Dynamics of charged in electronically and morphologically homogeneous single-walled carbon nanotubes

Yusong Baia, Jean-Hubert Oliviera, George Bullarda, Chaoren Liua, and Michael J. Theriena,1

aDepartment of Chemistry, French Family Science Center, Duke University, Durham, NC 27708-0346

Edited by José N. Onuchic, Rice University, Houston, TX, and approved December 8, 2017 (received for review July 22, 2017) The trion, a three-body charge- , offers unique SWNTs demonstrate a new lower-energy absorption, which opportunities to simultaneously manipulate charge, , and has been attributed to a direct ground-to-trion optical tran- + hυ + + excitation in one-dimensional single-walled carbon nanotubes sition (E 00 ! Tr 11, where Tr 11 denotes a low-lying elec- (SWNTs) at room temperature. Effective exploitation of trion tronically excited trion state) (5, 8); no experimental evidence, quasi- requires fundamental insight into their creation however, has confirmed the nature of the state produced by and decay dynamics. Such knowledge, however, remains elusive + SWNT E absorption. for SWNT trion states, due to the electronic and morphological 00 Here, we describe the transient absorptive and dynamical heterogeneity of commonly interrogated SWNT samples, and the properties of hole trions in length-sorted semiconducting (6,5) fact that transient spectroscopic signals uniquely associated with the trion state have not been identified. Here, we prepare length- SWNTs, wherein hole densities are rigorously con- sorted SWNTs and precisely control charge-carrier-doping densi- trolled. Owing to the electronic and morphological homogeneity ties to determine trion dynamics using femtosecond pump–probe of these SWNT samples, we clearly identify a trion transient spectroscopy. Identification of the trion transient absorptive hall- absorptive hallmark, which in turn enables us to correlate dy- mark enables us to demonstrate that trions (i) derive from a pre- namical processes characteristic of bright excitons, hole , cursor excitonic state, (ii) are produced via migration of excitons to and trions, and thus unambiguously unveil trion formation and CHEMISTRY stationary hole-polaron sites, and (iii) decay in a first-order man- decay dynamics. By comparing trion dynamics acquired from ner. Importantly, under appropriate carrier-doping densities, pumping in resonance with the E00 → E11 exciton transition, exciton-to-trion conversion in SWNTs can approach 100% at am- with those obtained from excitation of the previously assigned bient temperature. Our findings open up possibilities for exploit- “trion transition,” we ascertain charge-doped 1D SWNTs do ing trions in SWNT optoelectronics, ranging from photovoltaics + → + and photodetectors to spintronics. not possess a direct E 00 Tr 11 optical transition. Moreover, these dynamical studies demonstrate that under appropriate trion | exciton | single-walled carbon nanotube | dynamics | charge carrier-doping conditions, optical stimuli can result in near-unit conversion of excitons to trions, opening up possibilities for he trion, comprising an exciton and a charge (1), defines a SWNT-based optoelectronic devices that rely upon manipu- Tunique quasi- species by its hybrid nature: it simul- lating spin, energy, and charge. taneously carries excitation energy, net charge, and unpaired spin. Exploitation of trions in optoelectronics has been impeded Significance by their small binding energies (ΔETr) in conventional 3D (ΔETr ∼ 0.01–0.3 meV) (2) and 2D (ΔETr ∼ 1–5 meV) (3, 4) semicon- Formation of , such as excitons, polarons, and ductors, wherein trion observation is made possible under cryo- trions in semiconductors are the foundation for modern op- conditions (4). In sharp contrast, optical excitation of the semi- toelectronics. Unlike the widely investigated exciton and conducting single-walled carbon nanotube (SWNT) charged polaron, the trion, a three-body charge-exciton bound state, + ground state (E 00) gives rise to trions even at room temperature is less familiar due to its small binding energy in conventional (5–15), due to the drastically increased ΔETr (∼100 meV) in 1D inorganic semiconductors. Here, employing ultrafast spec- SWNTs that arises from reduced dielectric screening. Owing troscopy and rigorously controlled charge-doping levels, we characterize trion creation and decay in single-walled carbon to the substantial ΔETr, the tightly bound trion quasi-particles in SWNTs offer new opportunities to manipulate charge, spin, nanotubes (SWNTs), wherein trions are stable at room tem- and excitonic energy at room temperature. To fully un- perature. We show that SWNT trions derive exclusively from derstand and exploit the exceptional potential of SWNT trion a precursor exciton state, and importantly, that exciton-to- species, it is vitally important to attain fundamental insights trion conversion can approach unity under appropriate con- into the dynamics and mechanisms that characterize their ditions. Because trions simultaneously carry excitation en- creation and decay. ergy, charge, and spin, our findings may guide design of new Various transient optical methods have been used to indirectly SWNT-based optoelectronic devices, including photovoltaics, photodetectors, and spintronics. assess trion dynamics in SWNTs; such studies report trion for-

