Session T24: Focus Session: Excitonic Effects in Nanotubes

Time-Domain Ab Initio Studies of Photoinduced Electron-Phonon Dynamics in Carbon Nanostructures.

The electron-phonon interactions in carbon nanotubes and nanoribbons determine the response times of optical switches and logic gates, the extent of heating and energy loss in nanowires and field-effect transistors, and even a superconductivity mechanism. We have developed state-of-the-art non-adiabatic molecular dynamics techniques and implemented them within time-dependent density functional theory in order to model the ultrafast photoinduced processes in carbon nanostructures at the atomistic level and in real time. Our ab initio studies directly mimic the experimental data and reveal many intriguing features of the excitation dynamics, including non-radiative fluorescence quenching, fast intrinsic intraband relaxation, phonon-induced component of fluorescence linewidths, the importance of defects, the dependence of the relaxation rates on the excitation energy and intensity, spin-orbit interaction and a detailed understanding of the role of active phonon modes.   

Exciton Spectroscopy and Absorption Cross-section of Individual Single-Walled Carbon Nanotubes

Semiconducting Single-Walled Carbon Nanotubes (SWNTs) display intrinsic exciton luminescence which is highly sensitive to the nanotubes environment. For instance single-molecule chemical reactions with individual SWNTs could be observed through the stepwise changes of the luminescence intensity within submicrometer segments of single nanotubes. Analysis of the step amplitudes revealed an exciton diffusion range of $\sim $90 nm. Each exciton thus visits approximately 10$^{4}$ atomic sites during its lifetime, providing highly efficient sensing of local chemical and physical perturbations [1]. SWNT luminescence decays are also sensitive to extrinsic factors. Using highly luminescent individual (6,5) SWNTs, time-resolved spectroscopy revealed however systematic biexponential luminescence decays, with short and long lifetimes around 45 and 250 ps. This intrinsic behavior is attributed to the band-edge exciton fine structure with a dark level lying a few meV below a bright one. Combining such time-resolved studies with cw luminescence ones, the absorption cross-section of individual SWNTs was determined. A mean value of $\sim $1.10$^{-17}$ cm$^{2}$ per carbon atom is obtained for (6, 5) tubes excited at their second optical transition [2]. This was further corroborated by independent photothermal heterodyne measurements. Because this highly sensitive method relies only on light absorption, it readily detects metallic nanotubes as well as the emissive semiconducting species in various environments and allowed recording for the first time images and absorption spectra of individual SWNTs of both types [3]. \\[4pt] [1] Cognet et al \textit{Science} \textbf{316}, 1465 (2007) \\[0pt] [2] Berciaud et al \textit{Phys.Rev.Lett.} \textbf{101}, 077402 (2008) \\[0pt] [3] Berciaud et al \textit{Nanoletters} \textbf{7}, 1203 (2007)   

Exciton Distribution between the Bright and Dark States in Single Carbon Nanotubes Studied by Magneto-Photoluminescence Spectroscopy

We have performed micro-photoluminescence (PL) spectroscopy for single carbon nanotubes under magnetic fields at various temperatures. Sharp PL spectra of single carbon nanotubes allow us to directly observe the dark exciton PL peak a few meV below the bright exciton PL peak due to the Aharonov-Bohm effect [1]. From the PL intensity ratio of the dark to the bright excitons under magnetic fields, we found that the non-equilibrium (non-Boltzmann) distribution occurs between the bright and dark states, because phonons cannot scatter excitons between the two states with different parities [2]. Furthermore, we discuss the diameter dependence of the exciton population of the bright and dark states in single carbon nanotubes. [1] R. Matsunaga, K. Matsuda, and Y. Kanemitsu, Phys. Rev. Lett. \textbf{101}, 147404 (2008). [2] V. Perebeinos, J. Tersoff, and Ph. Avouris, Nano Lett. \textbf{5}, 2495 (2005).   

Chiral dependence of K-momentum exciton energies in carbon nanotubes

Fifteen of the sixteen excitons in the $E_{11}$ manifold of carbon nanotubes are nominally dark. Of these, the zero-momentum dark singlet has received the most experimental attention because it exhibits magnetic brightening. By contrast, here we focus on the $K$ and $K'$-momentum dark singlets. Absorptive ($X_{2})$ and emissive ($X_{1})$ sidebands appearing at $\sim $0.2 eV above and $\sim $0.13 eV below the bright exciton, respectively, have been interpreted in numerous ways in the literature. Recently, members of our group studied these sidebands in a (6,5) nanotube and concluded they could be used to energetically locate the $K$-momentum excitons (Torrens, et al, PRL 101, 157401 (2008)). Here we use a combination of experiment and theory to study $X_{1}$ and $X_{2}$ in at least ten samples that are highly purified in a single chirality and use these findings to study how the $K$-momentum exciton energy depends on chirality.   

