Ultrafast Spectral Exciton Diffusion in Single-Wall Carbon Nanotubes

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Ultrafast Spectral Exciton Diffusion in Single-Wall Carbon Nanotubes Studied by Time-Resolved Hole Burning Daniel Schilling, Christoph Mann, Pascal Kunkel, Friedrich Schöppler, and Tobias Hertel J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.5b06865 • Publication Date (Web): 01 Oct 2015 Downloaded from http://pubs.acs.org on October 9, 2015

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The Journal of Physical Chemistry

Ultrafast Spectral Exciton Diffusion in Single-Wall Carbon Nanotubes Studied by Time-Resolved Hole Burning Daniel Schilling,† Christoph Mann,† Pascal Kunkel,† Friedrich Schöppler,† and Tobias Hertel∗,†,‡ †Institute of Physical and Theoretical Chemistry, Faculty of Chemistry and Pharmacy, Julius-Maximilian University W¨ urzburg, Am Hubland, 97074 W¨ urzburg, Germany ‡Röntgen Research Center for Complex Material Systems, Julius-Maximilian University W¨ urzburg, Am Hubland, 97074 W¨ urzburg, Germany E-mail: [email protected]

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Abstract We have studied ultrafast spectral diffusion (SD) within exciton bands of semiconducting single-wall carbon nanotubes (s-SWNTs) using one- and two-dimensional, near-infrared transient hole burning spectroscopy and time-resolved fluorescence spectroscopy at temperatures between 15 K and 293 K. We find that inhomogeneous spectral broadening of 60 meV for s-SWNTs embedded in gelatin exceeds the homogeneous linewidth of 3.3 meV by over an order of magnitude. The experiments show that ultrafast spectral diffusion of excitons in gel-immobilized s-SWNTs on the 250 fs time-scale can be attributed to axial intra-tube exciton diffusion. Comparison with kinetic Monte Carlo simulations suggests that the length-scale characteristic of the granularity of the axial potential energy landscape is about 24 nm.

Keywords carbon nanotubes, exciton dynamics, transient absorption, inhomogeneous broadening, spectral diffusion, spectral hole burning

Introduction The photophysical properties of quantum emitters such as single-wall carbon nanotubes are of fundamental as well as applied interest due to the unique nature of photophysical phenomena in one-dimensional systems but also given the potential use of s-SWNTs in photonic devices. 1–5 However, s-SWNT photophysics are strongly affected by interactions with the environment which can lead to inhomogeneous line broadening, blinking and spectral diffusion. 6–11 While the specific origin and mechanism of environmental perturbations for the exciton dynamics remains subject to debate, it is important to understand the nature of the corresponding interactions and their implications for key photophysical properties of s-SWNTs such as radiative and non-radiative decay and electronic as well as vibrational 2


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dephasing. 12–15 Moreover, the extraordinary large surface-to-volume ratio of s-SWNTs and the corresponding surface sensitivity of their properties can give rise to large variations of key photophysical properties reported in the literature. Examples are the magnitude of photoabsorption cross sections, 16–19 PL lifetimes 20–23 or homogeneous linewidths of exciton bands. 12,24–27 This motivates the present study of photophysical properties of s-SWNTs in heterogeneous environments, which aims at exploring the effects of static spatial or dynamic potential modulations on exciton transport. The linewidths of optical transitions are commonly discussed in terms of homogeneous and inhomogeneous contributions. Within this framework, the nature of a specific linebroadening mechanism is classified as being homogeneous or inhomogeneous based on the time-bandwidth product of frequency spread ∆ω and characteristic time-scale ∆t of fluctuations within the associated spectral distribution. Transitions are said to be inhomogeneously broadened if this time-bandwidth product is significantly larger than 1. 28,29 The dynamical nature of spectral changes is thus intimately tied to the character of the broadening mechanism and can reveal valuable information about the nature and characteristics of interactions within and between quantum systems. Previously, exciton dephasing in carbon nanotubes has been studied using time domain photon echo 12 as well as stationary spectral hole burning 24 spectroscopy. For temperatures near 10 K the authors report dephasing times on the order of ≈ 250 fs corresponding to homogeneous linewidths of ≈ 5 meV. Somewhat surprisingly, coupling to phonon modes at higher temperatures is found to lead only to a small increase of dephasing rates, a fact that has been attributed to so called motional narrowing. 12 Exciton-exciton scattering may lead to an additional increase of dephasing rates. 12,24,25,30 According to Graham et al. the temperature dependence of exciton dephasing suggests coupling to acoustic phonon modes at temperatures below 80 K while coupling to optical phonon modes dominates dephasing at higher temperatures. 12,31 However, the largest contribution to absorption linewidths is attributed to exciton interactions with a strongly disordered environment.

