Population of Exciton-Polaritons via Luminescent sp3 Defects in Single-Walled Carbon Nanotubes.

Semiconducting single-walled carbon nanotubes (SWCNTs) are an interesting material for strong-light matter coupling due to their stable excitons, narrow emission in the near-infrared region, and high charge carrier mobilities. Furthermore, they have emerged as quantum light sources as a result of the controlled introduction of luminescent quantum defects (sp3 defects) with red-shifted transitions that enable single-photon emission. The complex photophysics of SWCNTs and the overall goal of polariton condensation pose the question of how exciton-polaritons are populated and how the process might be optimized. The contributions of possible relaxation processes, i.e., scattering with acoustic phonons, vibrationally assisted scattering, and radiative pumping, are investigated using angle-resolved reflectivity and time-resolved photoluminescence measurements on microcavities with a wide range of detunings. We show that the predominant population mechanism for SWCNT exciton-polaritons in planar microcavities is radiative pumping. Consequently, the limitation of polariton population due to the low photoluminescence quantum yield of nanotubes can be overcome by luminescent sp3 defects. Without changing the polariton branch structure, radiative pumping through these emissive defects leads to an up to 10-fold increase of the polariton population for detunings with a large photon fraction. Thus, the controlled and tunable functionalization of SWCNTs with sp3 defects presents a viable route toward bright and efficient polariton devices.

Exciton–polaritons are part-light, part-matter quasiparticles that form when an exciton interacts strongly with a cavity photon such that the energy exchange between them is faster than the decay of the separate components. They have attracted much attention for their unique properties, e.g., the ability to form nonequilibrium Bose–Einstein condensates (BECs)[1,2] with laser-like light emission[3] and associated quantum optical phenomena.[4] A wide range of emitters has been investigated with regard to polariton formation and condensation. Organic molecules,[5−7] conjugated polymers,[8−10] and fluorescent proteins[11] as well as low-dimensional semiconductors such as monolayered transition metal dichalcogenides[12] and single-walled carbon nanotubes (SWCNTs)[13] have been a special focus over the past decade due to their room-temperature stable excitons and diverse photophysics.

Exciton–polaritons are often created by hybridizing excitons with the fundamental mode of a planar microcavity. Two bright polariton modes, called upper (UP) and lower polariton (LP), are formed as shown schematically in Figure (center), with the energy gap at the exciton–cavity resonance being the Rabi splitting (ℏΩ). The energy difference between the exciton and the lowest cavity energy is termed detuning (Δ). In order to achieve polariton condensation, the polariton ground state, that is the LP branch zero-momentum k∥ state, has to contain a macroscopic population in analogy to BECs.[1] Efficient relaxation of excitations into the LP branch is therefore critical. The relaxation processes can be investigated by injecting polaritons off-resonance via exciting the emitter well above the strongly coupled, lowest excited state. Directly after excitation, an internal conversion into the emitter’s lowest excited state takes place, populating the so-called exciton reservoir.[3] The reservoir states are associated with high-momentum polariton states that can effectively be considered as weakly coupled excitons.[14,15] Theoretical studies on amorphous organic microcavities, which explicitly model the organic emitter on the molecular level, identify the exciton reservoir as polaritonic dark states.[16,17] In both scenarios, the reservoir states inherit the character of the underlying molecular excited state and are therefore long-lived. Ultrafast spectroscopy studies suggest that the reservoir states still undergo photophysical processes of the weakly coupled emitter.[18,19] In this picture, UP and LP represent additional decay channels for the excited state of the emitter. Kinetic considerations can be made to determine the fate of the exciton reservoir states.[20]Figure (center) depicts the three different decay processes of the exciton reservoir that have been proposed as population mechanisms of microcavity exciton–polaritons.[21,22] Polariton population by scattering of reservoir excitons with acoustic phonons in the case of crystalline solids[15] or molecular translational vibrations in case of amorphous solids[23] is one common mechanism (process i). For molecular emitters, the scattering of reservoir excitons with intramolecular vibrations is also possible (vibrationally assisted scattering, VAS) when the Rabi splitting is comparable to the energy of the vibration (process ii).[20,24] If the scattering processes i and ii are slow compared to the radiative rate of the reservoir excitons, radiative pumping can take place, i.e., excitons decay directly into the polariton modes (process iii).[25] Understanding the dominant relaxation processes and hence optimizing the employed materials, cavities, and experimental conditions are crucial to reach polariton condensation and lasing.

Figure 1

Schematic of (6,5) SWCNT energy levels and transitions as well as weakly and strongly coupled states in a microcavity. (Left) Excitonic states in pristine SWCNTs in the weak coupling regime. The main radiative transition is E11 (from the bright E11(B) exciton), followed by weaker, red-shifted transitions (Y1, X1, G1, Ox). E11(K) corresponds to a K-momentum dark exciton. (Center) Energy dispersion of SWCNT exciton–polaritons with upper (UP) and lower (LP) polariton modes (solid lines) in relation to the cavity mode and the dispersionless exciton (dashed lines). Polariton branches might be populated by scattering of the reservoir excitons with acoustic phonons (i), with optical phonons (ii), or by radiative pumping (iii). (Right) Excitonic states and transitions for a functionalized (6,5) SWCNT. New radiative channels (E11* and E11*–) and red-shifted emissions arise from luminescent sp3 defects. Scattering processes involving reservoir excitons of the functionalized SWCNT are omitted for clarity.

