Introduction

Single-walled carbon nanotubes (SWCNTs) are promising absorbers and emitters for optoelectronic devices, biological imaging, molecular sensing, and quantum photonic applications. 1,2 The optical emission of SWCNTs from the E 11 energy state is dominated by the radiative recombination of excitons featuring a large exciton binding energy up to 400 meV, 3 that makes them particularly promising for room temperature applications. A severe drawback is that the optical quantum yield (QY) from E 11 excitons remains rather low with typical values of 2-7%. [4][5][6] These low QYs are detrimental for optoelectronic device applications since the predominance of non-radiative (NR) optical recombination leads to strongly reduced optical emission rates of nanoscale light sources. One possible way to overcome this issue is to enhance the radiative rate over the NR rate by utilizing the Purcell effect. By coupling the exciton emission of individual SWCNTs to high quality (Q) factor optical modes created in fiber-tip-based dielectric cavities QY = 11% has been demonstrated, 6 and by further reducing the mode volume QY = 40% was achieved. 7 This approach however requires moving external mirrors and works only in a narrow spectral band and is thus not easily scalable to address large numbers of SWCNTs with varying chirality or for on-chip geometries. In contrast, by coupling to plasmonic nanocavity arrays on-chip one can enhance the QY over a broad spectral range covering various SWCNT chiralities with the best values up to QY = 64% in our recent demonstration. 8 Another promising approach is to directly alter the QY of the exciton emission in SWCNTs by utilizing covalent surface functionalization to trap excitons in energetically deep states, thereby avoiding coupling to the environment and possibly to NR recombination channels. By taking advantage of the unique morphology of SWCNTs, a wide variety of approaches to introduce defects and impurities into SWCNTs exist. 9 For example, chemical functionalization with oxygen forms ether and epoxide groups leading to the creation of strongly localized exciton emission located at about 100-300 meV (E 11 *) below the E 11 state. [10][11][12] These oxygen-related localization centers can be created by depositing SiO 2 onto SWCNTs, which has also led to the first observation of photon antibunching at room temperature from the E 11 * exciton emission that approaches the telecom wavelength. 13,14 Other agents for covalent sidewall functionalization such as 4-chlorobenzenediazonium tetrafluoroborate have been shown to lead to photoluminescence (PL) quenching at high concentrations, 15 while more recent work demonstrated that covalently attached aryl groups from aryl diazonium salts introduced at lower concentration levels can form sp 3 defects on the sp 2 lattice that lead to the reported QY of the E 11 * transition of up to 28%, 16 about an order of magnitude higher than the QY of E 11 excitons. Furthermore, previous work showed that the defect-related E 11 * emission is very sensitive to the SWCNT chirality leading to a systematic enhancement of the QY with decreasing nanotube diameter being most pronounced in the 800-1000 nm wavelength band that is covered by (5,4)-(7,5) chirality SWCNTs. 16 A similar trend was recently observed in the temporal dynamics of the exciton emission showing that the narrowest SWCNTs of (5,4) chirality show the longest spontaneous emission times (T 1 ) of up to 600 ps, while for larger (7,5) SWCNTs this can be as fast as 77 ps for the E 11 * excitons. 17 Beyond these initial studies, a better understanding of the relevant interplay between molecular functionalizing groups, a dispersion agent, and the degree of exciton localization is required to optimize the optical and transport properties of functionalized SWCNTs in applications such as light-harvesting photovoltaic devices and quantum light sources. Specifically, single-photon sources ideally require the emission of indistinguishable photons, i.e. long photon coherence times (T 2 ) that are equivalent to ultra-narrow spectral linewidths corresponding to the condition T 2 ∼ 2T 1 . 18 So far, the reported E 11 * emission in oxygen-functionalized SWCNTs has been found to be rather broad, covering several meV even at cryogenic temperatures 13 and emitted photons are thus orders of magnitude away from being indistinguishable. As is well known for the E 11 exciton emission, the spectral PL linewidth is affected by pronounced exciton-phonon dephasing 8,18 as well as by detrimental pump-induced spectral diffusion due to surfactant or substrate interactions. [19][20][21] It was recently shown that the interaction of E 11 excitons with acoustic phonons can be effectively suppressed in polyfluorene (PFO-BPy) wrapped SWCNTs, leading to record-narrow spectral linewidths down to 18 μeV implying transform limited photons. 8 However, values for the E 11 * excitons in 3,5-dichlorobenzene functionalized SWCNTs are still significantly broader, with 270 μeV linewidth. 22 Here, we systematically investigate the low-temperature exciton emission (E 11 and E 11 *) of individual SWCNTs that have been dispersed with sodium-deoxycholate (DOC) and PFO-BPy, are grown by laser vaporization (LV) as well as the CoMoCat technique and are functionalized with either oxygen or 3,5-dichlorobenzene functional groups. We show that the narrowest E 11 * linewidths (35 μeV) are achieved with LV-grown SWCNTs, wrapped with PFO-BPy and functionalized with 3,5dichlorobenzene. Remarkably, we also find that the pump power induced broadening for E 11 * excitons is suppressed 3-fold when compared to the E 11 excitons in the same SWCNTs, indicating that deeper confinement leads to better exciton protection from pump-induced dephasing.