mation and decay time constants that vary by many orders of Author contributions: M.J.T. designed research; Y.B., J.-H.O., and G.B. performed re- magnitude (11–14). Furthermore, corresponding mechanistic search; Y.B., J.-H.O., G.B., C.L., and M.J.T. analyzed data; and Y.B., J.-H.O., G.B., C.L., descriptions of trion generation and decay are ambiguous, due to and M.J.T. wrote the paper. the heterogeneity of the nanotube samples studied and the lack The authors declare no conflict of interest. of a clear trion spectral fingerprint. Indeed, recent experimental This article is a PNAS Direct Submission. and theoretical evidence for the suppression of exciton-free Published under the PNAS license. carrier scattering (16, 17) in SWNTs challenged the exciton- 1To whom correspondence should be addressed. Email: [email protected]. ∼ free hole scattering mechanism for ultrafast ( 50 fs) trion for- This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10. mation (15). Additionally, linear optical studies of charge-doped 1073/pnas.1712971115/-/DCSupplemental.

www.pnas.org/cgi/doi/10.1073/pnas.1712971115 PNAS Early Edition | 1of6 Downloaded by guest on October 2, 2021 Results and Discussion superstructures in D2O solvent (24). We emphasize that spec- S Acquiring Homogeneously Engineered SWNTs Samples. As a primary troscopic data demonstrate that the -PBN(b)-Ph5 polymer re- task for identifying trion dynamics, we acquired SWNTs having mains unoxidized by this procedure, as the semiconducting high uniformity of electronic structure (chirality) and length. polymer valence band energy is stabilized by over 400 meV rel- Dispersion of these SWNTs in the condensed phase by exploiting ative to that of the (6,5) SWNT (24). With length-sorted SWNTs a binaphthalene-based polyanionic semiconducting polymer in hand, and known nanotube concentrations in solution, the [S-PBN(b)-Ph ] that exfoliates, individualizes, and disperses stoichiometric oxidant enables precise control over hole density 5 h+ S SI Appendix SWNTs via a single-chain helically chiral wrapping mechanism, ([ ]) in -PBN(b)-Ph5-[(6,5) SWNTs] ( , Section 2). assures morphological homogeneity of these samples (Fig. 1A) Fig. 2A electronic absorption data that chronicle the oxidative S (18). These semiconducting polymer-SWNT superstructures titration of the -PBN(b)-Ph5-[(6,5) SWNT] superstructures → maintain a fixed polymer helical pitch length on the SWNT highlight the progressive diminution of E00 E11 transition surface (Fig. 1B). The robustness of the polymer-SWNT super- oscillator strength and the correlated rise of a heretofore structures in various aqueous and organic solvents enables unidentified lower-energy transition at ∼1,150 nm, with in- + − multiple rigorous separation procedures that permit isolation of creasing [h ] from 0 to 14.3 (100 nm) 1. The transition centered highly enriched (19) (purity > 90%), length-sorted (20) (700 ± at 1,150 nm has usually been ascribed to a trion optical transition + + 50 nm) (6,5) SWNTs: these S-PBN(b)-Ph -[(6,5) SWNTs] thus (E 00 → Tr 11) (5, 8); consistent with data described below, we 5 + + define uniquely engineered, consistent nanoscale carbon nano- denote this 1,150-nm transition as E 00 → E 11, an exciton tube superstructures (Fig. 1B and SI Appendix, Fig. S1) with transition dressed by the interactions with hole polarons. which to probe transient absorptive signatures and dynamics of trions. Fig. 1C provides benchmark transient absorption spectra Identification of SWNT Trion Transient Absorptive Signature. To for neutral S-PBN(b)-Ph5-[(6,5) SWNTs] in D2O solvent, fol- identify the trion transient absorptive signature, we acquired → broadband pump–probe transient data on hole-doped SWNTs in lowing E00 E11 (1,000 nm) optical excitation. Owing to the + high homogeneity of these (6,5) SWNT superstructures, tran- which [h ] was fixed and known; these studies unveiled a suspicious sient absorptive hallmarks for a broad range of quasi-particles transientabsorptionbandcenteredat1,190nm.Representative S are clearly visualized: these include a dominant E00 → E11 bleach transient absorption spectra of heavily hole-doped -PBN(b)- + −1 centered at ∼1,000 nm (21) and three positive transient ab- Ph5-[(6,5) SWNT] superstructures ([h ] ∼ 14.3 (100 nm) ) + + sorption bands observed to the red of this bleach, at ∼1,100 nm manifest E00 → E11 (∼1,000 nm) and E 00 → E 11 (∼1,150 nm) 3 3 (E11 → E11,BX) (20), ∼1,150 nm ( E11 → Enn) (22), and ∼1,200– bleaches, as well as a signal having an absorption maximum 1,300 nm (fast-decay signal, τ ∼ 0.7 ps) (23). near 1,190 nm (Fig. 2B). Importantly, this transient absorption Unambiguous analysis of trion dynamics also requires SWNTs manifold centered at 1,190 nm is absent in undoped, neutral S-PBN with rigorously controlled carrier-doping densities. For this (b)-Ph5-[(6,5) SWNTs], suggesting its correlation with nanotube reason, we prepared hole-doped SWNTs through established hole polarons. methods that exploit K2IrCl6 as an oxidant capable of stoichio- The 1,190-nm transient absorption signal is ascribed to a trion + + + metrically transferring holes to S-PBN(b)-Ph5-[(6,5) SWNT] transient absorptive hallmark (Tr 11 → Tr nm, where Tr nm