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Due to the dynamic nature of environmental perturbations, disorder may contribute to both, homogeneous as well as inhomogeneous broadening. A peculiar effect of the freezing of low frequency modes at low temperatures in combination with motional narrowing at higher temperatures is that the overall temperature dependence of pure dephasing in s-SWNTs was found to be rather weak. Moreover, the large exciton size on the order of 2 nm or more 32 may prevent the exciton from effectively coupling to some phonon modes thus contributing to low room temperature dephasing rates. 12 Here, we use one- and two-dimensional time-resolved spectral hole burning- and timeresolved photoluminescence spectroscopy to assess the timescales and magnitude of spectral fluctuations and exciton diffusion in the S1 exciton band of s-SWNTs. In agreement with earlier studies we find that inhomogeneous broadening represents the largest contribution to exciton bandwidths between 45 and 63 meV FWHM at room temperature. The homogeneous bandwidth is found to be only ≈ 3 meV. Moreover, we observe ultrafast spectral diffusion within the exciton band on timescales of < 500 fs. Hypsochromic spectral diffusion (to higher energies) is thermally activated whereas bathochromic SD (to lower energies) occurs spontaneously on a sub-picosecond timescale. Kinetic Monte Carlo simulations suggest that such SD can be attributed to axial exciton diffusion between s-SWNT regions subject to varying environmental perturbations with a characteristic length-scale of (24 ± 13) nm. At the same time, ultrafast exciton diffusion, facilitated by the low effective exciton mass of ≈ 0.01me 33 may also be responsible for motional narrowing which requires that fluctuations in the phase of the exciton wavefunction are sufficiently rapid to average out over the timescale given by the time-bandwidth product using the amplitude of the energy fluctuations.

Results and discussion The absorption spectrum of the first subband exciton from a (6,5)-enriched s-SWNT sample is shown in Fig. 1a) along with the spectrum of the 3 nm wide pump pulse centered at the

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Figure 1: a) Absorption spectrum of a s-SWNT gelatin film containing mostly semiconducting (6,5) s-SWNTs. The absorption feature peaked at 987 nm corresponds to excitation of the first subband exciton. The narrow-band excitation spectrum is shown in blue. b) Transient spectra at different pump-probe delays ranging from -0.15 ps (blue) to 20 ps (orange). c) False color plot of the spectrally and time-resolved optical transients showing ultrafast spectral broadening within less than 1 ps.

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peak of the exciton band at 987 nm. In Fig. 1b) we show normalized transient absorption spectra for resonant narrow-band excitation at room temperature and at selected pumpprobe delays up to 20 ps. A false color plot of the full dataset in Fig.1c) reveals the existence of both, short and long lived photobleach- and photoabsorption features. 34,35 The spectra can be well described by a superposition of Lorentzian photobleach (PB) and photoabsorption (PA) signals centered at 987 nm and 982 nm respectively. 36–40 At early times, the transient spectra of Fig. 1b) are substantially narrower than the typical FWHM of the exciton band of 60 meV, observed in the ground state absorption spectrum of Fig. 1a). The transient spectra also clearly show that the initial increase of spectral width of PA and PB components is extremely fast.