Results and discussion

To study the influence of the dispersant as well as the functional groups we will first focus on the spectral linewidth of the E 11 exciton transition targeting particularly individual SWCNTs with (5,4) and (6,4) chiralities. As illustrated in Fig. 1a, under 1.589 eV (780 nm) laser excitation, excitons are pumped non-resonantly below the E 22 exciton state, where absorption occurs via phonon-sideband transitions. 8,23 The corresponding emission spectra are shown in Fig. 1b, with signatures of the E 11 exciton zero-phonon line (ZPL) at 1.44 eV (860 nm) for (5,4) SWCNTs (top panel) and at 1.39 eV (890 nm) for the (6,4) SWCNTs (bottom panel). The Raman G-mode (D-mode) is visible in all optical spectra at 1.385 eV (1.425 eV). While pristine SWCNTs are dominated by the E 11 exciton emission and do not show any pronounced peaks in the long wavelength regime around 1000 nm, in contrast the spectra of all 3,5-dichlorobenzene-functionalized SWCNTs are dominated by the characteristic E 11 * exciton emission around 1000-1025 nm (1.20-1.24 eV). Note that the spectra in the E 11 regime are magnified six-fold to produce a comparable signal. In addition, the silicon detector quantum efficiency is more than five-fold lower at 1020 nm (8%) compared to 890 nm (45%), resulting in a relative zero-phonon line (ZPL) intensity ratio E 11 */E 11 of 34. This strong suppression of the E 11 exciton transition on the sidewall-functionalized SWCNTs clearly indicates that optically pumped excitons relax quickly into the lower lying E 11 * defect states before radiative recombination can occur through the E 11 channel. This is consistent with the picture that has been developed where defect state population occurs by diffusive trapping of the band-edge E 11 exciton. 17,24 Fig. 1c demonstrates emission from 10 individual SWCNTs that are dominated by one spectrally-sharp E 11 * exciton emission peak, accompanied in some cases by 12 additional emission lines with significantly weaker intensity. We have recently shown that the aryl defect sites in 3,5-dichlorobenzene-functionalized SWCNTs can give rise to an exciton manifold with 6 spectrally distinct transitions that occur over a wide wavelength range of 300 nm resulting from topological variations in the chemical binding configuration of the monovalent aryl groups. 22 The highest lying energy defect state is in the ortho L 90 configuration 22 that we attribute here to the origin of the E 11 * emission. While lower lying states in other configurations might be present, they are naturally excluded in our study since they are not spectrally observable with the silicon detector in our study.

