-free path in the diffusive scattering case is a complicated function involving complete and incomplete elliptic integrals of the first, second, and third kinds. Nevertheless, a linear combination of D and Dln (R/2D), where R is the outer circle radius, is shown to capture the functional dependence of Leff in the diffusive scattering case remarkably well over almost the entire parameter range. Hopefully, future experiments on single and well-controlled dielectric-core–metal-shell nanowires could differentiate between the two models.