Figure 2: Time dependence of the FWHM of the PB signal with rapid sub-ps spectral broadening to a FWHM of about 50 meV and a slower broadening by another 15 meV over the following 40 ps (T = 293 K). The time-dependence of the FWHM of the PB signal component shown in Fig. 2 was obtained using a Lorentzian fit to transient spectra. The FWHM of the PB feature is seen to increase on two time-scales, rapidly within 1 ps from below 10 meV to nearly 50 meV and considerably slower by another 15 meV over the following 40 ps. The width of the PB signal at time-zero is 7.7 meV, slightly increased from 4.5 meV at the onset of the first discernible 6


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transients around -0.2 ps. Time-zero is here defined as the time where the PB signal has reached half its maximum value. We note, that linewidths observed very early in transient spectra, in particular during interaction of the sample with the pump beam may also be affected by coherent artifacts 41 from perturbed free induction decay as well as by pumpprobe pulse coherences. 42 The interpretation of the spectral hole width in terms of its relationship to the homogeneous linewidth here also deserves some attention. In conventional spectral hole burning studies the spectral hole width Γ can be assumed to be twice of the homogeneous linewidth γ, as expected for the summation of line profiles over independent absorbers within an inhomogeneously broadened absorption profile. 43–45 The implied relationship between homogeneous linewidth and width of the photo-hole Γ = 2γ can then be used if the inhomogeneous width greatly exceeds the homogeneous linewidth and if the bandwidth of the pump pulse is small compared to the homogeneous linewidth. Comparison of the small PB widths near time zero with the absorption linewidth of 60 meV clearly suggests that the first condition is satisfied. But the finite spectral width of the excitation pulse in these experiments limits our ability to resolve small homogeneous linewidths to about 4 meV. By contrast, the homogeneous linewidth is said to be identical to the observed hole width (Γ = γ) if exciton-exciton collisions dominate homogeneous broadening, e.g. at higher excitation densities. 24 In our experiments we estimate that typical absorbed pulse fluences of 3.3 · 1012 cm−2 , and an absorption cross section 16 of 1.7 · 10−17 cm2 with an average tube length of 230 nm result in excitation densities with fewer than 35% of the s-SWNTs carrying more than one exciton. This as well as rapid non-radiative decay on the sub-nanosecond timescale 12,36,46 suggests that exciton-exciton collision-induced broadening can be neglected in our experiments. The linear increase of differential transmission signals up to excitation density of at least 4.0 · 1012 cm−2 justifies the assumption. Moreover the PB-FWHM does not exhibit any significantly collision-induced broadening over the linear range of excitation densities studied here (see supporting information Fig. S2). We thus conclude, that our ex-

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periments were performed in the weak excitation regime and that changes of the width of the spectral hole are mainly due to oscillator strength renormalization with negligible contributions from collision-induced broadening. After accounting for instrumental resolution this suggests that the homogeneous FWHM of the (6,5) exciton band at room temperature is 3.3 meV, i.e. over 99% of the spectral width of 60 meV is due to inhomogeneous broadening of the exciton band. 293 K

17 K

λex = 1020 nm

λex = 960 nm

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pump-probe delay / ps

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γhom Ei+1 Ei Ei-1 ∆x

Γinhom

Figure 3: a) False color plot of transient absorption spectra for narrow-band off-resonant excitation at 293 K (left column) and at 17 K (right column). The observed dynamics of population transfer at both temperatures as well as for both excitation energies are consistent with thermally activated diffusion of excitons along a potential energy landscape with random, short-range energy variations as indicated schematically in b). To obtain further insights into the dynamics of ultrafast spectral diffusion we next discuss hole burning experiments for non-resonant excitation of the exciton band. In Fig. 3a) we present pump-probe data for narrow-band excitation at 960 nm (top) and 1020 nm (bottom) 8


