NANO LETTERS
Coherent Phonon Dynamics in Single-Walled Carbon Nanotubes Studied by Time-Frequency Two-Dimensional Coherent Anti-Stokes Raman Scattering Spectroscopy
2009 Vol. 9, No. 4 1378-1381
Katsuyoshi Ikeda* and Kohei Uosaki DiVision of Chemistry, Graduate School of Science, Hokkaido UniVersity, Sapporo 060-0810, Japan Received October 6, 2008; Revised Manuscript Received January 14, 2009
ABSTRACT Coherent phonon dynamics in single-walled carbon nanotubes were studied using broadband coherent anti-Stokes Raman scattering microscopy in time-frequency domain. Zone-center G-phonons were coherently created by optical excitation with the relaxation time of 1.1 ( 0.1 ps, while zone-boundary D-phonons showed incoherent behavior, indicating electron-phonon, electron-defect, and phonon-phonon interactions in semiconducting nanotubes.
Single-walled carbon nanotubes (SWNTs) have attracted much attention since their discovery in 1991.1 Their unique electrical, optical, and mechanical properties are related to π-conjugated quasi-one-dimensional structures. Depending on their symmetry (n, m), they behave as semiconductors or metals.2 In semiconducting SWNTs, spectroscopic studies showed that the electronic excited states were excitonic in character with extraordinary high binding energy because of exciton wave function localization.3-5 Because of such a strong electron-phonon coupling, SWNTs are expected to exhibit special electron transport properties such as superconductivity.6 Moreover, ultrafast modulation of the electronic and optical properties could be possible via coherent control of SWNT-lattice vibration through the strong electron-phonon coupling.7 Studying the interactions and dynamics of electrons and phonons in SWNTs is of great importance for understanding their unique properties. Spontaneous resonance Raman spectroscopy is a powerful tool for studying electron-phonon coupling in frequencydomain.8 In this technique, dynamical information is averagedout and convoluted in line shapes of the spectra. Hence, there is a practical limitation to extract information about phonon dynamics from frequency-domain due to inhomogeneous broadening of line shapes. On the other hand, pump-probe spectroscopy is a useful technique to probe directly electronphonon dynamics in time-domain,7,9 but the application is * To whom correspondence should be addressed. E-mail: kikeda@ pchem.sci.hokudai.ac.jp. 10.1021/nl803027c CCC: $40.75 Published on Web 03/11/2009
2009 American Chemical Society
actually limited by several factors. In time-resolved electronic absorption spectra, for example, phonon dynamics appears as decaying oscillatory components; the phonon information is obtained by the Fourier transform. Therefore, the sensitivity and frequency-resolution in this technique are low especially for high-frequency phonons due to the limitation of the laser pulse duration. In time-resolved vibrational spectra such as time-resolved coherent anti-Stokes Raman scattering (CARS),10 frequency-domain information is not available without scanning of excitation wavelength; decoherence processes could be accompanied with a frequency shift or modulation. Therefore, there are both practical and fundamental considerations in time-frequency two-dimensional (2D) spectroscopy for more detailed dynamical studies. In this sense, broadband CARS spectroscopy,11,12 based on three-color mechanism, can be a useful 2D spectroscopic tool. The broadband CARS technique is rather simple, compared with conventional three-color CARS using three pulses, because only two pulses are needed for CARS emission as shown in Figure 1a; a broadband first pulse impulsively promotes molecules to vibrationally excited states through a two photon Raman process, and a delayed narrowband second pulse induces CARS emission from coherent superpositions to the ground state. By changing the delay time for the second pulse, therefore, one can expect to obtain time-resolved CARS spectra. Note that the phase-matching condition for CARS processes is relaxed when the excitation beams are
Figure 2. Stokes Raman spectrum of SWNTs excited by 785 nm CW laser radiation.
Figure 1. (a) The energy diagram of the three-color CARS process, where the pump and Stokes photons (ωpump and ωStokes) are provided from the single broadband pulse and the probe photon (ωprobe) from the delayed narrowband pulse. (b) Experimental setup of a timefrequency 2D-CARS microscope: BPF, bandpass filter; PCF, photonic crystal fiber; LPF, long-pass filter; SPF, short-pass filter.
