Nanotubes in polar media: polarons and excitons on a cylinder
Electrons and holes on semiconducting nanotubes immersed in sluggish polar media can undergo self-localization into polaronic states. We evaluate the binding energy $\bpol$ of adiabatic Fröhlich-Pekar polarons confined to a cylindrical surface and compare it to the corresponding exciton binding energy $\bexc$. The ratio $\bpol/\bexc$ is found to be a non-monotonic function of the cylinder radius $R$ that can reach values of about 0.35, substantially larger than values of about 0.2 for 2$d$ or 3$d$ systems. We argue that these findings represent a more general crossover effect that could manifest itself in other semiconductor nanostructures in 3$d$ polar environments. As a result of the strong polaronic effect, the activation energy of exciton dissociation into polaron pairs is significantly reduced which may lead to enhanced charge separation.