A C Photon energy (eV) 1.3 1.2 1.1 1.0 ~ 10 nm 15 0 Δ

E E E E Absorption (mOD) SO3Na 00 11 11 11,BX SO3Na 12 3E 3E O 11 nn -50 O O OR OR OR

O O n O RO RO RO 9 -100 NaO S 3 R = O O -PBN(b)-Ph5 NaO3S O -150

B Time (ps) 6

3 Fast-decay signal ( ~ 0.7 ps)

0 Z 1.2nm X 10 nm 100 nm 900 1,000 1,100 1,200 1,300 Y Wavelength (nm)

Fig. 1. Structure, morphology, and ultrafast pump–probe spectra of polymer-wrapped SWNTs. (A) Structural schematic of a chiral [arylene]ethynylene polymer-wrapped SWNT (Top); the polymer wraps the SWNT in an exclusive left-handed helical configuration that features a constant pitch length of 10 nm.

Molecular structure of the binaphthalene-based polyanionic semiconducting polymer, S-PBN(b)-Ph5 (Bottom). (B) Transmission microscopy image of an S-PBN(b)-Ph5-[(6,5) SWNT] obtained from aqueous suspension highlighting the individualized and helically wrapped nature of the polymer-SWNT su- perstructure. (Inset) A 3D topographic intermittent contact atomic force microscopy image of an S-PBN(b)-Ph5-[(6,5) SWNT] on a Si surface, underscoring the periodic surface morphology. (C) Representative 2D plot of transient absorption spectra for neutral S-PBN(b)-Ph5-[(6,5) SWNTs]; the horizontal axis, vertical axis, and color scale represent the probe wavelength (photon energy), pump–probe time delay, and the transient absorption signal, respectively. Positive signals indicate a pump-induced increase in absorption, while negative signals indicate pump-induced decrease in absorption; dotted lines highlight major 2 transition manifolds. Experimental conditions: λexc = 1,000 nm; solvent = D2O; T = 293 K; magic angle polarization; excitation pump power = 140 μJ/cm .

2of6 | www.pnas.org/cgi/doi/10.1073/pnas.1712971115 Bai et al. Downloaded by guest on October 2, 2021 ABPhoton energy (eV) Photon energy (eV) 1.3 1.2 1.1 1.0 1.3 1.2 1.1 1.0 6 10 1.0 [ +]: -1

0 (100 nm) Δ E00 E11 + + -1 E E Absorption (mOD) 0.3 (100 nm) E00 E11 00 11 -1 5 0.5 0.7 (100 nm) 0 3.5 (100 nm)-1 E+ E+ -1 + + 00 11 6.1 (100 nm) Tr 11 Tr nm -1

Absorption (a.u.) 14.3 (100 nm) 4 0.0 -10 900 1,000 1,100 1,200 1,300 Wavelength (nm) 3

= 1190 nm, Time (ps) C 1.0 Probe -20 [ +] = 14.3 (100 nm)-1 2 Probe = 1000 nm, [ +] = 0.0 (100 nm)-1

0.5 1

= 1000 nm, Absoprtion (a.u.) Probe [ +] = 14.3 (100 nm)-1 0 0.0 0.0 1.0 2.0 900 1,000 1,100 1,200 1,300 Time (ps) Wavelength (nm)

Fig. 2. Ground-state absorption and pump–probe transient absorptive dynamical data for hole-doped SWNTs. (A) NIR ground-state absorption spectra that CHEMISTRY chronicle the extent of hole injection into S-PBN(b)-Ph5-[(6,5) SWNTs]. Experimental conditions: [(6,5) SWNTs] ∼72.3 nM; SWNT length = 700 ± 50 nm; argon atmosphere; solvent = D2O; T = 293 K; optical path length = 2 mm; hole source (oxidant) = K2IrCl6.(B) Representative 2D transient absorption spectral plot for + −1 a heavily hole-doped ([h ] ∼ 14.3 (100 nm) ) S-PBN(b)-Ph5-[(6,5) SWNT] sample at the time delays noted; dotted lines highlight the major transition man- 2 ifolds. Experimental conditions: λexc = 1,000 nm; solvent = D2O; T = 293 K; magic angle polarization; excitation pump power = 140 μJ/cm .(C) Single- wavelength, picosecond time-domain kinetic traces that chronicle the dynamics for E11 excitons (λprobe = 1,000 nm): black, neutral SWNTs; red, hole-doped SWNTs; corresponding kinetic trace (green) highlighting the dynamics for hole trions (λprobe = 1,190 nm). Kinetic traces plotted with absolute Δabsorption normalized.