tightly focused.11 Under a microscopic condition, CARS emission is allowed in a wide frequency region at the same time. Consequently, time-resolved broadband CARS microscopy can directly access to coherent phonon dynamics in both domains. In this letter, we demonstrate time-frequency domain 2D-CARS microscopy with subpicosecond time resolution for observation of coherent phonon dynamics on the ground electronic potential surfaces of SWNTs. The experimental setup of the 2D-CARS microscope is shown in Figure 1b. The 70 fs output from a Ti:sapphire oscillator (Spectra-Physics, Tsunami, fundamental wavelength of 790 nm, repetition rate of 82 MHz) was split to two beams. One of the beams (50 mW) was introduced into a photonic crystal fiber (Crystal Fiber, Femtowhite 800) to generate a coherent supercontinuum. Then, the continuum was conditioned with an 800 nm long-pass filter. The other beam was spectrally narrowed by a custom-made laser line filter (Optical Coatings Japan, ∆ν ) 14 cm-1 fwhm). The obtained two beams were introduced collinearly into a 1.3 NA microscope objective lens. The broadband CARS emission in backreflected direction was analyzed by a CCD spectrometer (Roper Scientific). The time resolution of this broadband CARS microscope was confirmed to be less than 1 ps, due to the temporal broadening of the narrowband probe, by electronic sum frequency generation. The chirping of the broadband pump beam was negligible compared with the temporal duration of the probe pulses. SWNTs (95 wt % grade) were purchased from Carbon Nanotechnologies, Inc. The quantity of 0.002 wt % of the Nano Lett., Vol. 9, No. 4, 2009
nanotubes were dispersed into 2,2,3,3-tetrafluoro-1-propanol by sonication for 1 h; the solution was cast on a coverslip, and the solvent was allowed to evaporate. The sample density was high enough to exhibit ensemble-averaged spectra of the nanotubes with diameter distribution. Figure 2 shows a typical Stokes Raman spectrum of the SWNT sample measured by 785 nm CW laser excitation. Three peaks of Radial breathing modes (RBM) were found to be in the range of 200-270 cm-1, suggesting that semiconducting SWNTs with diameters of 0.9-1.2 nm were excited resonantly through the interband transitions of ES22.13 The appearance of the tangential graphite-like modes (G-band) at 1583 cm-1 also suggests that the semiconducting SWNTs were in resonance with the excitation.8 In addition to these first-order Raman bands, the disorder-induced band (D-band) was weakly observed around 1285 cm-1. Figure 3a shows a resonance anti-Stokes Raman spectrum measured by using quasi-monochromatic excitation with the narrowband 790 nm beam (1.57 eV), containing information about the electron-phonon coupling in frequency domain. The characteristic Raman bands, G- and D-bands, were found around 1585 and 1295 cm-1, respectively.2 Although the antiStokes Raman intensity is proportional to the population of optical phonons, it is often much larger than the value expected for thermal equilibrium in the case of SWNTs because Stokes and anti-Stokes Raman scattering can gain intensities from different nanotubes.14 The peak shift between Stokes and anti-Stokes D-bands is explained by so-called double resonance mechanism proposed for D-band appearance.15,16 The RBM peaks were not obtained in the present system. The 2D-CARS spectra for the same SWNTs are shown in Figure 3b. To our knowledge, this is the first example of CARS spectra of SWNTs in a wide frequency region including G- and D-bands. (So far, there has been few reports on CARS emission from SWNTs even in conventional narrowband CARS at single frequency.17) At the time delay of 0 ps, a nonresonant background signal was observed as a sum of various multiphoton processes.11 After the background rise vanished, the induced G-band peak still remained with the picosecond-order decay, indicating coherent vibrations of the nanotube lattices. Conversely, the D-band vanished 1379
Figure 4. (a) Anti-Stokes Raman spectrum of SWNTs with high defect density excited by the 790 nm narrowband pulses. (b) Timefrequency 2D-CARS spectra of SWNTs with high defect density.
Figure 3. (a) Anti-Stokes Raman spectrum of SWNTs excited by the 790 nm narrowband pulses. (b) Time-frequency 2D-CARS spectra of SWNTs. (c) Time-resolved CARS spectrum of SWNTs at 0.84 ps.
immediately after the excitation. Figure 3c shows a typical time-resolved broadband CARS spectrum, the cross section at 0.84 ps of the 2D-CARS spectrum. Again, one can clearly see that there is no D-band but there is the G-band. Interestingly, the G-band shape is slightly different from those in the conventional Stokes and anti-Stokes Raman spectra; the G- intensity was weaker in the time-resolved CARS spectrum. For more detailed investigation, SWNTs with high defect density, which were prepared by UV irradiation, were also examined. Figure 4 shows resonance anti-Stokes Raman and 2D-CARS spectra of the high-defect SWNTs. One can see that the D-band intensity in the frequency-domain Raman spectrum was indeed much higher. In the time-domain of the CARS spectrum, however, the D-band again rapidly vanished although it appeared more clearly at the 0 ps delay time. Since CARS probes coherent vibrations generated by pairs of pump- and Stokes-photons, the behavior of the D-band suggests that the coherency of the D-phonons is low. Such incoherent D-band behavior is consistent with the 1380
Figure 5. CARS intensity change at 1583 cm-1 in SWNTs as a function of delay time between the broadband pump and narrowband probe. The solid curve is obtained from a model that assumes instantaneous generation of hot G+-phonons, but takes into account the finite instrumental time resolution and the exponential dephasing.
