Ballistic corrections to weak-localization conductance of carbon nanotubes

Abstract

In the usual formulation of the weak localization(WL) effect, the mean free path of the conduction electron is assumed to be smaller than the geometric size of conductors. In multiwalled carbon nanotubes, however, the mean free path l is usually larger than its radius R. We consider ballistic correction to the usual WL conductance of multiwalled nanotubes within a semiclassical theory of disordered conductors. The ballistic correction to WL magnetoconductance is significant when the winding number of the associated interference paths is smaller than $\ensuremath{\sim}l/(2\ensuremath{\pi}R).$ In this regime, ballistic paths along the circumference of the nanotube cause an additional correction $\ensuremath{\delta}G\ensuremath{\sim}{G/(k}_{F}R),$ where ${k}_{F}$ is the Fermi wave vector. The ballistic corrections to the frequency-dependent conductance are significant when the frequency becomes comparable to the elastic scattering rate.