Journal ArticleWe studied the femtosecond dynamics of  photoexcitations in films containing semiconducting and  metallic single-walled carbon nanotubes (SWNTs), using various pump-probe wavelengths and intensities.We found that confined excitons and charge carriers with subpicosecond dynamics dominate the ultrafast response in semiconducting and metallic SWNTs, respectively. Surprisingly, we also found from the exciton excited state absorption bands and multiphoton absorption resonances in the semiconducting nanotubes that transitions between subbands are allowed; this unravels the important role of electron-electron interaction in SWNT optics

Korovyanko, O.

Vardeny, Zeev Valentine

English

The University of Utah: J. Willard Marriott Digital Library

Volume 92, Number 1 P H Y S I C A L  R E V I E W  L E T T E R Sweek ending9 JANUARY 2004Ultrafast Spectroscopy of Excitons in Single-Walled Carbon NanotubesO. J. Korovyanko,1 C.-X. Sheng,1 Z.V. Vardeny,1 A. B. Dalton,2 and R. H. Baughman2 1 Department of Physics, University of Utah, Salt Lake City, Utah 84112, USA ~Nano Tech Institute, University of Texas at Dallas, Richardson, Texas 75083, USA (Received 29 M y 2003; published 9 January 2004)We studied the femtosecond dynamics of photoexcitations in films containing semiconducting and metallic single-walled carbon nanotubes (SWNTs), using various pump-probe wavelengths and intensities. We found that confined excitons and charge carriers with subpicosecond dynamics dominate the ultrafast response in semiconducting and metallic SWNTs, respectively. Surprisingly, we also found from the exciton excited state absorption bands and multiphoton absorption resonances in the semi­conducting nanotubes that transitions between subbands are allowed; this unravels the important role of electron-electron interaction in SWNT optics.DOI: 10.1103/PhysRevLett.92.017403Because of the nanometer scale diameter and ex­tended dimension along the tube, single-walled carbon nanotubes (SWNTs) are considered to be quasi-one- dimensional (ID) solids [1], Depending on their chi- rality, SWNTs can be either semiconducting or metallic[2]. In recent years, much effort has been devoted to studying Coulomb interaction in quasi-ID  electronic systems [3]. Peierls instability in electron-phonon ID metal [4] and large binding energy excitons in ID semi­conductors [5] are two well-known examples of elec­tronic confinement in ID systems. Nevertheless, the role of electron-electron (e-e) interaction in SWNTs has not yet been studied in detail. Recent improvements in sample preparation led to the discovery of fluorescence in isolated SWNTs [6], and the realization that e-e inter­action in SWNTs is important [7-9]. In particular, it is clear that excitons are responsible for the measured fluo­rescence [6], and that the use of tight binding approxima­tion to calculate the electronic band structure cannot account for various features seen in the optical absorption spectrum of SWNTs [7-9].In this Letter, we provide further experimental evi­dence for the importance of e-e interaction in SWNTs. We measured the ultrafast dynamics of photoexcitations in films of SWNTs that contain both semiconducting (5) and metallic (M) nanotubes (NTs). From the transient photoinduced absorption bands, multiphoton absorption resonances, and polarization memory dynamics, we con­clude that the primary photoexcitations in S NTs are confined excitons with allowed optical transitions be­tween subbands; these transitions are strictly forbidden in the tight binding approximation. In contrast, the ultra­fast photoresponse in M  NTs is determined by hot carrier dynamics.We used the femtosecond two-color pump-probe corre­lation technique with linearly polarized light beams in a broad spectral range from 0.6 to 2.6 eV and pump inten­sities (I) ranging from 0.1 to 3000 /xJ/cm 2. For the high- intensity measurements, we used a titanium-sapphire laser amplifier system followed by an optical parametricPACS numbers: 78.47.