double resonance mechanism.16 In this mechanism, the zoneboundary D-phonons are allowed by the combination with elastic electron backscattering in the Brillouin zone because of the momentum conservation. In other words, the D-band resonance involves an incoherent electron scattering process mediated by a lattice defect. Conversely, the excitation of the zone-center G-phonons is not accompanied with incoherent electron-defect scattering, resulting in the coherent vibrations of the lattices. That is, the time-frequency 2D Nano Lett., Vol. 9, No. 4, 2009
spectra directly showed the difference of the resonance mechanisms between G- and D-phonons. As mentioned above, the intensity ratio of the G- peak to the G+ peak was slightly small in the 2D-CARS spectra, compared with the anti-Stokes Raman spectra. It is known that the G- line shape in spontaneous Raman spectra is significantly affected by resonances to metallic SWNTs; a characteristic broadening is observed as a result of the resonances between phonons and an electronic continuum (plasmons).18 Although the present excitation energy is mainly resonant to semiconducting SWNTs, a small contribution from metallic SWNTs is still expected.19 In addition, a pump-probe study on RBM dynamics by Gambetta et al.9 suggested that coherence was not generated in metallic SWNTs. By considering these circumstances, the observed difference in the G- peak could be due to the fast relaxation of the G-phonons in metallic SWNTs. For further discussion, individual SWNT should be examined with timeresolved CARS spectroscopy. Finally, we focus on the relaxation process of G+-phonons. To analyze the date, we assume that the inhomogeneous contribution is small and the response function for the relaxation of the G+-phonons can be modeled as an instantaneous rise at a delay time T0 followed by an exponential decay with time constant T2/2. Here, the total dephasing time T2 is expressed by using the pure dephasing time τph and the population lifetime T1 as follows: 2/T2 ) 2/τph + 1/T1.10 The experimental data was fitted, as shown in Figure 5, to a convolution of this response function with the instrument response function determined by time-domain electronic sum frequency generation from a silver film. The estimated decay time T2/2 at room-temperature was 1.1 ( 0.1 ps in both of the asproduced SWNTs and the high-defect SWNTs. Recently, the population lifetime T1 of G-phonons have been measured by incoherent time-resolved anti-Stokes Raman scattering and the lifetime was found to be 1.1-1.2 ps in semiconducting SWNTs.20,21 Therefore, one can reasonably assume τph . T1 at room-temperature. This result is consistent with the conventional Raman line width of semiconducting SWNTs.22 The observed short lifetime of the G-phonons implies anharmonic mode coupling between G-phonons and RBM-phonons.20 In fact, a frequency modulation of the G mode by the RBM has been reported, suggesting the anharmonic coupplig between these vibrations.9 In summary, dynamical study of coherent vibrations on the electronic ground potential surfaces of SWNTs was demonstrated using time-frequency 2D-CARS microscopy. The temporal variations of the spectra clearly and directly showed the difference of the dynamics between the zonecenter G- and zone-boundary D-phonons. This technique for simultaneous measurement in time-frequency domain opens up a number of new possibilities to study molecular dynamics because a correlation of vibrational modes in time-frequency regions is directly revealed in 2D spectra without any complicated analytic procedure. It has several advantages, including (i) accurate line shapes in frequency-domain due to the broadband excitation, (ii) direct measurement of vibrational coherency in time-domain, and (iii) easy access to dynamics of high-frequency vibration modes. These Nano Lett., Vol. 9, No. 4, 2009
