Coherent Electronic and Phononic Oscillations in Single-Walled

Letter pubs.acs.org/NanoLett

Coherent Electronic and Phononic Oscillations in Single-Walled Carbon Nanotubes Intae Eom,† Sohyun Park,†,⊥ Hae-Seon Han,‡ Ki-Ju Yee,§ Sung-Hoon Baik,∥ Do-Young Jeong,∥ Taiha Joo,*,† and Yong-Sik Lim*,‡ †

Department of Chemistry, POSTECH, Pohang 790-784, Republic of Korea Department of Nano Science & Mechanical Engineering and Nanotechnology Research Center, Konkuk University, Chungju, Chungbuk 380-701, Republic of Korea § Department of Physics, Chungnam National University, Daejon 305-764, Republic of Korea ∥ Quantum Optics Division, KAERI, Yuseong, Daejon 305-600, Republic of Korea ‡

ABSTRACT: Free induction decay of the coherent electronic transition and coherent phonon oscillations of the radial breathing mode in single-walled carbon nanotubes are simultaneously observed via direct resonant excitation of the lowest E11 optical transition in the near-infrared region from 0.939 to 1.1 eV. We show that coherent electronic oscillations corresponding to the detuning of the probe energy from resonance can be exploited for the chirality assignment of carbon nanotubes, together with the robust assignment of the coherent lattice vibrations resonantly excited by femtosecond pulses. Excitation spectra show a large number of pronounced peaks that map out chirality distributions in great detail. KEYWORDS: Free induction decay, coherent phonon, chirality, radial breathing mode, SWNT

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the feasibility of the chirality assignment of SWNTs by the frequencies of the radial breathing mode (RBM) obtained from a TA experiment excited by the E22 transition.10−14 This method has several advantages over the frequency-domain spectroscopies: excellent frequency resolution, absence of the Rayleigh scattering background at low frequencies, no interference from photoluminescence (PL), and direct measurement of vibrational dynamics. When a short pulse in resonance with the system passes through a molecular ensemble, transition dipoles with different frequencies are generated, and they spontaneously reradiate. The total reradiated electromagnetic wave, called a free induction decay (FID), yields the absorption spectrum upon Fourier transformation. The FID of an ensemble of molecules usually decays much faster than that of a single molecule.15,16 The electronic dephasing time of the E11 transition of an SWNT inferred from the absorption spectrum is longer than 100 fs, which provides an opportunity to observe the FID directly in the time domain. Here, we report the electronic FID and CP oscillations in semiconducting SWNTs at room temperature through the pump/dispersed probe TA experiment in the E11 optical region. The E11 resonant excitation allows the observation of the electronic FID directly and the elucidation of the difference in

ingle-walled carbon nanotube (SWNT) is an ideal onedimensional system for studying the effect of dimensionality on the interaction between electrons and phonons, which determines most of the properties of crystalline solids.1 Since the discovery of suspended SWNT, their optical properties in particular have been of great interest toward developing the theory of SWNTs and serve as a noninvasive and noncontacting approach of investigation.2 Spectroscopies in the frequency domain, such as photoluminescence excitation (PLE) and resonant Raman scattering (RRS) of SWNTs, have led to the definitive assignment of certain spectral features to their corresponding chiralities.3−5 However, most of the RRS experiments on carbon nanotubes were carried out in resonance with the E22 transition because of the lack of light sources and proper detection systems in the E11 transition region. The E22 excitation for both the spectroscopies mentioned above tends to complicate the investigation of the interactions between an exciton and a phonon/exciton as well as the chirality assignments of nanotubes in a sample ensemble owing to the fast decay of the photocarriers and remarkably weak strengths for the (n−m) mod 3 ≡ ν = +1 nanotubes beyond predictions.6−9 Alternative to the frequency-domain spectroscopies, phonon spectra can also be obtained from the time-domain optical method based on impulsive excitation. Coherent phonon (CP) wave packets are created by the impulsive excitation, and their motions can be recorded by a probe pulse in a pump/probe transient absorption (TA) experiment. Lim et al. demonstrated © 2012 American Chemical Society

Received: October 22, 2011 Revised: December 22, 2011 Published: January 23, 2012 769