Semiconducting single-walled carbon nanotubes (SWCNTs) have recently emerged as a very interesting material to create not only optically but also electrically pumped exciton–polaritons in the near-infrared (nIR).[13,26−30] They combine very high ambipolar charge carrier mobilities with large oscillator strength and narrow excitonic absorption and photoluminescence (PL) bands. In addition, cavities with SWCNTs can exhibit Rabi splittings[13] that are comparable to the energy of their longitudinal optical phonons (e.g., the G+ mode).[31] However, up to now, no polariton condensation could be demonstrated with SWCNTs, and hence, understanding their specific polariton population mechanism with respect to their photophysical properties has become crucial.

The photophysics of SWCNTs are rather complex (see Figure , left) and distinct from both inorganic and organic emitters. The geometric and electronic structure of a carbon nanotube can be derived from a rolled-up sheet of graphene and depends directly on the roll-up vector, i.e., the chirality vector (n,m), which determines the diameter and type of nanotubes (metallic or semiconducting). Here, we will only consider semiconducting SWCNTs and more specifically (6,5) nanotubes (diameter 0.757 nm), which can be sorted from mixed nanotube raw materials by selective polymer-wrapping in large amounts and with high purity.[32] The SWCNT band structure is that of a one-dimensional semiconductor with van Hove singularities that are nearly symmetrical for holes and electrons. The direct bandgap of nanotubes is inversely proportional to their diameter. The optical transitions of SWCNTs are excitonic with large exciton binding energies (200–400 meV).[33,34] They are commonly labeled according to the corresponding van Hove singularities with E11 and E22 and so on. For (6,5) nanotubes, the E22 transition in thin films is about 2.15 eV (576 nm) and the E11 transition is about 1.24 eV (998 nm). Internal relaxation from E22 to E11 occurs in less than one picosecond,[35] and thus, emission is only observed from E11 in the near-infrared. Furthermore, SWCNTs exhibit a valley structure and spin degeneracy leading to 4 singlet and 12 triplet excitons. Only one transition is allowed, and thus, PL from the bright singlet exciton with an odd parity and zero center-of-mass momentum, E11(B), is observable.[36] The dark even-parity singlet and all triplet states are energetically below E11(B), while another dark odd-parity singlet but with a K-point center-of-mass momentum E11(K) is above.

In addition to a strong and narrow E11(B) emission peak, a series of weak, red-shifted peaks are observed in the emission spectrum of (6,5) SWCNTs, which we will refer to as photoluminescence side bands (PSBs) and are shown in Figure (left). The G1 transition results from the decay of E11(B) excitons into the ground state under emission of a G0 phonon,[37] whereas the X1 transition originates from momentum-forbidden E11(K) dark excitons, which can only decay radiatively under emission of a D0 phonon.[37,38] The Y1 transition is believed to be of extrinsic origin and shows tube-to-tube variations.[39] The Ox transition, which we observe for (6,5) SWCNTs under ambient conditions, also shows batch-to-batch variations and might be connected to unintentional luminescent oxygen defects.[40]

The photoluminescence quantum yield (PLQY) of (6,5) SWCNTs in dispersions and thin films is relatively low (<3%), which is partially attributed to the large number of dark excitons but more importantly to quenching of the highly mobile excitons at the nanotube ends and nonradiative defects.[41] However, specific defects (variously named luminescent sp3 defects, organic color centers, or quantum defects)[42] can trap excitons and serve as radiative recombination sites, thus leading to a substantially increased PLQY (2 to 8-fold)[43,44] and also significantly longer fluorescence lifetimes (100–500 ps)[45,46] compared to those of mobile excitons. The deep optical traps (100–200 meV) lead to a strong red shift of the emission and facilitate high-purity single-photon emission at room temperature.[47,48] These defects can be created synthetically by arylation,[43,44] alkylation,[49] or covalent oxygen doping.[47] Depending on the binding configuration, two main types of defects have been identified, commonly named E11* (1.05 eV or 1180 nm) and E11*– (0.95 eV or 1300 nm) for (6,5) nanotubes (see Figure , right).[50−52] Due to the fast diffusive transport of excitons along the nanotubes, only a few luminescent sp3 defects are required to achieve strong emission from them, while their contribution to absorption remains negligible.[44] Hence, they might provide a unique way to improve the polariton population by radiative pumping of the LP branch without perturbing the polariton mode structure or creating additional (e.g., middle) polariton modes, as is usually observed for mixed emitter systems[53] or emitters with pronounced vibronic transitions.[8]

Here, we investigate the contributions of different possible population processes to the overall SWCNT exciton–polariton population in optical microcavities with pristine and sp3 defect functionalized (6,5) SWCNTs. By comparing calculated and experimental fluorescence lifetimes of reference films and microcavities with precisely tailored detunings and LP positions, we show that radiative pumping is the predominant polariton population mechanism and that luminescent sp3 defects increase the polariton population up to 10-fold compared to the pristine SWCNTs.