advantages were indeed demonstrated in this work; the small difference of the G- intensity in the broadband CARS would be hardly found in time- or frequency-domain 1D spectroscopy. The observed incoherence of the D-phonons directly supported the validity of the double resonance mechanism. The dephasing time of 1.1 ps found in this study suggested that the pure dephasing contribution to the line width was negligible at room temperature. How this dephasing time changes with temperature or other environmental parameters can provide us detailed insight into the dynamics of the system. Dynamical study of individual SWNTs under various conditions would clarify electron transport phenomena and optical behaviors, mediated by interactions among electrons, phonons, and defects in a one-dimensional electron system. Acknowledgment. This research was partially supported by Grant-in-Aid for Scientific Research (A) (2006-2009, No. 18205016) from JSPS and that on Priority Area “Strong Photon-Molecule Coupling Fields (No. 470) and Global COE program (Project No. B01: Catalysis as the Basis for Innovation in Materials Science) from MEXT, Japan. References (1) Iijima, S. Nature 1991, 345, 56. (2) Barros, E. B.; Jorio, A.; Samsonidze, G. G.; Capaz, R. B.; Filho, A. G. S.; Filho, J. M.; Dresselhaus, G.; Dresselhaus, M. S. Phys. Rep. 2006, 431, 261. (3) Wang, F.; Dukovic, G.; Brus, L. E.; Heinz, T. F. Science 2005, 308, 838. (4) Spataru, C. D.; Ismail-Beigi, S.; Benedict, L. X.; Louie, S. G. Phys. ReV. Lett. 2004, 92, 077402. (5) Lu¨er, L.; Hoseinkhani, S.; Polli, D.; Crochet, J.; Hertel, T.; Lanzani, G. Nat. Phys. 2009, 5, 54. (6) Tang, Z. K.; Zhang, L.; Wang, N.; Zhang, X. X.; Wen, G. H.; Li, G. D.; Wang, J. N.; Chan, C. T.; Sheng, P. Science 2001, 292, 2462. (7) Lim, Y.-S.; Yee, K.-J.; Kim, J.-H.; Ha´roz, E. H.; Shaver, J.; Kono, J.; Doorn, S. K.; Hauge, R. H.; Smalley, R. E. Nano Lett. 2006, 6, 2696. (8) Rao, A. M.; Richter, E.; Bandow, S.; Chase, B.; Eklund, P. C.; Williams, K. W.; Menon, M.; Subbaswarry, K. R.; Thess, A.; Smalley, R. E.; Dresselhaus, G.; Dresselhaus, M. S. Science 1997, 275, 187. (9) Gambetta, A.; Manzoni, C.; Menna, E.; Meneghetti, M.; Cerullo, G.; Lanzani, G.; Tretiak, S.; Piryatinski, A.; Saxena, A.; Martin, R. L.; Bishop, A. R. Nat. Phys. 2006, 2, 515. (10) Fayer, M. D. Ultrafast Infrared and Raman Spectroscopy; Marcel Dekker: New York, 2001. (11) Kano, H.; Hamaguchi, H. J. Raman Spectrosc. 2006, 37, 411. (12) Lee, Y. J.; Liu, Y.; Cicerone, M. T. Opt. Lett. 2007, 32, 3370. (13) Kataura, H.; Kumazawa, Y.; Maniwa, Y.; Umezu, I.; Suzuki, S.; Ohtsuka, Y.; Achiba, Y. Synth. Met. 1999, 103, 2555. (14) Brown, S. D. M.; Corio, P.; Marucci, A.; Dresselhaus, M. S. Phys. ReV. B 2000, 61, R5137. (15) Canc¸ado, L. G.; Pimenta, M. A.; Saito, R.; Jorio, A.; Ladeira, L. O.; Grueneis, A.; Souza-Filho, A. G.; Dresselhaus, G.; Dresselhaus, M. S. Phys. ReV. B 2002, 66, 035415. (16) Saito, R.; Jorio, A.; Souza Filho, A. G.; Dresselhaus, G.; Dresselhaus, M. S.; Pimenta, M. A. Phys. ReV. Lett. 2002, 88, 027401. (17) Baltog, I.; Baibarac, M.; Lefrant, S. J. Opt. A: Pure Appl. Opt. 2005, 7, 632. (18) Pimenta, M. A.; Marucci, A.; Empedocles, S. A.; Bawendi, M. G.; Hanlon, E. B.; Rao, A. M.; Eklund, P. C.; Smalley, R. E.; Dresselhaus, G.; Dresselhaus, M. S. Phys. ReV. B 1998, 58, R16016. (19) Souza Filho, A. G.; Jorio, A.; Samsonidze, G. G.; Dresselhaus, G.; Saito, R.; Dresselhaus, M. S. Nanotechnology 2003, 14, 1130. (20) Song, D.; Wang, F.; Dukovic, G.; Zheng, M.; Semke, E. D.; Brus, L. E.; Heinz, T. F. Phys. ReV. Lett. 2008, 100, 225503. (21) Kang, K.; Ozel, T.; Cahill, D. G.; Shim, M. Nano Lett. 2008, 8, 4642. (22) Jorio, A.; Fantini, C.; Dantas, M. S. S.; Pimenta, M. A.; Souza Filho, A. G.; Samsonidze, G. G.; Brar, V. W.; Dresselhaus, G.; Dresselhaus, ¨ nlu¨, M. S.; Goldberg, B. B.; Saito, R. Phys. M. S.; Swan, A. K.; U ReV. B 2002, 66, 115411.
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