Fig. 2a illustrates the effect of pump-induced broadening of the ZPL in the case of the E 11 exciton emission of an LV-grown SWCNT dispersed with PFO-BPy. Spectra recorded at the lowest pump powers display only a single ZPL transition while at higher pump powers (0.6-4 mW) additional energetically broad shoulders appear on the low-energy side. We have recently shown that side peaks can originate from phonon confinement effects and are particularly pronounced at an elevated pump power or temperature. 18,22,25 Here, we focused our study on the ZPL lineshape and carried out simple Lorentzian lineshape fits that ignore the additional phonon wings. The extracted Lorentzian linewidth values of the ZPL are plotted in Fig. 2b andc as a function of pump power comparing two surfactants (DOC and PFO) as well as two functional groups (oxygen and 3,5-dichlorobenzene). Exemplary pump power traces are shown in each case for two different SWCNTs. Most striking is that oxygen doping leads to a significantly broader ZPL compared to aryl sidewall functionalization, particularly at the highest pump powers. In the case of oxygen doping and DOC dispersant, the ZPL remains broad with 5-10 meV linewidth even at the lowest pump powers (Fig. 2b,top). In contrast, PFO-BPy-wrapped SWCNTs appear to be significantly better protected from pump-induced exciton dephasing and pump-induced spectral diffusion effects, displaying a sub-meV linewidth at a low pump power, which is in line with the previous reports on pristine SWCNTs. 8,18,25 However, under strong pumping oxygen-functionalized SWCNTs reach back to a 5 meV linewidth even when protected by PFO-BPy, indicating that the doping procedure induces a significant amount of mobile charges in the exciton vicinity that can give rise to pump-induced spectral diffusion broadening. This is consistent with density functional theory modelling and the contrasting blinking behavior observed for oxygen vs. aryl functionalization. 24 In contrast to the case of oxygen, the SWCNTs functionalized with 3,5-dichlorobenzene always display narrow linewidth values that are largely independent of the dispersant and remain spectrally narrow even under the highest pump powers with values of 0.3-0.8 meV (Fig. 2c).

The growth technique of the SWCNT host crystal plays an additional role in the achievable exciton linewidth. To this end, we compare in Fig. 3 SWCNTs that are commercially avail-able as CoMoCAT SWCNTs with those that have been grown via laser-vaporization (LV). For this comparison, both sets of SWCNTs were dispersed with PFO-BPy and underwent the same sidewall functionalization procedure with 3,5-dichlorobenzene (see methods). The result is a striking difference in the ZPL linewidth of the E 11 * exciton emission, showing that CoMoCAT SWCNTs typically do not reach the sub-meV regime at low pump powers and remain about 5-6 times broader compared to the LV-grown SWCNTs. We note that while this comparison was carried out under slightly different sonication conditions no straightforward evidence shows that this would cause a six-fold variation in the exciton linewidth. There is rather more evidence that the difference is caused by the growth technique since our findings are similar to the reports for the E 11 emission in pristine SWCNTs with high crystalline quality for LV growth. 26 Apparently, if the goal is to realize spectrally narrow exciton emission with near intrinsic properties the best combination is to utilize LV growth, PFO-BPy wrapping, and 3,5-dichlorobenzene functionalization.