Results and Discussion

A typical feature of SWCNT exciton–polaritons in planar microcavities is the noticeable change of emission intensity for different detunings,[13,26] which should be linked to the polariton relaxation mechanism. Here, we show this feature for a metal-clad microcavity with strongly coupled (6,5) SWCNTs embedded in a polymer matrix (Figure ). Thermally evaporated top and bottom gold mirrors with different thicknesses provided broadband reflectivity over the whole range of the InGaAs detector (0.82–1.37 eV) with reasonable quality factors of about 23. The inherent thickness gradient of the spin-coated SWCNT/polymer film from 240 to 330 nm enabled the observation and characterization of many different cavity detunings by moving to different positions on the sample. The PL and absorbance spectra of a reference film are given in Figure S1a–c (Supporting Information). By collecting angle-dependent reflectivity and emission spectra from the cavity in TM polarization via Fourier imaging (see the Methods section), we could clearly observe the upper and lower polariton modes close to the exciton absorption, thus confirming strong coupling (Figure a). Fitting the polariton modes (TM polarization) to a coupled oscillator model, as described in the Methods section, gave a Rabi splitting of 100 meV and a detuning of −68 meV.

Figure 2

PL spectra of a metal-clad microcavity containing a (6,5) SWCNT/polymer film. (a) Angle- and spectrally-resolved reflectivity (R) and emission (PL) spectra with marked E11 energy (gray dashed line), UP (dashed yellow line), cavity (dashed black line), and LP (dashed white line); the detuning is indicated as Δ. (b) Angle-integrated PL spectra as a function of sample position (i.e., film thickness). The PL of a (6,5) SWCNT film at several positions without a cavity is shown on the left as reference. (c) Data of (b) color coded for the respective SWCNT sideband transitions (Y1, blue; X1, green; G1, orange; Ox, purple). The PL spectrum of the reference is given as a black dashed line.

Figure b shows the confocally collected PL from the same microcavity as a function of position along the sample and hence film thickness. In this confocal configuration, the polariton emission was integrated over all angles up to 30° (Supporting Information, Figure S2). We attribute emission below the E11 exciton absorption to the lower polariton branch. The PL from different positions of a (6,5) SWCNT reference film without cavity is provided for comparison (Figure b, left). While the emission maximum of the reference remains essentially constant at the transition energy of the exciton (E11, 1.227 eV) with intensity fluctuations of about 35%, the polariton emission exhibits several maxima over the whole detection range with intensity differences of up to 90%. By scanning along the sample, the film thickness and consequently the detuning of the microcavity are changed. The variation of detuning leads to a red-shift of the polariton emission with distinct emission maxima. The occurrence of emission maxima along the LP branch is well-documented for organic exciton–polaritons[5,54−56] and indicative of the underlying population mechanism, e.g., vibrationally assisted scattering (VAS). Figure c reveals that the spectral positions of the observed emission maxima coincide strikingly well with the sideband emission energies of the (6,5) SWCNT PL spectrum, that is, the Y1 (1.205 eV), X1 (1.097 eV), G1 (1.050 eV), and Ox (0.970 eV) sidebands (Figure ). Consequently, these photoluminescence sidebands must play a prominent role in the polariton population of the system. Note that by changing the cavity thickness the transmission at the excitation wavelength also changes, which affects the relative intensities between maxima for different detunings. In this case, it coincides approximately with the emission maximum around X1. We will account for this effect in the population analysis in the last section.

On the basis of the observed emission pattern in Figure b, we can exclude scattering with acoustic phonons (Figure , process i) as the underlying population mechanism. Since the scattering rate depends on the phonon density of states (DOS)[23] and the one-dimensional SWCNT acoustic phonons exhibit characteristic van Hove singularities in their DOS,[57,58] a distinct emission pattern should be visible in the polariton PL, which we did not observe (compare Figure b). Note that even in the case of a constant DOS (as sometimes assumed[21]), the vanishing exciton fraction for larger negative detunings (here >150 meV) renders the population by scattering with acoustic phonons rather inefficient. Consequently, we will only consider vibrationally assisted scattering and radiative pumping (processes ii and iii in Figure ) as possible mechanisms for polariton population in this system.

All photoluminescence sidebands could pump the LP radiatively, whereas only the optically active D and G phonons, which are the origins of the X1 and G1 sidebands, may scatter reservoir excitons directly into the LP. Since only the former mechanism is able to account for all observed maxima, we propose that radiative pumping is the dominant population process. The introduction of luminescent sp3 defects to strongly coupled (6,5) SWCNTs, which should solely pump the polaritons radiatively, is not only a qualitative test and benchmark for this hypothesis (see below) but may also significantly increase the overall polariton population.

Precise control over the detuning of the microcavity is required to explore the impact of detuning and luminescent defects in detail. One of the shortcomings of changing the cavity detuning via the film thickness of the emitter layer, as shown in Figure , is that the number of emitters in the cavity also varies and thus the Rabi splitting. We can overcome this issue by creating cavities with uniform dense (6,5) SWCNT films and metal oxide (AlO) spacer layers with precisely controlled thickness to change the cavity tuning (see the Methods section). With this approach, we can exclude that the observed increase in emission at more negative detunings arises from an increased number of emitters. Lastly, we ensure that the SWCNT layer is always at the electric field maximum of the cavity’s fundamental mode and the number of weakly coupled SWCNTs is reduced. Samples with 10 different oxide thicknesses were prepared to tune the cavity over the whole SWCNT emission spectrum. To compensate for remaining thickness variations of the SWCNT layers, we employed transfer-matrix simulations to predict the LP position for the SWCNT layer thickness of choice, here 80 nm, for each oxide thickness (Supporting Information, Figure S3). By locating the sample positions with the corresponding LP energy, we were able to control the emitter layer thickness beyond the intrinsic accuracy of the employed spin-coating process for all subsequent experiments.