Controlling Optimal Excitation Wavelength of Energy Transfer from Photo-Excited Polymers to Single-Walled Carbon Nanotubes.

The optimal excitation wavelength for the energy transfer from aromatic polymers poly(9,9-dioctylfluoreny- 2,7-diyl) (PFO) to single-walled carbon nanotubes (SWNTs) is tunable in a wide wavelength range (from 388 to 480 nm) depending on the concentration of excess PFO polymers. The concentration governs the aggregation state and chain conformation of the polymers proximate to SWNT surfaces, which in turn alters the optimal excitation wavelength. This study suggests an exciting and convenient method of adjusting the desired optical wavelengths for the energy conversion, useful for polymer-SWNT composites in optoelectronic applications.   

Exciton Radiative Lifetimes and Their Temperature Dependence in Single-Walled Carbon Nanotubes

We have investigated the radiative lifetimes of excitons in single-walled carbon nanotubes (SWNTs) from simultaneous measurements of the photoluminescence (PL) lifetimes [1] and the PL quantum yields. A high-quality sample of PFO dispersed-SWNTs was used for the PL measurements. The evaluated radiative lifetimes were ${\sim5-15}$ ns for SWNTs with diameters ${\sim0.8-1.1}$ nm at room temperature. The radiative lifetimes increased with the tube diameter. The exciton spatial coherence volume (length) was of the order ${10} ^{2}$ nm along the tube axis, as deduced from the radiative lifetimes. Furthermore, we discuss the dynamics of bright and dark excitons [2] from the temperature dependence of the radiative lifetime (10 to 300 K).\\[3pt] [1] H. Hirori, K. Matsuda, Y. Miyauchi, S. Maruyama, and Y. Kanemitsu, Phys. Rev. Lett. ${\bf 97}$, 257401 (2006). \\[0pt] [2] R. Matsunaga, K. Matsuda, and Y. Kanemitsu, Phys. Rev. Lett. ${\bf 101}$, 147404 (2008).   

Effects of Exciton-Exciton Annihilation in Fluorescence of Individual SWCNTs

Most studies of SWCNT exciton relaxation have been performed on bulk samples, with clear conclusions hampered by the variety of structural types, lengths, and aggregation states. To avoid such problems, we use near-IR fluorescence microscopy to study nearly pristine individual nanotubes with optically resolvable lengths. We find emission proportional to excitation at low intensities. But for stronger excitation, an increasingly sub-linear dependence is observed, due to exciton-exciton annihilation within single nanotubes. Since annihilation depends on exciton lifetime and mobility, these parameters can be studied by analyzing measured intensity dependences. We compare data on exciton excursion ranges and emission efficiency in individual SWCNTs to numerical simulations to quantify exciton lifetime and diffusion for a variety of (n,m) structures. Preliminary results yield lifetimes of a few nanoseconds for nearly pristine, highly emissive nanotubes and reveal some dependence of lifetime on nanotube diameter.   

Exciton Dynamics in (6,5) carbon nanotubes

Single color (E22) pump-probe data on a solution of (6,5) nanotubes reveal that use of pulses shorter than the dephasing time scale precludes the formation of multiple excitons on a single nanotube. Subsequent relaxation dynamics of the single exciton exhibits stretched exponential behavior, and data from low to saturation fluence, and over 3 order of magnitude of time delay, is described by the same model. The stretched exponential model with its implication of a distribution of decay rates is attributed to a distribution of length-dependent effective lifetimes due to end-quenching via diffusion. Results give values for the dipole moment, E22 dephasing time and E11 diffusion coefficient.   

Exciton Dynamics in Individual Single-walled Carbon Nanotubes

Optical excitation of single-walled carbon nanotubes (SWNTs) results in strongly bound excitons. The dynamics and energetic pathways available to the exciton as it relaxes back to the ground state have recently received significant attention. We have performed transient absorption (TA) experiments on DNA-wrapped (6,5) SWNTs in the extremely low-excitation fluence regime. Excitation was provided by a Ti-sapphire oscillator whose output was focused into a highly nonlinear photonic crystal fiber generating a coherent, femtosecond white-light source. We found the recovery of the photobleach signal for excitons in the 1st and 2nd excited states (E$_{11}$and E$_{22})$ was governed by power-law dynamics. Interestingly, we also observed an induced absorption feature in the TA spectrum to the blue of the E$_{11}$ exciton that showed the same recovery dynamics as the photobleach signal, suggesting that they share a common origin. We will discuss the physical origins of the observed features in the TA spectrum in the context of current models of exciton states of the SWNT.