Electronic and optical gap renormalization in carbon nanotubes near a metallic surface

Abstract

Renormalization of quasiparticles and excitons in carbon nanotubes (CNTs) near a metallic surface has been studied within a many-body formalism using an embedding approach newly implemented in the GW and Bethe-Salpeter methods. The quasiparticle band-gap renormalization in semiconducting CNTs is found to scale as $\ensuremath{-}1/(2{h}_{a})$, with ${h}_{a}$ the apparent nanotube height, and it can exceed half an eV. Also, the binding energy of excitons is reduced dramatically---by as much as $75%$---near the surface. Compensation between quasiparticle and excitonic effects results in small changes in the optical gap. The important role played by the nanotube screening response in establishing these effects is emphasized and a simple electrostatic model with no adjustable parameters explains the results of state-of-the-art calculations and generalizes them to a large variety of CNTs.