To test the radiative pumping hypothesis, we prepared two identical sets of microcavities: one with pristine SWCNTs (Supporting Information, Figure S4) and one with 4-bromophenyl-functionalized SWCNTs[44] (Supporting Information, Figure S5). The red-shifted emission of the luminescent sp3 defects of the functionalized SWCNTs should exclusively lead to radiative pumping. The functionalization was performed on polymer-sorted (6,5) SWCNTs from the same dispersion batch to exclude processing variations (for a detailed description see the Methods section). The degree of functionalization was adjusted to maximize the total SWCNT PLQY (Supporting Information, Figure S1d) as it decreases again for very high defect densities.[44] Strong light-matter coupling of both the pristine and functionalized SWCNTs with the various microcavities was characterized by angle-resolved reflectivity and PL spectra. Fits and analysis were based on the coupled oscillator model (see the Methods section), and fit results are summarized in the Supporting Information (Figure S6).

We start by comparing the light-matter coupling of pristine and functionalized SWCNTs in precisely tuned microcavities with oxide spacers. Parts a and c of Figure show the angle-resolved reflectivity and PL spectra of microcavities with each type of SWCNTs tuned to the E11 transition. Both samples exhibit splitting into UP and LP modes, which is clear evidence for strong coupling of the E11 exciton to the cavity mode. The Rabi splitting is 128 meV for pristine and 106 meV for functionalized SWCNTs. The lower Rabi splitting of the functionalized SWCNTs is the result of a somewhat lower E11 absorption (Supporting Information, Figure S1c), as the coupling strength scales with the square root of the number of oscillators in the cavity. The cavity emission was studied under nonresonant excitation of the E22 transition. We verified that the excitation scheme was suitable for the pristine and functionalized SWCNT filled cavities, respectively, using photoluminescence excitation maps (Supporting Information, Figure S7). For both pristine and functionalized SWCNTs, we observe PL only from the LP branch. For Δ ≈ 0, the LP emission from the sample with functionalized SWCNTs is about 43% weaker than that of the pristine SWCNT. We attribute this reduction to the lower E11 emission intensity resulting from E11 excitons being funnelled to the sp3 defects.[44] Note that the luminescent sp3 defects themselves are only weakly coupled as their total number is very small and they do not show measurable absorbance in the SWCNT film around their expected absorption band of 1.086 eV (Supporting Information, Figure S1c). Consequently, no splitting at the E11* transition energy is observed in reflectivity and thus no additional polariton branches (Supporting Information, Figure S5).

Figure 3

Strong coupling with pristine and functionalized SWCNTs. (a) Emission and absorption of a pristine (6,5) SWCNT reference film (left) and angle- and spectrally-resolved reflectivity (R) and photoluminescence (PL) of a similar film embedded in a metal-clad microcavity indicating strong coupling. (b) Comparison between angle-resolved PL of two metal-clad cavities with pristine (left) and functionalized SWCNTs (right), tuned to G1 and E11* transitions, respectively. (c) Angle- and spectrally-resolved reflectivity and PL of a microcavity with functionalized SWCNTs as an active layer and emission and absorption of a functionalized (6,5) SWCNTs reference film (right). The cavity structure is given on top of each data set.

We now turn to a detuning value for which the pristine as well as the functionalized SWCNTs exhibit sideband emission that could radiatively pump the polaritons. Figure b depicts the angle-resolved PL of microcavities with pristine and functionalized SWCNTs tuned to the G1 and E11* transitions, respectively. The corresponding angle-resolved reflectivity data together with the full coupled oscillator fit results can be found in the Supporting Information (Figures S4–S6). For Δ ≈ −180 meV, the LP emission from the microcavity with functionalized SWCNTs is three times stronger than the LP emission from the cavity with pristine SWCNTs. We interpret this enhanced intensity and the spectral position of the LP emission of the cavity with functionalized SWCNTs as indicative of radiative pumping by the E11* transition, as it is the only mechanism by which this transition can contribute to the polariton population. Note that we assume that all emission from the polariton mode arises from polariton decay. However, the photonic part of the polaritons is an electromagnetic mode and could also act on weakly coupled states by Purcell enhancement. This possibility will be considered and excluded later (see below).

So far, we have obtained qualitative evidence for radiative pumping (Figure , process iii) of SWCNT exciton–polaritons by introducing luminescent sp3 defects. More direct confirmation of radiative pumping and the exclusion of ordinary Purcell enhancement of the PSBs and sp3 defect emission by the polariton mode can be gained by fluorescence decay measurements using time-correlated single-photon counting (TCSPC). Due to the restrictions of the measurement setup, the emission signal was collected from ±20° around k∥ = 0 (see the Supporting Information, Figure S2). Figure (lower panels) depicts the PL decay transients recorded for microcavities with pristine (a) and functionalized SWCNTs (b). The SWCNT layer thickness was kept at 80 nm for all samples, and the transients are plotted as a function of the LP energy at k∥ = 0 for each cavity. The reference spectra of the corresponding (6,5) SWCNT films are shown in the top panels, and the contributions of the different PSBs and defect transitions to the spectrum are highlighted as components of a multi-Lorentzian fit.