denotes a higher-lying hole-trion electronically excited state) In this model, we assume that hole polarons in 1D SWNTs in D2O based on dynamics analysis. Kinetic traces (λprobe = 1,000 nm) are stationary sites on the timescale of these experiments (akin to representing E11 exciton dynamics in neutral and hole-doped a 1D Wigner crystal) (26), contrasting the mobile nature of exci- S-PBN(b)-Ph5-[(6,5) SWNTs], and the 1,190-nm kinetic trace tons. This assumption is justified by considering the long-range evinced in hole-doped S-PBN(b)-Ph5-[(6,5) SWNTs], are plotted Coulomb repulsion among positively charged quasi-particles, and in Fig. 2C for comparison (absolute ΔAbsorption normalized). the fact that migration of such species is accompanied with sig- E11 exciton dynamics in neutral S-PBN(b)-Ph5-[(6,5) SWNTs] nificant outer-sphere reorganization energy in the condensed – are governed by a 1D diffusion-controlled exciton exciton an- phase (27). We fit the E11 exciton and hole trion kinetic data with nihilation (EEA) process (2E11 → E11,2 + E00 → E11 + E00, numerical solutions of the coupled differential equations that where E11,2 represents an E11 exciton within the second mani- describe the kinetic model in Fig. 3B (Methods and SI Appendix, fold) (21, 25), giving rise to a signal reduction of ∼50% within Sections 3.a and 3.b). As shown in Fig. 3C, the agreement between 2 ps (Fig. 2C). On the other hand, E11 exciton dynamics evinced our kinetic model and the experimental data provides compelling in hole-doped SWNTs manifest faster decay relative to that de- proof of a diffusion-controlled trion formation mechanism, and termined in their neutral analogs (Fig. 2C). Given the excess of determines directly SWNT hole trion formation and decay con- – 11 −1 6 −1/2 hole polarons relative to excitons in SWNTs for this pump probe stants (kTr ∼ 5.4 × 10 s ,andkE-Tr ∼ 4.5 × 10 nm s ). ∼ −1 h+ ∼ −1 experiment ([E11] 0.6 (100 nm) ;[ ] 14.3 (100 nm) ), We further studied the dependences of trion formation and we hypothesize that before EEA events, optically generated E11 decay dynamics upon hole polaron densities, and examined how + excitons diffuse to nearby hole-polaron sites and are trapped, [h ] impacts the diffusive behavior of excitons. As can be seen in forming hole trions. Furthermore, E11 exciton decay in hole- Fig. 4, a striking feature––manifest clearly in these dynamical doped SWNTs clearly correlates with the rise of the nascent data––is that the trion formation rate constant, kE-Tr* = transient absorption signal at 1,190 nm within ∼0.5 ps. As such, −1=2 + kE−Trt Nh + , depends on initial [h ], with kE-Tr* increasing − + the correspondingly evolved transient absorption manifold cen- monotonically from 3 × 1011 to 1 × 1012 s 1 as [h ] increases from tered at 1,190 nm is attributed to a trion transient absorptive −1 k k = × 11 −1 σ ∼ + → + 0.3 to 14.3 (100 nm) ,while Tr does not ( Tr 3.9 10 s , SD hallmark (Tr 11 Tr nm). 11 −1 1.3 × 10 s ,wherekTr is the average value for kTr,andσSD is the k SI Appendix Unveiling Trion Dynamics by 1D Diffusion Kinetic Model. Kinetic SD of Tr)( ,Section3.c.1). These observations are modeling of these exciton and trion signals reveals that trions congruent with the 1D diffusion-controlled trion formation/decaypffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi form via the diffusion of excitons to hole polaron sites; once picture highlighted in Fig. 3A. Additionally, as kEEA ∼ 32DE11=π formed, these quasi-particles decay in a first-order manner (21), where DE11 represents the exciton diffusion constant, we 2 −1 (schematically illustrated in Fig. 3A). We evaluated trion for- obtained a DE11 value of ∼0.9 cm s for S-PBN(b)-Ph5-[(6,5) mation and decay dynamics using a 1D diffusion kinetic model SWNTs] dispersed in D2O; note that this value is of the same order depicted in Fig. 3B, that also takes into account 1D diffusion- of magnitude compared with exciton diffusion constants derived controlled EEA processes explicitly described by Lüer et al. (21). from pump–probe measurements of xerogel-dispersed SWNTs