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electron−phonon interactions between the E 11 and E 22 transitions. The RBM intensities of ν = +1 semiconducting nanotubes are remarkably larger than those of ν = −1 semiconducting nanotubes; this relationship is exactly opposite that of the E22 transition. We demonstrate that the FID can be exploited as supportive data in the chirality assignment of SWNTs by the CP technique. SWNTs (HiPco batch HPR 104) were individually suspended with 1 wt % of cholate in D2O.17 Pump−probe TA measurements were performed on the solution in a quartz cell with an optical path length of 1 mm at ambient temperature. The light source was a home-built near-infrared cavity-dumped optical parametric oscillator (OPO) employing a periodically poled lithium niobate (PPLN) crystal as a gain medium.18 The probe beam was spectrally resolved by a monochromator (SP-150i, Acton) prior to the detection. The center wavelength of the OPO was tuned to 1150, 1200, 1250, and 1300 nm to investigate the E11 transition over a range of 1125−1320 nm (1.102−0.939 eV). Pulse energies of the pump and probe at the sample were adjusted to ∼10 nJ and ∼100 pJ, respectively, at a repetition rate of 1 MHz. Excitation intensity at the sample was 2 × 1014 photons/(cm2 pulse), and it was verified that the TA signals are free from the intensitydependent effects by lowering the pulse energy more than 10 times. The pulse duration was in the range of 65−70 fs, depending on the center wavelength. Figure 1a shows the TA signals at various pump and probe wavelengths. Most of the time profiles, except in the 1220− 1240 nm region where the contribution from the excited state absorption may be significant, can be fitted well by a sum of two exponentials: a fast component in the range of 700 fs−1.2 ps and a slow one in the range of 3−13 ps. The fast decay component is attributed to the intraband relaxation in the E11 band, as previously reported.7,19 The slow decay component may be assigned to the carrier recombination process at the E11 band edge of the resonantly excited SWNTs.7,8 The exciton− exciton annihilation process may not be responsible for the slow component because the pulse intensity was low enough to be free from the intensity-dependent effect.7,20 In all time traces of Figure 1a, we observe large-amplitude fast-damping oscillations at early times; they are the most conspicuous at negative time delays up to −500 fs. Once the large-amplitude oscillations are over, considerably smaller-amplitude CP oscillations of RBMs originating from the ground electronic state appear at later times. Figure 1b shows representative CP oscillations normalized to the TA signals at 0.5−1 ps. Each trace is a superposition of multiple oscillations with different frequencies and phases exhibiting a strong beat. The beat pattern changes with the photon energy, implying that the CP oscillations are dominated by RBMs resonantly enhanced by pulses commensurate with their unique electronic transitions, as in the RRS of SWNTs, which will be discussed in detail later. The large-amplitude oscillations seen at early times carry different characteristics from the CP oscillations in terms of their amplitudes and frequencies, and especially the probe wavelength dependence. We assigned them to the electronic free induction decay (FID)21 in the lowest excited E11 band. Note that these oscillations exist at negative time delay where the pump and probe pulses do not overlap in time. This electronic coherence between the ground and the E11 band generated by the preceding probe pulse is clear evidence for the FID. TA is a third-order nonlinear phenomenon in which the signal phase matching condition is ks = kpump − kpump + kprobe;

Figure 1. (a) Representative pump/probe transient absorption (TA) time profiles of HiPco single-walled carbon nanotubes (batch HPR 104) individually dispersed in an aqueous cholate suspension for different pump/probe wavelengths. Each oscillation trace was normalized by the average signal strength in the range of 0.5−1 ps. (b) Representative CP oscillation traces extracted from the TA signals at positive delay times after subtracting the exponential background. OD denotes the optical density. Pump/probe wavelengths are indicated in the figure.

that is, ks is the same as kprobe. Double-sided Feynman diagrams that correspond to the negative time are shown in Figure 2.