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at 293 K (left) and 17 K (right). Typical absorbed pulse fluences were 3 · 1012 cm−2 . Excitation on the high energy side of the exciton band at room temperature (Fig. 3 top left) reveals two distinct PB features, a short-lived narrow-band PB signal at the excitation wavelength and another, longer-lived broadened PB signal around 990 nm. The latter appears to emerge from the initial PB on the sub-ps timescale. Notably, the position of the broad low energy PB signal quickly settles slightly below the center wavelength of the ground state absorption spectrum at 987 nm as indicated by the dashed black line in Fig. 3a). This corresponds to an energy shift of 35 meV with respect to the initial PB signal (see Supporting Information Fig. S3). Room temperature excitation at energies below the band center leads to rapid sub-ps spectral broadening with only a slight shift of the PB feature towards higher energies on a timescale of about 4 ps (see lower left of Fig. 3a). At later times the maximum of the PB signal continues to migrate towards 1000 nm which is reached within about 40 ps, the same time-scale as that observed for the slow spectral broadening in Fig. 2. The total displacement of the PB here corresponds to an energy shift of only 24 meV. At low temperatures the dynamics of the center of gravity of the PB feature is similar (right top and bottom sections of Fig. 3a) but spectral broadening is much less pronounced if compared with the room temperature measurements. Instead we observe a long-lived residual narrow PB feature at the position of the initial photobleach for both high energy and low energy excitation. The shift of the high energy PB to longer wavelengths can be qualitatively attributed to a spontaneous bathochromic (”down-hill”) population transfer between different regions of a s-SWNT in an inhomogeneous environment as indicated schematically in Fig. 3b). The pump pulse generates an excited state population in regions of the s-SWNT where interactions with the environment cause the exciton transition to be resonant with the excitation. Subsequently, excitons migrate within the potential energy landscape along the nanotube axis and population is thereby transferred to lower energy sites through motion along an

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electronic and not a nuclear reaction coordinate. The negligible hypsochromic (”up-hill”) migration of the PB for excitation at low temperature and at low energies suggests that such population transfer requires thermal activation, in agreement with the notion of axial s-SWNT exciton diffusion within a broad distribution of local site energies. For a minority of excited states an activation also appears to be necessary for down-hill population transfer as evidenced by the long lived residual population that is resonant with the excitation pulse in the spectrum at low temperature and high excitation energy (top right of Fig. 3a). We infer from this that the potential energy landscape indicated in Fig. 3b) also provides some of the sites at higher energies with sufficiently large barriers to exciton migration which cannot be overcome readily by average kinetic exciton energies of about 1 meV corresponding to the thermal energy at 17 K. Similar exciton localization has also been observed in single nanotube near-field PL studies by Georgi et al. 47 Further support of diffusive exciton motion being responsible for ultrafast spectral diffusion can be obtained from the temperature dependent and spectrally resolved time-correlated single photon counting data shown in Fig. 4. In the top section of Fig. 4 we show photoluminescence spectra of the same exciton band at room temperature and at 65 K. To facilitate their comparison, spectra are plotted as a function of energy relative to the maximum of the exciton band. This reveals that emission from the high-energy side of the exciton band is less pronounced at low temperature. This is in agreement with the expectation of a smaller thermal population of high energy sites at low temperatures. The temperature dependence of the photoluminescence decay at low temperatures likewise also shows that higher energy sites decay more rapidly because population transfer to lower energy states effectively competes with non-radiative decay. By contrast, the PL decay does not depend on transition energy if temperatures are raised, due to rapid thermally activated axial exciton redistribution among all potential energy sites. Both, off-resonant hole burning as well as time-correlated single photon counting experiments thus support the notion of spectral diffusion being due to ultrafast diffusive population

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Figure 4: Temperature and energy dependence of PL lifetimes from the first subband exciton as determined by spectrally resolved and time-correlated single photon counting. PL lifetimes at low temperatures increase for low energy states while high energy states are more rapidly depleted. This is consistent with the notion of axial exciton diffusion leading to ultrafast bathochromic population transfer. The reduced intensity of the high-energy wing of the low-temperature exciton spectrum also suggests that PL at low temperatures originates preferentially from lower energy sites.