With SWCNT samples prepared in this way, we now turn to a systematic study that compares the E 11 exciton linewidth with the E 11 * exciton linewidth in the same SWCNT. The key question is if the strong localization of the exciton in the vicinity of the 3,5-dichlorobenzene group leads to significantly better protection of E 11 * against environmental dephasing compared to the energetically shallower disorder localization of the E 11 exciton. 13 To answer this question more systematically and to enable the recording of optical spectra at the lowest excitation powers, we have embedded the functionalized SWCNTs into metallo-dielectric antenna (MDA) arrays. As we have shown recently in the case of pristine SWCNTs, light collection efficiencies (LCE) up to 92% for the E 11 emission at 890 nm can be achieved by coupling the exciton emission to an MDA. 25 Following the three-layer design rule n 1 < n 2 < n 3 introduced by Lee et al., 27 we have assembled here the arrays of MDA with embedded functionalized SWCNTs as shown schematically in Fig. 4a andb. The patterned air gaps (n 1 =1 ) on the top of a metal mirror (Ag) are created by capping with a polystyrene (PS) layer (n 2 = 1.56) utilizing a polymer-releasetransfer technique that is similar to the assembly of monolayer heterostructures. 28 With the PS layer in place, which also protects the air gaps from filling with solvents, SWCNTs were drop cast and subsequently functionalized (see methods), followed by a second layer of PS and capping with a 300 µm commercial sapphire substrate (n 3 = 1.76). Fig. 4c shows an optical image of the fully assembled MDA stack featuring an array of square-shaped MDA cavities with 3 μm side length. Note that while the use of a 300 µm thick sapphire substrate will substantially broaden the far-field emission profiles (Fig. 4d), the achievable LCE when collected with a high numerical aperture (NA = 0.81, collection angle ±54°) microscope objective degrades only slightly at 1000 nm from 85% for 200 nm sapphire thickness to 80% at 300 µm thickness (Fig. 4e). As a result, embedding SWCNTs into the MDA allows for a six-fold enhanced LCE compared to a bare dipole emitter on a substrate (14%, the dashed line in Fig. 4e). An exemplary emission spectrum recorded at a pump power of 361 μW for the E 11 * exciton transition of an LV-grown, PFO-BPy wrapped, and 3,5-dichlorobenzene functionalized SWCNT located inside the MDA cavity is shown in Fig. 5a together with a single Lorentzian fit that yields a linewidth of 172 μeV. The Lorentzian exciton linewidth values of the ZPL are shown in Fig. 5b as a function of excitation power. Initially the linewidth increases sublinearly until saturation sets in at higher pump powers (Fig. 5b). The narrowest linewidth the doping-induced E 11 * approaches at the lowest pump power is found from Voigt deconvolution to be 35 µeV, which is significantly narrower compared to the previously observed linewidth values of about 270 µeV in 3,5-dichlorobenzene functionalized SWCNTs. 22 This is a combined result of the six-fold enhanced LCE provided by the MDA that allows recording exciton spectra down to lower pump power limits as well as the use of the LV-grown material (Fig. 3), compared to the CoMoCAT material in ref. 22.

Given that the ZPL stays well-defined with sub-1 meV values even at the highest pump powers one can exclude temperatureinduced linewidth broadening effects by the incident laser power. A significantly increased SWCNT temperature would lead to thermal break-up of the fragile phonon confinement, with their characteristic confinement energy of about 2 meV that gives rise to a drastic linewidth broadening of up to 10 meV at temperatures above about 80 K or under laser- induced plasmonic heating. 8 Likewise, we exclude excitonexciton scattering as a cause of linewidth broadening that is often observed in 1D excitons, 29 since the observation of strong photon anti-bunching in our previous work 8,13,14 indicates that the number of excitons in these localized systems at cryogenic temperatures is well below 2. In contrast, the fact that the exciton ZPL remains Lorentzian even up to the highest pump powers (Fig. 5a) implies a homogeneous dephasing process, such as random telegraph noise caused by fluctuating charges in the exciton vicinity, as is known for excitons in quantum dots. 30,31 In this model, one assumes that the laser pumps charges out of trap states with a concentration N that reside in the vicinity of the exciton and cause rapid quantum-confined Stark-shifts onto the Lorentzian exciton spectrum, i.e. al i n ewidth broadening in time-integrated spectra. Based on Monte-Carlo simulations of the trapping and detrapping of single charges, it is predicted that the additional linewidth broadening Γ SD due to pump-induced charge fluctuations follows as