Figure 2. Two-level system (excited, |e⟩, and ground, |g⟩, states) double-sided Feynman diagrams for the time ordering of the probe− pump sequence of a TA experiment in the rotating-wave approximation. The left and right vertical lines represent the ket and bra of the density matrix, respectively. Time increases from bottom to top. k represents the wave vector of the in/out-going field. The arrows on the left and right vertical lines represent the field−matter interactions on the ket and bra states, respectively. ρij represents a nonzero density matrix element during the time interval. After the second field−matter interaction, R1 create an excited state population, while R2 create a ground state population. 770

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During the probe−pump time delay τ, the system is in electronic coherence between the ground and E11 state, which decays within the electronic dephasing time. In general, the electronic dephasing time is much shorter than 100 fs for a molecule in solution,22,23 which is short compared to the experimental time resolution of a typical TA experiment and/or dynamics of interest; therefore, it can be ignored for the most part.22−25 However, the electronic dephasing time of the SWNTs, as inferred from the absorption line width, is about 200 fs,17 much longer than the time resolution of the current experiment. Exciton dephasing time of the SWNTs measured by the photoluminescence line width of a single nanotube was reported to be ∼130 fs at room temperature for the diameter of 1 nm.26 Ma et al. also reported the dephasing time of 162 fs for the (6,5) nanotube at room temperature from the photon echo experiment.27 The damping time constants of the initial oscillations are also around 200 fs throughout the whole wavelength range, which is in good agreement with the electronic dephasing time of the SWNTs. The long dephasing time may be due to the environment of the SWNTs used in the experiment. Judging from the molecular dynamics simulation for the dispersed CNTs in an SDS micelle, there is no water density in the direct vicinity of the tube wall.17 Therefore, the electronic coherence of the micelle-suspended CNTs seems to be only weakly disturbed by surrounding solvent molecules. The long exciton dephasing time of SWNT could be rationalized by the fact that the electronic dephasing time for an extended system such as ordered molecular aggregate is much longer than a small molecule due to the averaging effect of the system−bath interaction.28,29 Figure 3 presents the frequency dependence of the FID signal on the probe energy, obtained by the Fourier

frequencies increase (or decrease) linearly with a slope of 1. This behavior arises from the narrow band detection of the probe pulse and can be easily understood from the solution of the optical Bloch equation. The coherence (off-diagonal element of the density matrix, ρeg, in Figure 2) in the weak field limit evolves exponentially according to the equation exp[−(Γ + iΔ)t], where Γ is the dephasing rate, Δ = ω0 − ωl is the detuning from resonance, and ω0 and ωl are the resonance and laser frequencies, respectively. However, the pump spectrum in this work is much wider than the absorption line width of the SWNTs. Therefore, the oscillation of the FID shown in Figure 1a is actually caused by the detection stage due to the narrow band detection of the probe; that is, ωl should now be the detection frequency. This feature could then be utilized to confirm the resonant frequencies of the SWNTs; ω0 could be obtained from Δ and ωl. When the pump wavelength is 1200 nm (1.033 eV), where transitions from ∼1170 to ∼1230 nm region are excited resonantly, the major peak (Δ) is observed near 510 cm−1 at the probe detection wavelength (ωl) of 1165 nm (∼1.064 eV); this peak shifts downward linearly as the probe energy decreases. When the pump wavelength is 1250 nm (0.992 eV), three peaks are observed at around 150, 320, and 460 cm−1 at the probe detection wavelengths of 1220 nm (1.016 eV), and these peaks also shift downward linearly as the probe energy decreases. When the pump wavelength is 1300 nm (0.954 eV), the major peak is observed near 430 cm−1 at the probe detection wavelengths of 1340 nm (0.925 eV), and this peak shifts downward linearly as the probe energy increases. All linear lines in Figure 3, denoting the dependence of oscillation frequency on the detuning from absorption resonance, have the same slope of 1 in units of eV, which confirms the FID’s characteristics. From the intercept, resonance wavelengths (ω0) should be at 1241 (0.999), 1268 (0.978), and 1293 (0.959) nm (eV), which can be assigned to (9,5), (8,7)/(11,1), and (14,0) SWNTs, respectively. These absorption wavelengths are consistent with the values obtained from the CP results described later. Nevertheless, because the free induction decay is fast, high-frequency FID signals, which arise from the large detuning from resonance, are more reliable in the determination of the resonance frequencies, whereas the bands near zero frequency are not well determined, as the FID decays within a single oscillation. Although showing weaker strength, FID signals from (11,3) and (10,3)/(10,5) tubes could also be identified. The strong FID peak (center panel) with resonance frequency at 1.007 eV could not be assigned to a one-photon resonance of SWNT. We therefore assigned it to the RBM phonon sideband of the (8,7) tube (E11 + 231 cm−1 = 1.007 eV) due to the strong exciton−phonon coupling.13,30 Thus, direct observation of the electronic FID in the TA signals facilitates the chirality assignment and the composition analysis for a given CNT ensemble. Along with the strong electronic FID as shown in Figure 1, weak CP oscillations due to the RBM are also apparent. They were analyzed by the linear prediction singular value decomposition (LPSVD) method,31 which is more appropriate than the conventional FFT method in extracting damped sinusoids with overlapping frequencies.13 Figure 4 shows the LPSVD analysis results, and the chiralities of these peaks were assigned according to the Weismann empirical fit32 along with the absorption and the FID spectra. Frequencies of the peaks and their assignments are listed in Table 1 together with the theoretical frequency, E11 bandgap, chirality, and the corre-