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transfer along the nanotube axis. The width of the energy distribution of sites along the s-SWNT axis as well as some of the characteristics of the associated potential energy landscape may thus be inferred from the inhomogeneous broadening as well as from the details of the observed population dynamics. We next discuss the use of kinetic Monte Carlo simulations to further explore the nature of one-dimensional exciton diffusion in a potential energy landscape of the type indicated in Fig. 3b. Kinetic Monte-Carlo Simulations (KMC) were carried out for an ensemble of randomly distributed excitons in a potential energy landscape with a Gaussian spread of energy levels. 48–50 The width of this distribution of 60 meV was chosen to correspond to the inhomogeneous room temperature linewidth found in the ground state absorption spectra as discussed above. In Fig. 5a) we have reproduced the energy distribution among the first hundred lattice sites of such a potential energy landscape including the random distribution of excitons. The corresponding potential energy histogram with 60 meV FWHM is shown to the right of this landscape. A typical exciton energy distribution for narrow-band excitation at 960 nm is shown in Fig. 5b along with histograms of the exciton energy distribution after a given number of simulation steps. The evolution of this distribution in time and space is obtained using the Metropolis algorithm which gives the probability of particle jumps to a neighboring lattice site with higher energy as P± ∝ exp(−∆E/kB T ). 50,51 Jumps to neighboring lattice sites with lower or equal energy occur spontaneously with a probability of 1. 50,51 At early times the initial particle distribution shown in Fig. 5b is seen to rapidly evolve toward lower energies. This fast process is attributed to the availability of low energy sites next to positions occupied by the initial particle distribution. Jumps to levels with higher energy are improbable unless the energy difference is small with respect to kB T . In Fig. 6 we compare experimental with simulated transient hole burning spectra for excitation at 960 nm and at room temperature. The latter are obtained by summing over spectra from all populated energy sites with the homogeneously broadened line shape derived from transient spectra at small pump-probe delays and from the corresponding homo-

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Figure 5: a) The energies of the first hundred lattice sites used in kinetic Monte Carlo simulations. The distribution has a width of 60 meV and a includes a set of randomly distributed excitons (black markers). b) Horizontal waterfall plot with energy histograms of the exciton distribution at different simulation-times (increasing from left to right). 0 ps 0.25 ps

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0.50 ps 0.75 ps 1 ps 10 ps

Figure 6: Experimental (left) and simulated (right) hole burning spectra for excitation at 960 nm at room temperature. geneous linewidth discussed above. The simulated spectra qualitatively follow the behavior of experimental spectra with a rapid population transfer to lower energies and a gradual disappearance of the concentrated population at the excitation energy. The Monte Carlo simulations were then compared with the expected experimental diffusion kinetics by monitoring the root mean square displacement of exciton trajectories within the 1D potential landscape. Best agreement of experimental spectra with simulated trajecto13



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ries is obtained for 4D/∆x2 = (3.5 ± 0.8) ps−1 where ∆x is the distance between lattice sites in the simulation. Assuming a 1D diffusion constant of 5 cm2 s−1 this would suggest a lattice site spacing of (24 ± 13) nm, where the error margins indicate the uncertainty obtained if different experimentally reported diffusion constants with values ranging from 1 cm2 s−1 to 10 cm2 s−1 are used for D. 20,32,52 Within the model discussed above this length corresponds to the spatial extent of plateau-regions with nearly constant potential energy.