Figure 4

(a) Top panel shows the multi-Lorentzian fit to the PL of a pristine SWCNT film. The center panel depicts the short lifetime component of the cavity fluorescence decay (black circles) as a function of k∥ = 0 emission energy. The k∥ = 0 emissions of the respective cavities (solid lines) are normalized to the detuning with maximum intensity. The short lifetime components of the SWCNT emission bands without cavity (colored squares) are indicated for comparison. Lower panel: fluorescence decay traces of the cavities and instrument response function (IRF). (b) Respective data for functionalized SWCNTs with E11* and E11*– emissions.

All transients, for the microcavities, as well as for the pristine and functionalized reference samples, were well-described by a biexponential decay (for representative histograms and fit results see the Supporting Information, Figures S8 and S9). The short lifetime component of individual, pristine SWCNTs has been attributed to the decay of the E11 population through radiative and nonradiative channels, followed by a slower decay attributed to the redistribution of the exciton population between bright and dark states.[59,60] Depending on the environment of the nanotubes, these lifetimes can be significantly shortened by quenching and even be reduced to a monoexponential decay.[60] Indeed, the transients of the E11 exciton and Y1 sideband are detection limited, and we attribute this fast decay to an increased number of nonradiative decay channels in SWCNT networks compared to individual or freestanding nanotubes. The other PSBs of pristine SWCNTs exhibit values between 8 and 80 ps for the short lifetime component and 100 to 300 ps for the longer lifetime component.

The E11* and E11*– emission dynamics of functionalized (6,5) SWCNTs with sufficiently low sp3 defect densities, as those employed here, can be considered to be decoupled from the E11 exciton dynamics. Here, the short lifetime component is interpreted as the redistribution between trapped bright and dark excitons and the long lifetime component as the subsequent decay through radiative and nonradiative channels.[45,46] We find 60–100 ps for the short and 200–300 ps for the long lifetime components of the functionalized (6,5) nanotubes. For both oxide spacer microcavities with pristine and functionalized SWCNTs, the fluorescence lifetimes are equal or even slightly longer compared to those of the corresponding weakly coupled sidebands (Figure a,b, center panel and the Supporting Information, Figure S9). Such similarities between the fluorescence lifetimes of cavities and weakly coupled references were reported previously[14,61] and interpreted as evidence for radiative pumping by Grant et al.[56]

To understand the measured PL decays and lifetimes better, we considered polariton dynamics as well as the Purcell effect. For a kinetic interpretation of the polariton fluorescence decay, we make the following assumptions. As can be calculated from the polariton line width, the polariton radiative decay in our samples is on the order of a few tens of femtoseconds (Figure ). Hence, we assign the lifetimes observed in the TCSPC experiments as the underlying rate limiting step of the polariton population.[14] Filling of the exciton reservoir should occur very rapidly after excitation at 575 nm (E22) due to ultrafast conversion from the E22 to E11 manifold (<1 ps).[35] Hence, we assume the rate limiting step to be scattering from the exciton reservoir into the polariton states. If the polaritons were radiatively pumped (Figure , process iii), the observed fluorescence lifetime should be approximately equal to that of the underlying emitter, because a radiative decay of a reservoir exciton must occur prior to polariton population. With this notion, we assume that the fraction of weakly coupled radiative decay is not affected significantly by the polaritons or the cavity, an assumption that we will further discuss in connection with the Purcell effect. If vibrationally assisted scattering (VAS) (Figure , process ii) occurred in our system, it should lead to a significant reduction of the observed polariton fluorescence lifetime compared to the decay of the weakly coupled reference considering an estimated scattering rate of 90−500 fs–1 for this process (see the Supporting Information for detailed calculation). In that case, the exciton reservoir would exhibit an additional nonradiative decay channel into the polariton modes and the overall measured fluorescence decay would be shortened substantially.

Figure 5

Comparison of experimental and calculated fluorescence lifetimes: black diamonds, short lifetime component of the cavity fluorescence decay; blue circles, estimated lifetime for phonon assisted scattering (VAS); red triangles, polariton lifetime calculated from the observed LP line widths. Open symbols correspond to data from pristine SWCNTs, and filled symbols to data from functionalized SWCNTs, respectively. Colored large squares (pristine SWCNTs) and circles (functionalized SWCNTs) indicate the short lifetime component of the reference films (no cavity).