Figure 3. FFT power spectra of the oscillatory components in the negative time delay TA signal for three pump energies at λpump = 1300, 1250, and 1200 nm. The arrows indicate directions of the peak positions.

transformation of the TA signals at negative time delay. As the probe detection wavelength is varied, the oscillation 771

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measured by the Raman scattering in resonance with the second (or higher) optical transition.33 Inspection of Figure 4 gives an estimate of the chirality distribution of the HiPco SWNTs. Using the empirical relation between the RBM frequency and the tube diameter,3 distribution of the tube diameters for the present HiPco sample can be estimated at 0.81−1.12 nm from the highest (290.1 cm−1) and lowest (212.1 cm−1) RBM frequencies observed in this work, which is in good agreement with the well-known size distribution of the HiPco ensemble of 1.0 ± 0.1 nm in diameter.34 In fact, SWNTs with diameters from 0.9 to 1.0 nm, indicating tubes of (12,1) and (11,1) branches of (2n + m), show stronger CP amplitudes than those with larger (∼1.1 nm) or smaller (∼0.8 nm) diameters. The intensity of each peak is proportional to the square of the electron−phonon coupling matrix element of the tube as well as the population within the ensemble. The last column in Table 1 lists the intensities of the RBM peaks shown in Figure 4. Higher RBM peak intensities for smaller chiral angle and smaller diameter, irrespective of the type ν, are reproduced. Intensities of the ν = +1 SWNTs, such as (11,1) and (9,2) branches, which are negligible for the E22 excitation on the same HiPco sample,10 are markedly larger than those of the ν = −1 tubes such as (12,1), (10,2), and (14,0) branches. For example, intensities of the ν = +1 tubes, e.g., (11,1), are larger by more than 10 times those of the ν = −1 tubes with similar diameters, e.g., (12,1) and (10,2), as shown in Table 1. Taking into account the full (both sides) Raman excitation profile (REP) contribution spanning the double maxima of REP, the intensity difference between all zigzag tubes of ν = +1 and ν = −1 types is estimated to be 4−5, which is nearly an order of magnitude difference from the E22 excitation result. This is clear evidence supporting the prediction of the RBM Raman intensity by the extended tight binding theory and ab initio calculations,35,36 where the magnitude of the electron−phonon coupling matrix elements at the E11 (E22) transition should be higher for the ν = +1 (ν = −1) type due to the alternate change of the transition energies lying on the two sides of the K point between these two types. It also indicates that the magnitudes of the electron−phonon coupling matrix elements of the E11 and E22 transitions could be different by only a factor of 2 or 3, which seems to be consistent with the recent extended tight binding calculation based on the excitonic picture, where the intensity for ν = −1 tubes is, at most, 2 or 3 times larger than that of ν = +1 tubes, even for the E22 transition without exciton−exciton resonance.37 More accurate theoretical calculations are needed for the exact ratio of RBM peaks between ν = +1 and ν = −1 tubes for the E11 transition. In conclusion, apart from the coherent phonon oscillations due to the coupling between the 1-D exciton and phonons, we reveal novel electronic oscillations (FID) due to the detuning between the optical field and 1-D excitons. This study extends a number of new possibilities in the study of SWNTs, providing several advantages of the CP technique over the traditional CW characterization methods by adopting a nondegenerate TA scheme, as opposed to the typical degenerate scheme. In particular, the strength of the FID signal is much higher than that of the CP signal because it is proportional only to the absorption intensity, unlike the CP technique; also, its frequency is changeable to the detuning from the resonance, which makes chirality assignment easier. As for the coherent phonons resonantly excited by the E11 transition, the RBM intensities of ν = +1 nanotubes are larger by at least 4 times that

