We have measured the electric field modulated absorption of a sample of single-walled nanotubes (SWNT) suspended in a solid polyvinyl alcohol matrix. The electroabsorption (EA) spectrum roughly follows the first derivative of the absorption with respect to photon energy, scales quadratically with the electric field strength, and shows a pronounced anisotropy of light polarization with respect to the applied electric field direction. These findings indicate a quadratic Stark effect caused by a change in the polarizability of the excited states, which is common to quasi-one dimensional (1D) excitons in organic semiconductors. The EA spectrum is well described by calculations involving electron-electron interaction in the model Hamiltonian of both zigzag and chiral nanotubes. We have calculated the EA spectra for both zigzag and chiral nanotubes within a model Hamiltonian that includes electron-electron interactions. The calculations reproduce the observed quadratic Stark shift of the lowest optical exciton, as well as the more complicated behavior of the EA spectrum in the energy region that corresponds to the next higher exciton. Our findings show that the low-lying absorption bands in semiconducting SWNT are excitonic in origin, in agreement with transient optical measurements that identify the primary photoexcitations in SWNT as quasi-1D excitons with a substantial binding energy.
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