Bai et al. PNAS Early Edition | 3of6 Downloaded by guest on October 2, 2021 A Optical excitation Exciton diffusion,

pump = 1,000 nm trion formation - +++- + +

+ + E 00 E11 Tr 11 First-order trion decay BC E11,2

1.0 + + oscillator strength -1/2 11 nm 21 1/2 EEA E11

5 -1/2 -1/2 E-Tr ~ 1.3 × 10 nm s E-Tr h+ E11 ~ 5.3 × 1011 s-1 0.5 Tr

~ pump 1/2 -1/2 E E bleach 10 EEA E11 Δ Absorption (a.u.) 00 11 1,000 nm Tr

+ E 00 0.0 0123456 Time (ps)

Fig. 3. One-dimensional diffusion kinetic model describing hole trion formation. (A) Schematic description of hole trion formation in hole-doped, optically + + excited semiconducting SWNTs. (B) Diagrammatic representation of the four-state model used to fit the E00 → E11 and Tr 11 → Tr nm kinetic traces, where the + + −1 NX(t)(X = E11,E11, 2,Tr 11,orh ) corresponds to the densities [(100 nm) ] of these quasi-particles at a certain time t, k10 is the intrinsic first-order decay rate constant for bright singlet excitons in (6,5) SWNTs, k21 is the rate constant for the first-order decay from the second to the first exciton subband, kTr is the first- −1/2 −1/2 order decay rate constant of trions, kEEAt NE11 is the EEA rate constant, and kE-Trt Nh+ is the trion formation rate. Note that all rate constants are in units −1 + + of ps .(C) Kinetic traces for E00 → E11 bleaching oscillator strength (red, scattered square), Tr 11 → Tr nm transient absorption oscillator strength (green, scattered circle), and corresponding numerical fits (solid curves) obtained using the kinetic model depicted in B. Note that data represented in C do not correspond to single-wavelength kinetics, as they are acquired from integrated Gaussian functions fitted to the corresponding spectral signals (SI Appendix, Section 3.b).

+ + (21) and fluorescence quenching studies of SWNTs suspended from a direct E 00 → Tr 11 optical transition, optically pumping in agarose gels (28). Furthermore, an excitonpffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi diffusion length may this band should result in instantaneous formation of hole trions be determined from the relation LE11 = DE11τE11 (29) (where in hole-doped SWNTs, and hence an immediate observation of + −1 + → + τ is the exciton decay time constant). For [h ] ∼ 14.3 (100 nm) the trion transient absorption signal, Tr 11 Tr nm.However, E11 – SWNTs, τE11 is ∼0.5 ps, indicating that LE11 is ∼6nm,which pump probe transient optical measurements of hole-doped + −1 matches closely the half spatial separation between hole polarons SWNTs ([h ] ∼ 14.3 (100 nm) ) in which excitation is centered (dh+/2 ∼ 3.5 nm). This correlation between L and dh+/2 is con- in this absorption manifold, demonstrate a gradual rise of the E11 + → + SI Appendix sistent with the notion that trion formation in optically excited hole- Tr 11 Tr nm signal ( , Section 5). These data in- + → + doped SWNTs derives from an exciton diffusion process that occurs dicate that an E 00 Tr 11 transition possesses little or no oscillator on a timescale over which hole polarons are effectively stationary. strength at 1,150 nm. Moreover, following excitation at ∼1,130 nm, Importantly, these experimental data and the corresponding nu- the resultant transient kinetic traces representative of E11 exciton merical simulation of these results (SI Appendix,Section4)indicate and hole trion dynamics mirror those obtained for excitation at that exciton-to-trion conversion can approach unity under hole-doping 1,000 nm (SI Appendix,Fig.S15). Such dynamical similarities fur- − levels that range from 6.1 to 14.3 (100 nm) 1 (SI Appendix,Fig.S13). ther demonstrate the 1,150-nm absorption characteristic of hole- + → + BasedonthekineticmodelinFig.3B, the exciton decay rate in doped SWNTs is not an E 00 Tr 11 transition, but a signature of hole-doped SWNTs is determined by ðdN =dtÞ = ð−k N Þ + an exciton absorption that is dressed by a Fermi sea of excess À Á À E11 Á decay 10 E11 + → + A −1=2 2 −1=2 carriers, congruent with the E 00 E 11 assignment in Fig. 2 . −k t N + −k - t Nh + N ,whereinð−k N Þ, EEA E11 E Tr E11 10 E11 −1=2 2 −1=2 ð−k t N Þ, and ð−k - t Nh + N Þ represent the Conclusions EEA E11 E Tr E11 three exciton decay channels (intrinsic first-order decay, EEA, In summary, we have shown that trion quasi-particles form from and trion formation, respectively). Using the kEEA and kE-Tr exciton migration to stationary hole polaron sites in optically values obtained in these studies, our numerical simulations excited, charged semiconducting SWNTs, while trion decay is a demonstrate that trion formation defines the dominant exciton first-order process. These data demonstrate that under the ex- + decay channel for hole-doped SWNTs in which [h ] ranges from perimental conditions here, trions are not produced by direct − 6.1 to 14.3 (100 nm) 1. optical excitation of any ground-state absorption associated with hole-doped SWNTs, contrasting sharply the photophysics of The Nature of Previously Assigned Trion Optical Transition. The na- carrier-doped conventional semiconductors, wherein trions may scent 1,150-nm band in Fig. 2A, previously ascribed to trion be produced via an optical transition from the ground state. This + + + optical transition (E 00 → Tr 11) (5, 8), is purely excitonic (E 00 → work further establishes a SWNT hole trion transient absorptive + + + E 11) in nature. If the 1,150-nm absorption in Fig. 2A originates signature (Tr 11 → Tr nm): as trion formation requires the