Figure shows the experimentally determined short lifetime components of the fluorescence decay of SWCNTs in a microcavity (black diamonds) and the calculated fluorescence lifetimes expected in the VAS limit in the absence of radiative pumping (blue circles). Open symbols represent data for microcavities with pristine SWCNT, and closed symbols represent data for microcavities with functionalized SWCNT. For both the microcavity and reference, we observed a biexponential decay. Within the investigated time frame (10 ns), we can exclude a scenario in which the sub-bandgap states transfer population via a nonradiative mechanism with a rate slower than the radiative decay of the weakly coupled SWCNTs. Such an additional decay channel would still lead to a noticeably faster decay for the microcavity compared to the reference. We can also exclude a scenario in which the LP decays on the same time scale as the fluorescence from the sub-bandgap states, as this would lead to a triexponential decay. Comparing the microcavity lifetimes with the corresponding lifetimes of the pristine and functionalized reference films (X1, G1, Ox, E11*, E11*–, colored squares and circles), we find almost identical values, which indicates the absence of VAS and is clear evidence together with the observed biexponential decay for radiative pumping.

Shahnazaryan et al. hypothesized that the lower polariton may serve as a decay channel for dark excitons in SWCNTs, leading to PL quantum yields approaching unity.[62] An activation of dark excitons of the proposed magnitude should drastically shorten the cavity fluorescence lifetime compared to the fluorescence lifetime of the reference, as the dark states could decay via the short-lived LP branch. In steady state cavity PL, the emission (and population) maximum would be observed at the energy of the lowest dark exciton around 1.19 eV. Experimentally, we do not observe either signature, i.e., drastic shortening of the cavity fluorescence lifetime or an emission maximum at the lowest dark exciton energy. Hence, we conclude that an activation of dark excitons by polaritons in microcavities based on (6,5) SWCNT networks does not occur or at least not to a detectable degree.

So far, we have assumed that the observed emission from the polariton mode only arises from the radiative decay of occupied polariton states. However, the photonic fraction of a polariton is an electromagnetic mode in the classical sense and could enhance a radiative transition, such as a SWCNT PSB, via the Purcell effect. In that case, tuning the LP to either the X1 or E11* transition would result in a 7-fold decrease of the radiative lifetime (see the Supporting Information for detailed calculation and Figures S10 and S11). For a moderate nonradiative decay rate, this should lead to a shortening of the fluorescence lifetime, which we do not observe (see Figure ). In fact, we observe slightly longer lifetimes for the microcavities. Note that, if the accelerated radiative decay was still small compared to the nonradiative decay, no Purcell enhancement would be observed. This result agrees well with the notion that weakly coupled emission within the cavity is reabsorbed by the polariton states. Simply speaking, if the emission leaked directly out of the cavity, e.g., through the transparent part of the polariton mode, the resulting cavity fluorescence decay would be unavoidably shortened in comparison to the reference (Purcell effect). On the basis of this argument, we conclude that the observed LP emission solely arises from occupied polariton states.

For an estimate of the relative contributions of radiative pumping by the different PSBs and the sp3 defects to the polariton population, we analyze the polariton population as a function of detuning. The exciton–polariton population NP is not directly proportional to the PL intensity IP but to IP/α2 because the radiative decay increases with the square of the photon fraction α for a given population.[14]Figure shows the LP population as a function of the LP position, calculated from emission averaged over ±1.5° around k∥ = 0 (see also the Supporting Information, Figure S12) and corrected for the respective photon fraction determined by the coupled oscillator fit to the corresponding reflectivity data (Supporting Information, Figures S4 and S5). To compare populations at different detunings, the data was also corrected for the relative change in excitation efficiency for each cavity structure (Supporting Information, Figures S13 and S14). The uncertainties in Figure arise from averaging over ±1.5° around k∥ = 0 and the excitation efficiency correction (Supporting Information, Figure S14). The error calculation is described in the Supporting Information. The PL spectra of pristine and functionalized SWCNT films are given as references.

Figure 6

Calculated polariton population for SWCNT filled microcavities at k∥ = 0 as a function of the LP position for (a) pristine SWCNTs and (b) for functionalized SWCNTs. The black solid line is a guide for the eye. For the functionalized SWCNTs, the relative change in population compared to the respective pristine sample is indicated in red for an increase and in blue for a decrease. The PL spectra (red shaded areas) of pristine and functionalized SWCNT films are presented for comparison.

The LP populations in both data sets in Figure approximately follow the pristine and functionalized SWCNT emission spectra except for a deviation below 1.0 eV. This resemblance strongly suggests that radiative pumping accounts for the majority of the polariton population for the detectable emission angles. The polariton population at k∥ = 0 of a microcavity with pristine SWCNT is maximized when the LP is tuned to the E11 emission (Figure a). Note that due to the large Rabi splitting of 133 meV this is realized for 85 meV detuning. For the functionalized SWCNTs (Figure b), the population at 85 meV detuning is reduced to approximately one-third of the pristine SWCNTs. This reduction corresponds to the decrease in E11 emission for the functionalized reference films compared to pristine SWCNTs and agrees well with population by radiative pumping. Consequently, the polaritons are most likely populated radiatively for small and positive detunings. However, more reliable evidence would require the temporal resolution of the fluorescence decay of the E11 transition, which was not possible with the available TCSPC setup.

The LP population of the pristine SWCNTs below 1.0 eV increases slightly and does not follow the emission spectrum. This deviation is even more pronounced for functionalized SWCNTs with luminescent sp3 defects (Figure b). The underlying further red-shifted defect states (E11*–) are believed to have a higher PLQY due to their deeper optical trap depth and increased radiative lifetime,[45] which could be a possible explanation. However, this was not directly corroborated by the fluorescence lifetime data obtained here and therefore remains elusive.