. Since N is linearly proportional to pump power P it follows that Γ SD ffiffiffi P p , i.e. the pump-induced linewidth broadening follows a slope exponent of 0.5. 30,31 The black solid-line in Fig. 5b plots the total linewidth

for one case, where the constant Γ 0 is the residual linewidth (35 μeV) and α is a fit parameter, providing striking agreement between the experimental linewidth data and theoretical predictions of the charge-trap model. The linewidth slope is also in agreement with the comparable results for the E 11 excitons of pristine SWCNTs in our previous work. 8 It is furthermore expected that the degree of linewidth broadening should depend on the degree of 0D exciton localization, i.e. excitons localized into energetically deeper states are better screened from pump-induced charge fluctuations. To this end, we point out that our functionalized SWCNTs display emission from both E 11 excitons localized by random (energetically shallow) potential fluctuations with single-photon anti-bunching typically vanishing above 100 K, as well as emission from the energetically deeper (ΔE ∼ 200 meV) localized E 11 *e x c i t o n s bound to the location of 3,5-dichlorobenzene that displays antibunching up to room temperature. This allows a clear comparison of linewidth values for 0D excitons with a strongly varying confinement energy within the same SWCNT. The top panel in Fig. 5b shows the resulting ZPL linewidth ratio between E 11 and E 11 *, which indicates that at each pump power the resulting linewidth of the defect-localized exciton is three-fold narrower compared to E 11 excitons. This signature clearly indicates a reduced environment interaction and susceptibility to pumpinduced dephasing for the deeper localized exciton states.

In the trap-state model, the three-fold reduced exciton linewidth corresponds to an effective reduction of the charge trap concentration N by a factor of 9 (N ∼ Γ 2 ) that is interacting with the E 11 * excitons compared to the E 11 excitons. While the exact energy structure of these trap states is unknown, it is plausible to assume that E 11 * excitons are effectively more detuned from the trap states and thus are less affected by the pump-induced Stark-shifts. At the microscopic level, the concept of exciton emission oscillator strength f provides additional insights. It is known from time-dependent density functional theory calculations that f for aryl-functionalized SWCNT excitons is systematically smaller than f for pristine SWCNT excitons. For example, the ortho L 90 configuration of the sidewall-attached aryl amounts to f = 9, while in contrast the pristine E 11 exciton has an oscillator strength of f = 34, or approximately f =3-4 per nm length of carbon nanotubes. 32 In the case of the cryogenic spectroscopy of pristine SWCNTs, typical E 11 localization in random potential fluctuations is reported on the length scale of 3-5 nm, 18,[33][34][35] resulting in a range for the exciton oscillator strength of f =9 -20. The systematically larger oscillator strength of E 11 excitons leads directly to a stronger Stark-interaction between the exciton dipole and the electric fields of the charge fluctuations, and thus a broader ZPL. While a detailed theoretical model is beyond the scope of this work, our experimental findings provide a clear path to create quantum light emission from functionalized SWCNTs with a superior spectral linewidth.

Experimental

Carbon nanotube synthesis

CoMoCat SG65i SWCNTs were purchased from Southwest Nanotechnologies. Samples are produced by the CoMoCAT™ synthesis process and the commercial supplier reports an average diameter of 0.78 nm and a content of (6,5) chirality that is larger than 40%. The laser vaporization (LV)-grown SWCNTs for this study were produced in the LV process 36 at a furnace temperature of 800 °C, and all syntheses were run at a power density of ∼100 W cm -2 (λ = 1064 nm, Nd:YAG). Such samples contain a broad distribution of small-diameter SWCNTs (0.6 < d < 1.2 nm), with significant amounts of (5,4) and (6,4) nanotubes.