+p, 72.20.Jv, 78.55.Kz, 78.67.Champlifier having 100 fs pulses at photon energies of 1.55 eV and from 0.7 to 1.1 eV as well as frequency- doubled pulses from 1.8 to 2 eV. Four percent of the out­put was split to generate white light supercontinuum for the probe beam in the spectral range from 1.2 to 2.7 eV. For the low-intensity measurements, we used a titanium- sapphire pumped optical parametric oscillator with 100 fs pulses, which extended the transient photo­modulation (PM) spectral range into the mid-IR from 0.56 to 0.73 eV and 0.84 to 1.02 eV. The transient PM signal, [A T(t)/T]  is the fractional change in transmis­sion, which is negative for photoinduced absorption (PA) and positive for photobleaching (PB). To obtain the transient polarization memory, P(t), we measured A T /T  for pump-probe polarizations either parallel (ATp) or perpendicular (ATpe) to each other, and calcu­late Pit) =  (ATp -  A7)„ )/(A7), + ATpe).The SWNTs were grown using a modified gas phase process (HiPco), and were supplied by Carbon Nano­technologies Inc. The raw material was initially dispersed in deionized water using an anionic surfactant lithium dodecyl sulfate. SWNT thin films were subsequently prepared on silica substrates by successive dip coating followed by a ten-hour bake at 70 °C. The films were annealed for 5 h in A r atmosphere at 600 °C. The NTs contain approximately 12%-15% by weight Fe catalyst but are otherwise relatively free of carbonaceous im puri­ties commonly associated with other production methods. Atomic force microscopy and resonant Raman spectros­copy suggested an average NT length of ~400 nm, and a diameter distribution ranging from 0.8 to 1.2 nm.A typical absorption spectrum of the SWNT films is shown in the Fig. 1 inset. Three prominent absorption bands and a shoulder are seen at 0.8 eV (A), 1.35 eV (B),1.9 eV (C), and 2.5 eV (D), respectively, which are super­imposed onto broad background absorption [10,11]. BandsA, B, and D were previously assigned [1,11] to the in- homogeneously broadened interband optical transitions in 5 NTs from various valence subbands to their respec­tive conduction subbands with the same index, nr, namely017403-1 0031-9007/04/92(l)/017403(4)$20.00 © 2004 The American Physical Society 017403-1Volume 92, Number 1 P H Y S I C A L  R E V I E W  L E T T E R Sweek ending9 JANUARY 2004FIG. 1. The transient PM spectra of a SWNT film at t = 0 (full line) and t = 500 fs (dotted line) excited at 1.55 eV; the dashed line is a guide to the eye. Various PB and PA bands are assigned The inset shows the absorption spectrum of the film, where bands A to D are assigned.in =  1 ,2, and 3, respectively [Fig. 2(a)]. On the contrary, band C at 1.9 eV was assigned [1411 to the in =  I inter­band transition in M  NTs.The transient PM spectra of a SWNT film at 300 K excited at 1.55 eVand measured at delay times t =  0 andFIG. 2. Schematic representation of the excited states and optical transitions of S NT in the tight binding (a) and exciton picture (b), respectively, (a) The electron dispersion relation [£(£)] and the allowed interband optical transitions involving subbands with indices m of 1 to 3; optical transitions among subbands in the conduction or valence bands are strictly for­bidden. (b) Various excitons (Exj and Ex2) in the NT configu­ration coordinate, Q, and their associated optical transitions from the ground state (GS) (A to D, full lines), and Exj (PA! to PA3, double lines).t =  500 fs, respectively, are shown in Fig. 1; the spectra contain contributions from both the high- and low- intensity laser systems, which were normalized to each other in the mid-IR spectral range. The PM spectra reveal two PB bands that peak at 0.79 [PB(A)[ and 1.35 eV [PB(B)1, respectively; two PA bands with peaks around 0.6 (PA,) and 1.6 eV (PA2),and the threshold of a third PA band (PA3) at 1.03 eV. Since the PB bands correspond to absorption bands A and B of S NT (Fig. 1 inset), we assign them as photobleaching of these two bands. The PB is due to either fc-space state filling [12] or Q-space filling [131, depending on whether carriers [Fig. 2(a)! or excitons (Fig. 2(b)] are photogenerated at t =  0. From the transient dynamics seen in Fig. 3, it is clear that PB(B) decays much faster than PB(A), in agreement with previous literature [10]. We thus explain PB(B) fast decay as due to photoexcitation thermalization from in =  2 to in =  I subbands. The transient PA, on the other hand, was inter­preted [10] as due to transient dynamics of the absorptiont(ps)FIG. 3. Transient dynamics of various PA and PB bands in the PM spectrum of Fig. 1. (a) PB(A) and its associated PA! and