For the population ratio between functionalized and pristine SWCNTs (Figure b and the Supporting Information, Figure S15), we find an increase of the polariton population for all detunings at which the LP overlaps with the sp3 defect emission bands. For LPs overlapping with the E11 emission, we find a decrease. This reflects the relative change in the emission spectrum from pristine SWCNT to functionalized SWCNT, as described earlier. For highly emissive polaritons (photon fractions >98%), we find the highest population, which is 5-fold higher compared to the respective pristine sample (∼0.92 eV, Figure ), while the Rabi splitting is only slightly reduced (∼15%–25%). For detunings around 1.0 eV, we even find enhancements of about 10-fold (photon fractions >90%). Additionally, the polariton population depends almost linearly on the E11* defect emission intensity (tuned by different excitation powers), which further corroborates the notion of radiative pumping (Supporting Information, Figure S16).

We conclude that radiative pumping dominates the polariton population of pristine and functionalized SWCNTs. The resulting limitation of the polariton population by the low SWCNT PLQY can be overcome using luminescent sp3 defects. While the total PLQY of functionalized (6,5) nanotubes is at best doubled,[44] the polariton population can be increased up to 10-fold. Furthermore, the defect emission can be spectrally tuned by changing the substituents and their binding patter.[63,64] Thus, radiative pumping of polaritons by synthetic sidebands constitutes a viable route to decouple the polariton population from the exciton fraction of the polariton state and the phonon DOS of the emitter. In contrast to organic molecules with pronounced vibronic progressions, the oscillator strength of the functionalized nanotubes is not distributed over one or more middle polaritons, owing to the low defect absorption. This distinction makes the observed radiative pumping of SWCNT exciton–polaritons by luminescent sp3 defects a unique approach to manipulate and increase the polariton population in a resonant cavity. Further angle-resolved fluorescence lifetime measurements on the femtosecond time scale are required to gain more direct insights into the underlying dynamics.

Conclusion

With this comprehensive study, we have shown that the predominant population mechanism of SWCNT exciton–polaritons is radiative pumping. The polariton fluorescence decay closely resembles the biexponential decay of weakly coupled SWCNT reference samples at various wavelengths, thus excluding vibrationally assisted scattering. The spectral emission shape of both pristine and functionalized SWCNTs can account for the observed polariton population within the investigated range of detunings. The established dominant role of radiative pumping further indicates that polariton population is mainly limited by the low PLQY of SWCNTs. The introduction of luminescent sp3 defects to the SWCNTs increases the PLQY while only slightly reducing the absorption of the fundamental E11 transition and without creating new polariton modes. Hence, microcavities containing functionalized SWCNT exhibit strong coupling with the same polariton branches as those with pristine nanotubes. However, functionalized SWCNTs increase the polariton population at highly emissive detunings (photon fractions >90%) up to 10-fold. Tuning of the defect emission by changing the substituents and the binding pattern could be further employed to decouple the polariton population from its exciton fraction and tune it to relevant wavelengths. Overall, luminescent sp3 defects constitute a viable and versatile approach toward bright and efficient SWCNT-based polariton devices through radiative pumping.

Methods

Selective Dispersion of (6,5) SWCNTs

As described previously,[32] (6,5) SWCNTs were selectively extracted from CoMoCAT raw material (Chasm Advanced Materials, SG65i-L58, 0.38 g L–1) by shear force mixing (Silverson L2/Air, 10 230 rpm, 72 h) and polymer-wrapping with PFO-BPy (American Dye Source, Mw = 40 kg mol–1, 0.5 g L–1) in toluene. Aggregates were removed by centrifugation at 60 000g (Beckman Coulter Avanti J26XP centrifuge) for 2 × 45 min with intermediate supernatant extraction. The resulting dispersion was split into two parts: one for the pristine SWCNT samples and one for sp3 functionalization.

SWCNT Functionalization

Polymer-sorted (6,5) SWCNTs were functionalized with sp3 defects following the previously reported method.[44] Briefly, a toluene solution of 18-crown-6 (99%, Sigma-Aldrich) was added to the as-prepared SWCNT dispersion. Subsequently, a solution of 4-bromobenzenediazonium tetrafluoroborate (96%, Sigma-Aldrich) in acetonitrile was added. The amounts were chosen such that the mixture contained 0.36 mg L–1 (6,5) SWCNT (corresponding to an E11 absorbance of 0.2 for 1 cm path length), 7.6 mmol L–1 18-crown-6, and 0.369 mmol L–1 diazonium salt in an 80:20 vol % toluene/acetonitrile solvent mixture. The reaction mixture was left at room temperature in the dark for 16 h without stirring. Subsequently, the reaction mixture was passed through a PTFE membrane filter (Merck Millipore, JVWP, 0.1 μm pore size) to collect the SWCNTs. The filter cake was washed with acetonitrile and toluene to remove unreacted diazonium salt and excess polymer.