Figure 7: a-c) 2D spectral hole burning data for pump-probe delays ranging from 0 ps to 2 ps constructed from transient absorption spectra taken at excitation energies indicated by the horizontal axis. (d-f) spectra obtained from the kinetic Monte Carlo simulations. At 0 ps transient signals are narrow and centered on the diagonal, with a significant broadening already observed after 0.3 ps, i.e. at the PB maximum. After 2 ps spectral features are clearly displaced from the diagonal and have become strongly broadened. This behavior is a direct manifestation of spectral diffusion. In addition, we also find good qualitative agreement of simulations with experimental 14


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data by a comparison of experimental and calculated two-dimensional hole burning spectra at different pump-probe delays seen in Fig. 7. The left panels show false color representations of 2D transient maps obtained by tuning the narrow-band excitation pulse across the exciton resonance. The right panels show the corresponding normalized transient 2D spectra at the same pump-probe delays. Interestingly, some of the insights gained from these simulations are related to shortcomings of the simple diffusion model outlined above. Specifically, we find that the agreement of simulated with experimental spectra depends somewhat on the type of distribution used for characterizing the potential energy landscape. For example, the inhomogeneously broadened transient photo-hole has somewhat broader wings than the Gaussian energy distribution used for the simulations. The existence of a greater abundance of low-lying energy levels than suggested by the Gaussian energy distribution used in the simulations is also evident from diamond shaped resonances in two-dimensional photoluminescence excitation data. 53,54 In contrast, inhomogeneous Gaussian broadening of energy distributions in excitation and emission would yield circularly symmetric photoluminescence excitation resonances. However, if a Lorentzian shaped energy distribution is used in the above simulations we find that agreement with experimental spectra is reduced because excitons rapidly become trapped in sites energetically far away from the center of the distribution leaving the transient spectrum strongly distorted toward long wavelengths. The above simulation thus facilitates a good qualitative description of 1D spectral and spatial exciton diffusion processes with more specific information about the detailed character of the potential energy distribution possibly imbedded in the data. The key conclusion from the discussion above is that ultrafast spectral exciton diffusion is consistent with ultrafast spatial exciton diffusion in a potential energy landscape characterized by short range modulations. The characteristic length-scale of these modulations is on the order of 24 nm, several times the frequently quoted exciton electron-hole correlation length of about 2 nm. 32 An interesting comparison can be made between the ultrafast spectral diffusion here

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observed in s-SWNTs and the time-scale of spectral diffusion more frequently observed in molecular systems. In the latter, SD time-scales have been found to bridge orders of magnitude as determined by different spectral diffusion mechanisms. 55–61 Generally SD mechanisms are based on the influence of microscopic fluctuations of the electric fields in the vicinity of the studied molecules. In the majority of systems this requires molecular rearrangements, which take considerably more time to modify the local electric fields than the one-dimensional exciton diffusion discussed here. Specifically, molecular reorganization in the vicinity of or within fluorophores by means of translation or rotation rearrangements frequently leads to heterogeneous line broadening on the ps to ns time-scale. 58

Conclusion We have reported on ultrafast spectral diffusion within exciton bands of s-SWNTs using oneand two-dimensional, near-infrared transient hole burning spectroscopy and time-resolved fluorescence spectroscopy at temperatures between 15 K and 293 K. The experiments revealed that over 99% of the linewidth of (6,5) s-SWNTs embedded in a gelatin matrix can be attributed to inhomogeneous broadening with a homogeneous linewidth of only 3.3 meV. Transient spectra obtained for resonant and off-resonant excitation at 293 K and 15 K clearly show that ultrafast spectral diffusion of excitons in gel-immobilized s-SWNTs occurs on the 250 fs time-scale and is attributed to efficient axial intra-tube exciton diffusion. This is consistent with previous observations of large exciton diffusion coefficients on the order of 10 cm2 s−1 and a granularity of the exciton potential energy landscape on a length-scale of (24 ± 13) nm. This also suggests that axial exciton diffusion may be considerably improved if the granularity of the perturbations of the exciton transition by interactions with the environment can be reduced.