4of6 | www.pnas.org/cgi/doi/10.1073/pnas.1712971115 Bai et al. Downloaded by guest on October 2, 2021 step yielded length-sorted polymer-wrapped (6,5) SWNTs]. The resulting sample was desalted via centrifugal filtration. The sample was washed k t -1/2N , t = 0.5 ps E-Tr h+ with and then taken up in the desired solvent mixture (18). This solution 1.0 (Trion formation) was used with no further modifications. ) -1 Optical Configuration of the Ultrafast Pump–Probe Setup. Ultrafast transient absorption spectra were obtained using standard pump–probe methods. Optical pulses (∼150 fs) centered at 780 nm were generated using a Ti:sap- kTr (Trion decay) 0.5 phire laser (CPA-2001; Clark-MXR), which consists of a regenerative amplifier seeded by a mode-locked fiber oscillator. An optical parametric amplifier (TOPAS-C; LIGHT CONVERSION) generates excitation pulses tunable in wave-

ate constant (ps length from the UV through the near-infrared (NIR) region. The pump beam R was chopped at half the laser repetition rate (∼500 Hz). A fraction (<5%) of the output from the regenerative amplifier was passed through an optical 0.0 delay line, and focused onto a 2-mm c-cut sapphire plate to generate a white- light continuum used as the probe beam. The polarization and attenuation of 0 36912 15 the pump and probe beams were controlled by a λ/2 wave plate and Rochon [ +] (0.01 nm-1) prism polarizer pairs. Pump/probe polarization was set to magic angle (54.7°) ∼ + for these experiments. The pump spot-size diameter was 0.2 mm. After Fig. 4. Hole trion formation and decay rate constants as a function of [h ]. passing through the sample, the probe light was focused onto the entrance Summary plot of hole trion formation and decay rate constants as a function + slit of the computer-controlled image spectrometer (SpectraPro-2150i; Acton of [h ]. Note that the hole trion formation rate constant is determined from Research Corporation). Transient absorption data acquired over the 0.9–1.4-μm −1/2 the expression kE-Trt Nh+ (as both exciton and hole polaron concentra- + NIR region were recorded using a liquid-nitrogen-cooled InGaAs 512-element tions vary as a function of time); here t is selected at 0.5 ps; as [h ]isa linear array detector (Roper Scientific) interfaced to a SpectraPro-2150i function of time, this value is acquired from numerical simulation based on spectrometer. All these experiments utilized a 2-mm-path-length fused-silica rate equations derived from the kinetic model in Fig. 3B; hole trion decay sample cell; all transient optical studies were carried out at 20 ± 1 °C. All rate constants are directly represented by k , as trion decay is a first-order Tr transient spectra reported represent averages obtained over five scans, with process (a 3D plot describing hole trion formation and decay dynamics as + each scan consisting of ∼100–200 data points. In these experiments, the functions of time and [h ] may be found in SI Appendix, Fig. S9). Error bars delay line utilizes a computer-controlled delay stage. Delay times up to 6 ns represent the uncertainty from fitting the exciton and trion kinetic traces. were achieved using a Compumotor-6000 (Parker). CHEMISTRY

Brief Description of 1D Kinetic Model. Based on the 1D diffusion kinetic model coexistence of an exciton and a charge carrier, we emphasize that + → + shown in Fig. 3B, the relevant rate equations/ordinary differential equations the Tr 11 Tr nm transition defines an unequivocal spectroscopic (ODEs) follow: fingerprint for any study that aims to investigate optically driven