Film Preparation

The as-prepared pristine SWCNT dispersion was passed through a PTFE membrane filter (Merck Millipore, JVWP, 0.1 μm pore size), and the filter cake was washed with toluene. Each SWCNT filter cake, pristine and functionalized, contained about 180 μg of SWCNTs on the basis of absorbance and filtered volume of the respective dispersion. The filter cakes were peeled from the PTFE membrane and transferred into a 5 mL round-bottom flask. They were washed three times with toluene at 80 °C for 15 min to ensure complete removal of free wrapping polymer. Subsequently, 0.8 mL of a 2 g L–1 PFO-BPy solution in toluene was added, and the mixture was sonicated for 1 h. Afterward, 0.2 mL of toluene was added in 50 μL steps, each followed by 15 min of sonication until a homogeneous liquid with a honey-like viscosity was obtained. The final dispersions were spin coated at 2000 rpm on glass substrates (Schott, AF32eco, 300 μm), yielding an average film thickness of about 80 nm with 1.13 wt % SWCNT.

Microcavity Fabrication

Prior to deposition, all substrates were cleaned by ultrasonication in acetone and 2-propanol for 10 min, respectively, and UV ozone treatment (Ossila E511, 10 min). A 100 nm thick Au mirror was thermally evaporated onto polished Si substrates with a 2 nm Cr adhesion layer. Subsequently, an AlO spacer layer of respective thickness was deposited by atomic layer deposition (Ultratech, Savannah S100, precursor trimethylaluminum, Strem Chemicals, Inc.) at a temperature of 80 °C. The SWCNT layer was prepared as described above, and a second AlO spacer was deposited. Thermal evaporation of 40 nm Au as a semireflective top mirror completed the cavity.

Optical Characterization

All absorption spectra were recorded with a Cary 6000i absorption spectrometer (Varian). For angle-resolved reflectivity measurements, a white light source (Ocean Optics, HL-2000-FHSA) was focused onto the sample by an infinity corrected ×100 nIR objective with 0.85 NA (Olympus, LCPLN100XIR). The resulting spot diameter of ∼2 μm defined the investigated area on the sample. For angle-resolved PL measurements, the white light source was replaced with a 640 nm laser diode (Coherent OBIS, 5 mW, continuous wave) and reflected laser light was blocked by a long-pass filter (850 nm cutoff). The reflected/emitted light from the sample was imaged from the back focal plane of the objective onto the entrance slit of a spectrometer (Princeton Instruments IsoPlane SCT 320) using a 4f Fourier imaging system (f1 = 200 mm and f2 = 300 mm). The resulting angle-resolved spectra were recorded by either a 640 × 512 InGaAs array (Princeton Instruments, NIRvana:640ST) or a 1340 × 400 Si CCD camera (Princeton Instruments, PIXIS:400) in case of high-energy UP modes. A linear polarizer was placed in front of the spectrometer to select between TE and TM polarization.

For PL lifetime measurements, the sample was excited by the spectrally filtered output of a picosecond-pulsed supercontinuum laser source (Fianium WhiteLase SC400) focused by the same objective (Olympus, LCPLN100XIR) and imaged confocally onto an Acton SpectraPro SP2358 spectrograph (grating 150 lines mm–1). The scattered laser light was blocked by a dichroic long-pass filter (830 nm cutoff). A liquid nitrogen cooled InGaAs line camera (Princeton Instruments OMA-V) enabled spectral acquisitions to find the desired cavity spectrum. The lifetime measurements were accomplished with a time-correlated single-photon counting scheme. The spectrally selected PL emission was focused onto a gated InGaAs/InP avalanche photodiode (Micro Photon Devices) via a ×20 nIR optimized objective (Mitutoyo). Statistics of the arrival times of the photons were acquired with a time-correlated single-photon counting module (Picoharp 300, Picoquant GmbH). The instrument response function (IRF) was estimated for each sample from the fast, detector-limited PL decay of the (6,5) SWCNTs at the E11 transition at 1015 nm.

Data Analysis and Simulation

To analyze the experimentally obtained angle-resolved reflectivity and photoluminescence data, the coupled oscillator model was applied.[3] The Hamiltonian in the basis of uncoupled oscillators exciton and photon iswhere E is the energy of the E11 excitonic transition and ℏΓ is the half width at half-maximum (HWHM) for the homogeneously broadened line. The energy dispersion of the cavity is given byfor a cavity tuned to E0(θ) = E + Δ, with Δ being the cavity detuning and ℏΓ the HWHM of the cavity mode. The coupling potential VA of the two oscillators is related to the Rabi splitting at E = E by .

With the eigenvalues of the Hamiltonianin the basis of the coupled oscillators |UP⟩ and |LP⟩, the experimental UP and LP dispersion can be fitted. As an initial value for the effective refractive index neff, the geometric mean of the host polymer and spacer refractive indices at 998 nm, was used (2.36 for TE and 2.28 for TM). The photonic (excitonic) fractions α (β) of the new eigenstates (Hopfield coefficients) were calculated by their projection onto the uncoupled cavity and exciton modes, that is, αUP=|⟨UP|C⟩|2 and βUP=|⟨UP|X⟩|2 for UP and likewise for LP. Transfer-matrix simulations were performed as described previously.[13] For the given SWCNT concentration of 1.13 wt %, the sample reflectivity was simulated for different thicknesses (see Figure S3, Supporting Information). With this approach, the desired SWCNT layer thickness on a given sample was found experimentally by matching the lower polariton energetic position to that of the simulation.