Session V2: Excitons in Single-Walled Carbon Nanotubes

Photoexcitation dynamics in SWCNT from sub-10 fs to ms

Photophisics in Single Walled Carbon Nanotubes, SWCNT-PEG, prepared by HiPco embedded PMMA is investigated with cw and pulse photo-excitation. Using ultra-short pulses in the visible and near infrared, with time duration of 7 fs and 20 fs respectively, pump-probe spectroscopy is carried out in SWCNT-PEG films in air at room temperature. Photo-bleaching recovery and photoinduced absorption build-up, upon excitation into the second absorption band, are time resolved providing a time constant of 40 plus/minus 5 fs. This is associated to exciton relaxation within semiconducting NTs, due to Fano-type resonances between localized excitonic levels and the underlying continuum density. Pumping in different regions of the absorption spectrum and probing a broad range of wavelengths, gives a complete description of the phenomenon. After relaxation, the decay of the equilibrated exciton occurs with a broad distribution of time constants, which is consistent with the inhomogeneous broadening of the sample. When using the shortest pulses (sub-10 fs) coherent phonons are clearly detected in the transmission difference traces. A radial breathing mode (RBM) at 250 wavenumber is observed, with dephasing of 1.2 ps. Anharmonic coupling between the RBM mode and the G-mode is detected for the first time in the time domain. Using cw excitation at 2.3 and 1.3 eV we observed photorefractivity in SWCNT-PEG samples, kept in vacuum at low temperature, in close analogy with conjugated polymers. Charges, which are photogenerated in the films, can separate giving rise to local electric fields which in turn induce Stark shift of the excitonic resonance.   

Ultrafast and CW Optical Probes of Photoexcitations in Semiconducting Carbon Nanotubes

Ultrafast dynamics of photoexcitations in semiconducting single walled carbon nanotubes (S-NT) in the form of films and D$_{2}$O solutions, have been investigated using low intensity high repetition rate femtosecond laser system based on Ti-sapphire optical parametric oscillator in the spectral range from 0.13 to 1.05 eV. Various transient photoinduced bleaching (PB) and photoinduced absorption (PA) bands were observed, which also show pronounced polarization memory. The PA spectrum does not show Drude free carrier absorption, but instead is composed of two PA bands below the PB of the lowest S-NT absorption band. Also the PB spectrum exactly follows the cw photoluminescence (PL) emission spectrum. We therefore conclude that the primary photoexcitations in S-NT are \textit{excitons} polarized along the NTs. We thus conjecture that the S-NT absorption bands are excitonic in origin; this conclusion is also supported by electroabsorption measurements that show quadratic Stark shift of the absorption bands. In addition, we found that the PL emission is also polarized; from the average PL polarization degree and ps transient polarization memory decay we estimate the PL lifetime in isolated S-NTs in solution to be of the order of 500 ps. Non-radiative decay processes dominate this relatively long PL lifetime. From the PL lifetime and the minute PL quantum efficiency we estimate the radiative PL lifetime in S-NTs to be $\sim \quad \mu $sec. This shows that the lowest lying exciton in S-NTs has small oscillator strength, and is in fact dark. The similarity of the PA spectrum in S-NTs and $\pi $-conjugated polymers indicates that quasi-1D excitons dominate the photophysics in both organic semiconducting materials. From this and the photon energy of the PA band we estimate the binding energy of the lowest exciton in S-NTs with diameters $\ge $ 1 nm to be $\sim $0.4 eV; in good agreement with two-photon absorption spectroscopy.\newline \newline Supported in part by the DOE.   

Photophysics of single-walled carbon nanotubes: similarity with $\pi$-conjugated polymer

Coulomb electron-electron (e-e) interactions among the $\pi$-electrons have a strong effect on the energy spectra of semiconducting single-walled carbon nanotubes (S-SWCNTs), because of their quasi-one-dimensionality. The primary photoexcitations in S-SWCNTs as a consequence of e-e interactions are excitons, as opposed to free electrons and holes. There already exists a vast literature on excitons in $\pi$-conjugated polymers, the other class of carbon-based quasi-one-dimensional semiconductors. In order to seek guidance from this knowledge base, we have performed theoretical calculations of the excited state electronic structures, linear absorptions and excited state absorptions for ten different S-SWCNTs with a wide range in diameters, \footnote{H.~Zhao, {\it et al.}, cond-mat/0506097; J.~W. Kennedy, {\it et al.}, cond-mat/0505071.} within the same correlated $\pi$-electron model that has previously been applied to $\pi$-conjugated polymers. We found remarkable similarities in the excitonic energy spectra and nonlinear optical properties of S-SWCNTs on the one hand, and $\pi$-conjugated polymers on the other. The ``essential states'' model \footnote{S.~N. Dixit, D.~Guo, and S.~Mazumdar, Phys. Rev. B {\bf 43}, R6781 (1991).} of third-order optical nonlinearity, previously developed for $\pi$-conjugated polymers, applies also to S-SWCNTs (with minor modifications for chiral S-SWCNTs which lack center of inversion). Our theory is able to explain semiquantitatively the results of nonlinear spectroscopic measurements on both S-SWCNTs and $\pi$-conjugated polymers. For wide S-SWCNTs with diameters ranging from 0.8--1.0 nm, we calculate exciton binding energies of 0.3--0.4 eV, in strong agreement with the values predicted from the experiments. We also remark on the occurrence of dark excitons below the optical excitons in the S-SWCNTs, \footnote{H. Zhao and S. Mazumdar, Phys. Rev. Lett. {\bf 93}, 157402 (2004).} and the consequence thereof on the photoluminescence of these materials.   

Dephasing and weak localization in an interacting 1D system

We study the transport properties of interacting electrons in a disordered quantum wire (e.g. carbon nanotube) within the framework of the Luttinger liquid model. The conductivity at finite temperature is nonzero only because of inelastic electron-electron (e-e) scattering. We demonstrate that the notion of weak localization (WL) is applicable to the strongly correlated one-dimensional electron system and calculate the WL correction to the conductivity at not too low temperatures. The relevant dephasing rate is governed, for spinless electrons, by the interplay of e-e interaction and disorder. This WL dephasing rate is parametrically different from the dephasing rate of Aharonov-Bohm oscillations in a ring. Our approach, combining bosonization with fermionic treatment of the problem, provides a framework for systematically studying the mesoscopic phenomena in strongly correlated 1D electron systems. In the end, the fate of dephasing at lower temperatures (in the strong-localization regime) is briefly discussed.   

Tuning photo-carrier lifetimes by the atomic structure and environment of single-walled carbon nanotubes

Carrier relaxation in single-walled carbon nanotubes depends on their chirality, the tube's atomic structure. Excitons decay by interacting with phonons in most tubes, but a fast electron-electron channel becomes available in a subset of tubes. Carrier relaxation at the band gap depends on the tube's environment, with an order of magnitude difference between isolated (10-100 ps) and bundled tubes (1 ps). In this talk we discuss carrier relaxation in carbon nanotubes after photoexcitation. Our results explain the varying luminescence intensity in nanotubes and why nanotube bundles do not emit light. We estimate nanotube abundances from luminescence and discuss our concepts in view of non-linear optical devices made from single-walled carbon nanotubes.