1 1 free-carrier generation in SWNTs. Importantly, under appropriate dNE11 − − = − − ð − Þ 2 2 + − ð − Þ 2 + + − k10NE11 kEEA t t0 N k21NE kE-Tr t t0 Nh NE11 [1] charge-doping conditions ([h ] ∼ 6.1–14.3 (100 nm) 1), exciton-to- dt E11 11, 2 trion conversion can approach 100% following optical stimuli. dNE 1 − 1 11, 2 = ð − Þ 2 2 − Because these tightly bound trions undergo drift in electric field kEEA t t0 N k21NE [2] dt 2 E11 11, 2 (30), which results in simultaneous transportation of energy,

+ charges, and spin, these trion formation and decay dynamical dN 1 Tr11 − = ð − Þ 2 + − + kE-Tr t t0 Nh NE11 kTrNTr [3] data may guide design of new SWNT-based optoelectronic devices dt 11 important for photovoltaics, photodetectors, and spintronics. dNh+ − 1 = − ð − Þ 2 + + + kE-Tr t t0 Nh NE11 kTrNTr [4] Materials and Methods dt 11 + + Additional details regarding the materials characterizations, spectroscopic where NX (X = E11,E11, 2,Tr 11,orh ) is the density (/100 nm) for the cor- −1 measurements, and data processing may be found in SI Appendix. responding quasi-particles, k10 = 0.048 ps is the intrinsic first-order decay −1 rate constant for bright singlet excitons in (6,5) SWNTs (31), k21 = 23 ps is Preparation of Polymer-Wrapped (6,5) SWNTs. Approximately 10 mg of the rate constant for the first-order decay from the second to the first ex- – nanotubes (704148 1G lot# MKBJ6336V; Sigma-Aldrich) were added to a citon subband (32), kTr is the first-order decay rate constant of trions, −1/2 −1/2 vial containing 20 mL of aqueous 1.04% (wt/vol) sodium deoxycholate. kEEA(t − t0) is the EEA rate constant, and kE-Tr(t − t0) is the trion for- −1/2 The vial was bath sonicated for 15 min and then tip sonicated for 2 h mation rate constant. Note that (i) t0 is a fitting parameter; (ii)the(t − t0) (Ultrasonic Liquid Processors, S-4000; MISONIX) at a power level of 12 W. dependence of EEA and hole trion formationpffiffiffi processes originate from 1D The mixture was centrifuged (Optima TLX Ultracentrifuge) at 90,000 ×g diffusion (29); and (iii) kE-Tr = kEEA/2 2 (21). Providing initial values for Nx, for 1 h and the top 80% of the supernatant was collected. An aqueous the optimal numerical solutions of ODEs [1]–[4] can be solved in the process two-phase extraction (ATPE) method (19) was utilized to purify (6,5) of fitting the experimentally acquired E and Tr+ kinetics. A more detailed “ ” 11 11 SWNTs. Briefly, after addition of SWNTs to the ATPE system, (6,5) description regarding kinetic modeling is provided in SI Appendix. SWNTs were isolated in a given phase by varying SDS concentration of the system. Once isolated, the layer containing the desired SWNTs was col- ACKNOWLEDGMENTS. We thank Prof. P. Zhang for many helpful discus- lected and an equal volume of aqueous 2% (wt/vol) sodium cholate was sions. Y.B. acknowledges the generous support from the Fitzpatrick Institute added. To prepare polymer-wrapped SWNTs, the previous solution was for Photonics at Duke University for a John T. Chambers Scholars Award. This added to an aqueous mixture of the desired polymer dispersant. Surfac- work was funded by the Division of Chemical Sciences, Geosciences, and tant and unbound polymer were removed by exchanging the solution into Biosciences, Office of Basic Energy Sciences, of the US Department of Energy a buffer solution and subjecting to gel permeation chromatography [this through Grant DE-SC0001517.

1. Lampert MA (1958) Mobile and immobile effective-mass-particle complexes in non- 5. Matsunaga R, Matsuda K, Kanemitsu Y (2011) Observation of charged excitons in metallic solids. Phys Rev Lett 1:450–453. hole-doped carbon nanotubes using photoluminescence and absorption spectros- 2. Munschy G, Stébé B (1974) Existence and binding energy of the excitonic ion. Phys copy. Phys Rev Lett 106:037404. Status Solidi B 64:213–222. 6. Park JS, et al. (2012) Observation of negative and positive trions in the electro- 3. Stébé B, Ainane A (1989) Ground state energy and optical absorption of exci- chemically carrier-doped single-walled carbon nanotubes. J Am Chem Soc 134: tonic trions in two dimensional semiconductors. Superlattices Microstruct 5: 14461–14466. 545–548. 7. Mouri S, Miyauchi Y, Iwamura M, Matsuda K (2013) Temperature dependence of 4. Kheng K, et al. (1993) Observation of negatively charged excitons X- in semiconductor photoluminescence spectra in hole-doped single-walled carbon nanotubes: Implica- quantum wells. Phys Rev Lett 71:1752–1755. tions of trion localization. Phys Rev B 87:045408.