Figure 4. RBM spectra obtained by the LPSVD analysis. Each RBM is identified by an oval and its chiral index. Pump wavelengths are centered at 1150, 1200, 1250, and 1300 nm, and the probe wavelengths are listed on the right axis. Numbers in red and purple colors denote 2n + m for ν = +1 tubes and ν = −1 tubes, respectively.

Table 1. Frequencies (ωRBM), Dephasing Time (T2) of the Radial Breathing Modes, Intensities of Resonant Excitation Profile (I) Retrieved from the LPSVD Analysis Together with Their Chirality Assignments, Theoretical Frequency T (ωRBM ),32 Transition Energy (E11), and the Chirality Type [(n−m) mod 3] for the Assigned Nanotubesa ωRBM (cm−1)

T2 (ps)

T ωRBM (cm−1)

E11 (nm)

(n,m)

(n−m) mod 3

I (au)

212.1 214.2 225.1 230.9 233.2 236.8 239.4 242.8 250.2 257.4 257.5 264.0 277.1 279.8 290.1

2.5 2.3 3.0 7.5 30 4.6 1.7 4.7 10.9 2.0 1.4 2.3 1.6 2.3 2.8

212.2 213.6 225.3 229.1 233.0 237.2 241.6 243.9 251.3 256.6 256.6 265.3 278.5 282.1 289.9

1307 1295 1250 1267 1197 1171 1244 1172 1250 1263 1101 1053 1113 1023 1139

(13,2) (14,0) (10,5) (8,7) (11,3) (12,1) (9,5) (8,6) (10,3) (11,1) (9,4) (10,2) (8,4) (7,5) (9,2)

−1 −1 −1 +1 −1 −1 +1 −1 +1 +1 −1 −1 +1 −1 +1

35.4* 35.4* 22.5 35.2 72.7† 38.1 251† 205† 430† 386† 19 31.2 94.7 24.7 169

a

The asterisks (∗) indicate the equal contribution for two nearby peaks. The daggers (†) indicate the tubes that have the full (both sides) contribution of REP by its double peak feature; the others have only a half (one-side) contribution due to off-resonance excitations. The fwhm of double peaks of ν = +1 tubes, e.g., (11,1), (10,3), and (9,5), are as small as 25−30 nm. Note also that the (11,3) tube shows a very sharp phonon peak, i.e., long T2 reaching 100 ps.

sponding mod type of the assigned nanotubes. The average peak positions of the experimental RBM frequencies are consistent with the theoretical values. All RBMs of ν = −1 nanotubes found in the CP study on the E22 optical transition10 are reproduced in this work. The peak positions of the semiconducting SWNTs also match well with the values 772

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of ν = −1 nanotubes, which is in striking contrast to the E22 transition. Finally, combined with the CP technique that has several advantages over the frequency domain spectroscopies, the FID study will allow us to explore the metallic carbon nanotubes that have the E11 resonances in the visible range.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] (Y.-S.L); [email protected] (T.J.). Present Address ⊥

Samsung LCD Business Co., Ltd.

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ACKNOWLEDGMENTS Y.S. acknowledges J. Kono at Rice University for helpful discussions. This work was supported by the National Research Foundation of Korea (NRF) funded by the Korea government (MEST) (2011-0000248, 2011-0001215) and in part by the Global Research Laboratory Program (2011-00131). Y.L. and K.Y. acknowledge the support by the NRF grant (20100022691, 2010-0028165) and the Korea Atomic Energy Research Institute (KAERI). S.B. acknowledges the support by the NRF grant (2008-03535).

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