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Polarons and excitons on a cylinder: a simplified model for nanotubes in polar environments

Excess charge carriers on semiconducting nanotubes immersed in sluggish polar environments can undergo self-localization into polaronic states. Using a simplified model of electrons and holes of equal effective masses and confined to a cylindrical surface in the three-dimensional polar medium, we evaluate the binding energy Ebpol of adiabatic Fröhlich–Pekar polarons and compare it to the corresponding exciton binding energy Ebexc. The ratio Ebpol/Ebexc is found to be a non-monotonic function of the cylinder radius R which, in an idealized model, can reach values of about 0.35, substantially larger than values of about 0.2 for two-dimensional (2D) or three-dimensional (3D) systems. We argue that these findings represent a more general crossover effect that could manifest itself in other semiconductor nanostructures in 3D 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.