Measurements of exciton binding energies in single wall nanotubes using field dependent photocurrent spectroscopy

We have used electric field dependent photocurrent measurements to distinguish between band-to-band and excitonic transitions in the excitation spectrum of a single wall nanotube capacitor. The zero field photocurrent spectrum is limited to carriers excited into continuum states that can freely diffuse from the nanotubes and into the metal contact. Application of an applied field allows for the separation of the bound exciton states via field ionization. Near the E$_{11}$ resonance, both excitonic and band-to-band transitions are resolvable with a binding energy of 109 meV. This is in reasonable agreement with recent theory for 1.3 nm diameter nanotubes$^{1}$. Near the E$_{22 }$resonance, we observe only a single field independent peak in the photocurrent spectrum indicating a fast decay of the exciton into the lower energy continuum states. Surprisingly, we are also able to resolve an exciton resonance associated with metallic nanotubes. Theory shows that in metallic nanotubes, optical transitions between the overlapping states at the Fermi energy are disallowed, giving rise to a symmetry gap$^{2}$. We measure the binding energy of the metallic exciton to be 49 meV for 1.3 nm diameter tubes. \textbf{References} (1) Perebeinos, V.; Tersoff, J.; Avouris, Ph., \textit{Phys. Rev. Lett.} \textbf{2004}, 92, 257402. (2) Spataru, C.D.; Ismail-Beigi, S.; Benedict, L.X,; Louie, S.G. \textit{Phys. Rev. Lett.} \textbf{2004}, 92, 077402.