Carbon nanotube dispersion

Surfactant dispersion. LV-grown SWCNTs were dispersed in a 1.04% (m/v) sodium deoxycholate (DOC) solution in nanopure H 2 O at a nanotube concentration of 1 mg mL -1 , base sonication for 1 hour with a tip sonicator of 1/4″ at a power output of 0.9 W mL -1 (Sonic Vibra cell with tip CV18-9909, 8 W) while being immersed in an ice bath. (6,5) chirality nanotubes were then sorted out by the aqueous two-phase extraction method. 37 Polymer dispersion. In the case of the CoMoCAT material (data in Fig. 3), 20 mg of PFO-bpy was dissolved in 10 mL of toluene, after which 10 mg of CoMoCAT SG65i SWCNTs was placed into the poly[(9,9-dioctylfluorenyl-2,7-diyl)-alt-co-(6,60-{2,20-bipyridine})] (PFO-bpy) solution. These mixtures were bath-sonicated for 1 hour with no cooling, after which the samples were immediately centrifuged at 30 000g (Beckman ultracentrifuge using a SW32Ti rotor) in thin polyallomer centrifuge tubes for 5 min at 20 °C. In the case of the LV-grown material, 1 mg mL -1 of raw LV soot was mixed into a solution of 2 mg mL -1 of PFO-BPy in toluene. This solution was then sonicated with a 1/2 in. probe tip for 30 min at 40% power (Cole-Parmer CPX 750) in a bath of cool (18 °C) flowing water for heat dissipation. After sonication, solutions were centrifuged at 30 000g for 5 min (Beckman ultracentrifuge using a SW32-Ti rotor). For cavity-integration, PFO-BPy dispersed LVgrown SWCNTs in toluene were deposited directly onto the MDA arrays followed by 105 °C baking on a hot plate for 3 hours.

Surface functionalization

Surface functionalization was carried out in a dip-doping process. To this end, the substrate containing dried out LVgrown SWCNTs, either with DOC or PFO-BPy wrapping as a dispersant, has been immersed in an aqueous solution of 3,5dichlorobenzene diazonium (0.7 mg mL -1 in nano-pure water) or, alternatively, exposed to a droplet of the same solution for 3-5 minutes. The doping process is stopped by putting the substrate into 1% (w/v) DOC for another 3 minutes. The substrate containing functionalized SWCNTs is then dried in air before optical measurement. To prevent substrate-induced spectral diffusion, we have coated the Si/SiO 2 carrier substrates with a 2 nm thin layer of Al 2 O 3 following our previous work. 8 In addition, we have also carried out oxygen doping using LVgrown SWCNTs by over-coating with a 10 nm electron-beamdeposited SiO 2 layer. 38 The deposition rate was 0.2 nm s -1 using a 99.99% pure SiO 2 target (CERAC). The base pressure of the chamber was 2.8 × 10 -8 torr and the substrate was maintained at room temperature.

Photoluminescence spectroscopy

Micro-photoluminescence (μ-PL) measurements were performed inside a closed-cycle cryostat with a 3.8 K base temperature and ultralow vibration (attodry1100) at a pressure of 10 -6 bar. A red laser diode, emitting at 780 nm in continuous wave mode, was used for excitation. A laser spot size of about 0.85 microns was achieved using a cryogenic microscope objective with a numerical aperture of 0.82. The relative position between the sample and laser spot was adjusted with cryogenic piezo-electric xyz-positioners. Spectral emission from the sample was collected in a multimode fiber, dispersed using a 0.75 m focal length spectrometer, and imaged with a liquid nitrogen cooled silicon CCD camera.

Conclusions

We have shown that the E 11 excitons in oxygen-functionalized SWCNTs remain rather broad with up to 10 meV linewidth at high pump powers (5 mW), while, in contrast, the spectral linewidth in 3,5-dichlorobenzene functionalized SWCNTs is found to be about one order of magnitude narrower. In all cases, wrapping with PFO-BPy provides significantly better protection against pump induced dephasing compared to DOC. To study the influence of exciton localization on pumpinduced dephasing we have further embedded the functionalized SWCNTs into an MDA cavity to enhance light extraction. Our dataset demonstrates that the strong localization of 0D excitons attributed to the E 11 * emission of 3,5-dichlorobenzene quantum defects is significantly better at protecting against environmental dephasing, leading to a 3-fold suppression of pump-induced broadening compared to the E 11 excitons in the same SWCNT. Even at the highest pump powers the E 11 * emission can be as narrow as 110 µeV (∼175 µeV on average), which is promising towards efficient single-photon sources that maintain their coherent properties despite significant charge fluctuations in the device.