PA2 bands, (b) PB(B) and its associated PA3. The inset in (a) shows AT(t) at 0.9 eV in parallel and perpendicular pump- probe polarizations, and the consequent polarization memory P{t) decay.017403-2 017403-2V o l u m e  9 2 , N u m b e r  1 P H Y S I C A L  R E V I E W  L E T T E R Sweek ending9 JANUARY 2004background (Fig. 1). However, when examining the full PM spectrum obtained here (Fig. 1), we see that the PA spectrum does not agree with this interpretation f 10], since it contains two well-resolved peaks (PA] and PA2, respectively) and a threshold of another (PA3). Moreover, the transient PA and PB are correlated, indicating that they share a common origin.The transient dynamics of the various PA and PB bands in the PM spectrum are shown in Fig. 3. It is seen that, whereas PB(A) dynamics are sim ilar to that of PA] and PA2 [Fig. 3(a)] showing a lifetime of about 700 fs, PB(B) dynamics are correlated with that of PA3 showing a life­time of about 150 fs. In addition, the polarization memory dynamics P(t) of PB(A) [Fig. 3(a) inset] also correlates with P(t) of PA | and PA2 bands (not shown). Moreover, from the initial P(0) value of 0.45, we conclude that the PA and PB bands are polarized parallel to the NT axis. The correlation between the various PA and PB bands indicates that the PA bands should be associated with the prim ary photoexcitations in S  NT, rather than with the global 77 plasmon f 10]. It is noteworthy that photogen­erated carriers in more common semiconductors do not show structured PA bands; instead their PA is in the form of a structureless Drude free carrier absorption that peaks at low energies [14]. In SWNTs, however, there is the possibility that the PA bands associated with the photo­generated carriers would show peaks that correspond to transitions between subbands, namely, electron (hole) transitions from m to m + 1 within the conduction (va­lence) subbands [Fig. 2(a)]. These optical transitions that are polarized along the NT are strictly forbidden in the tight binding model [1,15], since the angular momentum is not conserved. We therefore conclude that “free” charge carriers are not the prim ary photoexcitations in S  NT.Our results can be well explained, however, when e-h interaction [7-9] is taken into account. In this case, ex­citons are the prim ary excitations in S  NT, where the e-h correlation leads to allowed optical transitions between subbands. The optical transitions of photoexcited exciton can be viewed in this picture as an electron promotion from m =  1 to higher m in the conduction subbands, and simultaneously a symmetric hole promotion from m =  I to a lower valence subband with higher m. Such optical transitions are allowed since both linear and angular momenta are conserved; namely, Ak =  ke -  kh =  0, and Am =  m e -  m h =  0. Simultaneously, energy is also conserved if  the e-h  binding energy is taken into account. A schematic representation of excitons and their optical transitions is given in Fig. 2(b). In this picture, bands A,B, and D are due to excitons, Exj, Ex2, and Ex3, respec­tively. Excitons in ID have relatively large binding energy and “steal” most of the oscillator strength from the interband transition [5,7] explaining the large absorption strength of bands A, B, and D in S  NT [7]. Moreover, PA bands such as PAj and PA2 from Exj and PA3 from Ex2 [see Fig. 2(b)] may be also formed. Our data can be well explained using the exciton picture: Excitation into bandB creates Ex2 that instantaneously forms PB(B) due to phase space filling and a correlated PA band (PA*). Consequently, Ex2 excitons decay within 150 fs [Fig. 3(b)] to the lower Exj excitons that form PB(A) and two associated PA bands, PAj and PA2, respectively, all having slower dynamics [Fig. 3(a)].Further support for the exciton picture is provided by the polarization memory dynamics, P(t) given in the Fig. 3(a) inset We discovered that all transient PB and PA bands in the PM spectrum possess polarization mem­ory, namely, A Tp{t) =#= ATpe{t) [Fig. 3(a) inset]. P{t) de­cays within a few ps, and its dynamics are the same for each PB and its correlated PA bands. Photogenerated free carriers in SWNTs cannot have polarization memory that decays within several ps since they should be delocalized along the tube (that is not straight) very