Evidence for Strong Electronic Correlations in the Spectra of Gate-Doped Single-Wall Carbon Nanotubes

We have investigated the photophysical properties of electrochemically gate-doped semiconducting single-wall carbon nanotubes (s-SWNTs). A comparison of photoluminescence (PL) and simultaneously recorded absorption spectra reveals that free-carrier densities correlate well with the first sub-band exciton or trion oscillator strengths but not with PL intensities. We thus used a global analysis of the first sub-band exciton absorption for a detailed investigation of gate-doping, here of the (6,5) SWNT valence band. Our data are consistent with a doping-induced valence band shift according to Delta epsilon(v) = n x b, where n is the free-carrier density, epsilon(v) is the valence band edge, and b = 0.15 +/- 0.05 eV . nm. We also predict such band gap renormalization of one-dimensional gate-doped semiconductors to be accompanied by a stepwise increase of the carrier density by Delta n = (32m(eff)b)/(pi h)(2) (m(eff) is effective carrier mass). Moreover, we show that the width of the spectroelectrochemical window of the first sub-band exciton of 1.55 +/- 0.05 eV corresponds to the fundamental band gap of the undoped (6,5) SWNTs in our samples and not to the renormalized band gap of the doped system. These observations as well as a previously unidentified absorption band emerging at high doping levels in the Pauli-blocked region of the single-particle Hartree band structure provide clear evidence for strong electronic correlations in the optical spectra of SWNTs.