Electron-Electron Interaction Effects on the Optical Excitations of Semiconducting Single-Walled Carbon Nanotubes

We report correlated-electron calculations of optically excited states in ten semiconducting single-walled carbon nanotubes with a wide range of diameters. Optical excitation occurs to excitons whose binding energies decrease with increasing nanotube diameter, and are smaller than the binding energy of an isolated strand of poly-(paraphenylene vinylene). The ratio of the energy of the second optical exciton polarized along the nanotube axis to that of the lowest exciton is smaller than the value predicted within single-particle theory. The experimentally observed weak photoluminescence is an intrinsic feature of semiconducting nanotubes.

Figure 1

(Left) Schematic of the four degenerate single-particle excitations from the highest occupied to the lowest unoccupied one-electron levels in SWCNTs. (Right) These degeneracies are split by $H_{e\mathrm{\text{−}}e}$, and only the highest state is strongly dipole allowed. Rapid relaxation occurs to the lowest forbidden exciton, radiative relaxation from which is forbidden.

Figure 2

Absorption spectra of (8,0) nanotube from (a) Hückel, (b) Hartree-Fock, and (c) SCI calculations. Shaded peaks indicate transverse polarized absorptions. The inset shows longitudinal (solid arrows) and transverse (dashed arrows) excitations.

Figure 3

Calculated energies of the two lowest excitons vs inverse diameter of the SWCNTs.