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Methods Sample preparation. The nanotube sample used for this study was prepared by density gradient ultracentrifugation 62 from commercial CoMoCAT SG65 material (SouthWest NanoTechnologies Inc.) which yields aqueous suspensions strongly enriched in the (6,5) s-SWNT species. Subsequently, s-SWNTs are dialyzed against 2% SC solution for removal of iodixanol and immobilized in a thin 6% gelatin film containing ≈ 1% SC and SDS respectively with an OD of 0.65 at the first subband exciton transition. In Fig. 1a) we have reproduced the near infrared region of the absorption spectrum around the lowest subband, S1 absorption feature (more details and the complete absorption spectrum can be found in the Supporting Information Fig. S1). The spectral width of the first (6,5) s-SWNT subband absorption at 987 nm was 60 meV and is significantly broader than in the aqueous suspension from which this sample was prepared and lends itself to spectral diffusion studies. Optical measurements. Spectral hole burning experiments were performed using the output of an optical parametric amplifier (OPA9450, Coherent Inc.) driven at 250 kHz by a regenerative amplifier (RegA9050, Coherent Inc.). The whitelight continuum for probe pulses was generated by focusing a 30% fraction of the RegA output into a sapphire crystal. Narrow-band excitation pulses were obtained by spectral filtering of the OPA output pulses with custom made ≈ 3 nm bandpass filters (LC-987NB3-25 and LC-1045NB3-25, Laser Components GmbH) giving nearly bandwidth-limited 505 fs pulses at 987 nm (Fig. 1a). Wavelength tuning for off-resonant excitation was achieved by twisting the bandpass filter relative to the optical path which allowed us to obtain excitation pulses down to 930 nm central wavelength with less than 20% spectral broadening of the pump pulse. The pump beam was attenuated using a neutral density filter, focused into the sample by use of a 250 mm lens to a ≈ 60 µm to 80 µm spot and overlapped with the probe beam which was focused to ≈ 40 µm. Stray light from pump intensity was minimized by choosing a clear sample volume and was blocked using an aperture after the sample. Further reduction of artifacts due to stray light intensity in our resonant excitation experiments was achieved 17



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by perpendicular polarization of pump and probe beam at the sample and transmitting the probe polarization after the sample by use of a polarizer. Typical pump fluences at the sample were 1 µJ cm−2 (3 · 1012 cm−2 photon fluence), unless otherwise stated. Data was acquired with a 150 lines/mm and 600 lines/mm grating spectrograph (Shamrock 303i, Andor Technology PLC) and a CCD camera (Newton DU920P BR-DD, Andor Technology PLC) at 500 Hz readout rate. All transient spectra were corrected for differential transmission signal at negative pump-probe delays, i.e. -30 or -50 ps. For time-correlated single-photon counting (TCSPC) experiments the sample was excited in resonance with the (6,5) S2 exciton at 570 nm with the output of the optical parametric amplifier at 250 kHz. Pulse fluences were on the order of magnitude of 2 · 1015 cm−2 . Photoluminescence was collected in epi-geometry with a x10 objective (Olympus) and detected with a avalanche photodiode (PDM-series, MPD together with a HydraHarp 400, Picoquant) after spectral filtering in a spectrograph (Shamrock 303i, Andor Technology PLC) yielding a bandwidth of 5 nm. Excitation intensity was rejected by use of a dichroic mirror (cut-off wavelength 738 nm) and a 950 nm long pass filter. The instrument response function (IRF) was recorded using a fraction of scattered 980 nm radiation. Temperature dependent experiments were carried out using a closed-cycle helium refrigerator system (Compressor SC, Cryodyne Refrigeration system, CTI Cryogenics) whose cold head was in contact with the sapphire sample substrate. For investigation of the inhomogeneous broadening we recorded 2D hole burning spectra by scanning the excitation wavelength over the absorption linewidth from 930 nm to 1045 nm. 2D spectra were composed of single transient absorption spectra at given pump-probe delays and scaled such that 2D spectrum parts under blue edge and red edge excitation have the same differential transmission signal at 987 nm which stem from slightly different excitation fluences.

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Acknowledgement D.S. acknowledges financial support by the DFG within the GRK1221.

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Supporting Information Available This material is available free of charge via the Internet at http://pubs.acs.org/.

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Ultrafast Spectral Exciton Diffusion in Single-Wall Carbon Nanotubes

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