Bai et al. PNAS Early Edition | 5of6 Downloaded by guest on October 2, 2021 8. Jakubka F, Grimm SB, Zakharko Y, Gannott F, Zaumseil J (2014) Trion electrolumi- 21. Lüer L, et al. (2009) Size and mobility of excitons in (6,5) carbon nanotubes. Nat Phys nescence from semiconducting carbon nanotubes. ACS Nano 8:8477–8486. 5:54–58. 9. Brozena AH, Leeds JD, Zhang Y, Fourkas JT, Wang Y (2014) Controlled defects in 22. Park J, Deria P, Therien MJ (2011) Dynamics and transient absorption spectral sig- semiconducting carbon nanotubes promote efficient generation and luminescence of natures of the single-wall carbon nanotube electronically excited triplet state. JAm trions. ACS Nano 8:4239–4247. Chem Soc 133:17156–17159. 10. Akizuki N, et al. (2014) Nonlinear photoluminescence properties of trions in hole- 23. Korovyanko OJ, Sheng C-X, Vardeny ZV, Dalton AB, Baughman RH (2004) Ultrafast doped single-walled carbon nanotubes. Phys Rev B 89:195432. spectroscopy of excitons in single-walled carbon nanotubes. Phys Rev Lett 92: 11. Santos SM, et al. (2011) All-optical trion generation in single-walled carbon nano- 017403. tubes. Phys Rev Lett 107:187401. 24. Deria P, Olivier J-H, Park J, Therien MJ (2014) Potentiometric, electronic, and transient 12. Nishihara T, Yamada Y, Kanemitsu Y (2012) Dynamics of exciton-hole recombination absorptive spectroscopic properties of oxidized single-walled carbon nanotubes he- in hole-doped single-walled carbon nanotubes. Phys Rev B 86:075449. lically wrapped by ionic, semiconducting polymers in aqueous and organic media. 13. Yuma B, et al. (2013) Biexciton, single carrier, and trion generation dynamics in single- J Am Chem Soc 136:14193–14199. walled carbon nanotubes. Phys Rev B 87:205412. 25. Ma Y-Z, Valkunas L, Dexheimer SL, Bachilo SM, Fleming GR (2005) Femtosecond 14. Nishihara T, Yamada Y, Okano M, Kanemitsu Y (2013) Trion formation and re- spectroscopy of optical excitations in single-walled carbon nanotubes: Evidence for combination dynamics in hole-doped single-walled carbon nanotubes. Appl Phys Lett exciton-exciton annihilation. Phys Rev Lett 94:157402. 103:023101. 26. Deshpande VV, Bockrath M (2008) The one-dimensional Wigner crystal in carbon 15. Koyama T, Shimizu S, Miyata Y, Shinohara H, Nakamura A (2013) Ultrafast formation nanotubes. Nat Phys 4:314–318. and decay dynamics of trions in p-doped single-walled carbon nanotubes. Phys Rev B 27. Newton MD, Sutin N (1984) Electron transfer reactions in condensed phases. Annu 87:165430. Rev Phys Chem 35:437–480. 16. Konabe S, Matsuda K, Okada S (2012) Suppression of exciton-electron scattering in 28. Cognet L, et al. (2007) Stepwise quenching of exciton fluorescence in carbon nano- doped single-walled carbon nanotubes. Phys Rev Lett 109:187403. tubes by single- reactions. Science 316:1465–1468. 17. Mouri S, Matsuda K (2012) Exciton-hole interactions in hole-doped single-walled 29. Kang K, Redner S (1985) Fluctuation-dominated kinetics in diffusion-controlled re- carbon nanotubes evaluated by absorption spectral changes. J Appl Phys 111:094309. actions. Phys Rev A Gen Phys 32:435–447. 18. Deria P, et al. (2013) Single-handed helical wrapping of single-walled carbon nano- 30. Sanvitto D, et al. (2001) Observation of charge transport by negatively charged ex- tubes by chiral, ionic, semiconducting polymers. J Am Chem Soc 135:16220–16234. citons. Science 294:837–839. 19. Khripin CY, Fagan JA, Zheng M (2013) Spontaneous partition of carbon nanotubes in 31. Berciaud S, Cognet L, Lounis B (2008) Luminescence decay and the absorption polymer-modified aqueous phases. J Am Chem Soc 135:6822–6825. cross section of individual single-walled carbon nanotubes. Phys Rev Lett 101: 20. Park J, Deria P, Olivier J-H, Therien MJ (2014) Fluence-dependent singlet exciton dy- 077402. namics in length-sorted chirality-enriched single-walled carbon nanotubes. Nano Lett 32. Manzoni C, et al. (2005) Intersubband exciton relaxation dynamics in single-walled 14:504–511. carbon nanotubes. Phys Rev Lett 94:207401.

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