Electron-electron interaction effects on the photophysics of metallic single-walled carbon nanotubes

Abstract

Single-walled carbon nanotubes are strongly correlated systems with large Coulomb repulsion between two electrons occupying the same $p_z$ orbital. Within a molecular Hamiltonian appropriate for correlated $\pi$-electron systems, we show that optical excitations polarized parallel to the nanotube axes in the so-called metallic single-walled carbon nanotubes are to excitons. Our calculated absolute exciton energies in twelve different metallic single-walled carbon nanotubes, with diameters in the range 0.8 - 1.4 nm, are in nearly quantitative agreement with experimental results. We have also calculated the absorption spectrum for the (21,21) single-walled carbon nanotube in the E${}_{22}$ region. Our calculated spectrum gives an excellent fit to the experimental absorption spectrum. In all cases our calculated exciton binding energies are only slightly smaller than those of semiconducting nanotubes with comparable diameters, in contradiction to results obtained within the {\it ab initio} approach, which predicts much smaller binding energies. We ascribe this difference to the difficulty of determining the behavior of systems with strong on-site Coulomb interactions within theories based on the density functional approach. As in the semiconducting nanotubes we predict in the metallic nanotubes a two-photon exciton above the lowest longitudinally polarized exciton that can be detected by ultrafast pump-probe spectroscopy. We also predict a subgap absorption polarized perpendicular to the nanotube axes below the lowest longitudinal exciton, blueshifted from the exact midgap by electron-electron interactions.

References in corpus (7)

• Exciton binding energies in carbon nanotubes from two-photon photoluminescence
• Electron-electron interaction effects on optical excitations in semiconducting single-walled carbon nanotubes
• Cross-polarized optical absorption of single-walled nanotubes probed by polarized photoluminescence excitation spectroscopy
• Universal properties of quasi-one-dimensional excitons in semiconducting single-walled carbon nanotubes and $\pi$-conjugated polymers
• Quantitative calculations of the excitonic energy spectra of semiconducting single-walled carbon nanotubes within a $\pi$-electron model
• pi-Electron theory of transverse optical excitons in semiconducting single-walled carbon nanotubes
• Dynamical symmetry enlargement in metallic zigzag carbon nanotubes

Cited by in corpus (4)

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• Unusual low-temperature behavior in the half-filled band of the one-dimensional extended Hubbard model in atomic limit
• Quantum Otto engine mimicking Carnot near pseudotransitions in the one-dimensional extended Hubbard model in the atomic limit