quickly following their generation at t =  0. The prim ary photoexcitations in the alternative model are excitons, confined in space within a few lattice constants. Because of this localiza­tion in space, such excitons would show polarization memory at t =  0, which may decay at t >  0 due to excitons diffusion along the NT. Sim ilar photoinduced polarization memory and decay was seen before in quasi- ID conducting polymers, and, in particular, for photo­induced soliton pairs in fibrils of trans-(CH)A- [16]; similarly, P(t) was analyzed using soliton diffusion along the fibrils. P(t) w ithin this model is given by P(t) =  P(0) e x p ( - 4 D t /R 2), where D  is the photoexcitation dif­fusion constant, and R is the average “ radius of curva­ture” of the fibrils in the film. Using this “exciton diffusion along the N T” model to interpret the polariza­tion memory decay in SWNTs, we calculate from R =  300 nm a diffusion constant D ~  120 cm2/s  for the photogenerated excitons in S  NTs.Additional support for allowed intersubband transi­tions in S  NTs is provided by the resonant multiphoton excitations seen in Fig. 4(a). The transient PM spectrum at t =  0 excited at 1 eV is shown at two different excita­tion intensities, I  =  300 /xJ/cm 2 and /  =  1.5 m J/cm 2. In addition to the trivial PB(A) [17] (not shown here) and its relatively longer decay, we also see PB(B) at low I. Since band B lies higher than the excitation photon energy, then its photobleaching can be explained only by a two- photon-absorption (TPA) process into states at 1.6 eV[13]. However, to account for such a strong A T / T  signal (—5%), the TPA process should be resonantly enhanced via an intermediate allowed state. A reasonable assump­tion for the TPA intermediate state is band A, whereas the final state is band B. This again suggests that A —> B intersubband transition is allowed; consistent with the exciton model presented in Fig. 2(b).The PM spectrum at high I  [Fig. 4(a)] shows that PB(B) is gradually overwhelmed by another PA band, PA*, whereas the photobleaching of band C (M  NT) and band D (S  NT) dramatically increase. We interpret PB(D) and its large value (—10%) as resonant three- photon absorption. Even though three-photon absorption0 1 7403 -3 0 1 7403 -3V o l u m e  9 2 , N u m b e r  1 P H Y S I C A L  R E V I E W  L E T T E R Sweek ending9 JANUARY 2004<11.2 1.4 1.6 1.8 2 2.2 2.4 P h o to n  E n e r g y  (eV )2.6$<P h o t o n  E n e r g y  (e V )FIG. 4. Transient PM spectra at / =  0 excited at (a) 1 eV at two different pump excitation intensities, /  =  300 ^ J /c m 2 (squares) and /  =  1.5 m J/em 2 (solid line), and (b) at 2.0 eV. Various PB and PA bands are assigned. The inset in (b) shows the transient decay of PB(C) excited at 2.0 eV.is in general a very weak process, resonant three-photon absorption is apparently strong 118). This process can be also viewed as sequential excitation via allowed in ­termediate states, namely A —> B —> D showing that not only A —> B transition, but also B —> D transition is allowed.The PM spectrum excited at 2 eV into band C (M  NT) is shown in Fig. 4(b). Two PB bands are apparent; PB(B) of S  NTs and PB(C) of M  NTs. We note that PB(C) occurs either upon interband transition at 2 eV [Fig. 4(b)] or upon high-intensity excitation at I eV [Fig. 4(a)], Since in M  NTs there are no allowed optical transitions between 0.7 and I eV fl], we conjecture that PB(C) simply occurs by carrier heating 119). This shows that the prim ary photoexcitations in M  NTs are freecarriers with extremely fast P it) decay (not shown here). At / =  0. these are “ hot carriers,” for which the electronic temperature Te is not yet established; this explains the immediate appearance of PB(C) in the PM spectrum. Because of e-e collisions, the electron system reaches the quasiequilibrium state described by a tem ­perature Te, whereas most of the PM spectrum of M  NTs occurs close to the Fermi energy 119). This explains the ultrafast decay (—200 fs) of PB(C) [Fig. 4(b) inset). 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Ultrafast spectroscopy of excitons in single-walled carbon nanotubes

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Ultrafast spectroscopy of excitons in single-walled carbon nanotubes

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