Plasmonic Crystals for Strong LightâMatter Coupling in Carbon

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Plasmonic Crystals for Strong Light-Matter Coupling in Carbon Nanotubes Yuriy Zakharko, Arko Graf, and Jana Zaumseil Nano Lett., Just Accepted Manuscript • DOI: 10.1021/acs.nanolett.6b03086 • Publication Date (Web): 23 Sep 2016 Downloaded from http://pubs.acs.org on September 25, 2016

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Plasmonic Crystals for Strong Light-Matter Coupling in Carbon Nanotubes Yuriy Zakharko*, Arko Graf, and Jana Zaumseil* Institute for Physical Chemistry, Universität Heidelberg, D-69120 Heidelberg, Germany

ACS Paragon Plus Environment

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ABSTRACT

Their high oscillator strength and large exciton binding energies make single-walled carbon nanotubes (SWCNTs) highly promising materials for the investigation of strong-light matter interactions in the near-infrared and at room temperature. To explore their full potential, highquality cavities - possibly with nanoscale field localization - are required. Here, we demonstrate the room temperature formation of plasmon-exciton polaritons in monochiral (6,5) SWCNTs coupled to the sub-diffraction nanocavities of a plasmonic crystal created by a periodic gold nanodisk array. The interaction strength is easily tuned by the number of SWCNTs that collectively couple to the plasmonic crystal. Angle- and polarization resolved reflectivity and photoluminescence measurements combined with the coupled-oscillator model confirm strong coupling (coupling strength ~120 meV). The combination of plasmon-exciton polaritons with the exceptional charge transport properties of SWCNTs should enable practical polariton devices at room temperature and at telecommunication wavelengths.

KEYWORDS: plasmon-exciton polaritons, plasmonic crystals, single-walled carbon nanotubes, surface lattice resonances, strong coupling.


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Light-matter interaction is a key aspect of future photonic and optoelectronic devices. Control over the coupling strength between emitters and a cavity allows for the observation of various physical phenomena from spontaneous emission enhancement via the Purcell effect (in the weak coupling regime)1 to Bose-Einstein condensation,2–4 room-temperature electrically-pumped polariton lasing,5 an all-optical polariton transistor6 and non-classical light generation7 in the strong coupling regime. The relation between the average dissipation rate in the system (γ) and the exciton-cavity energy exchange rate - called the Rabi splitting ( Ω) - leads to a transition from the weak (γ> Ω) to the strong (γ< Ω) coupling regime. The Rabi splitting can be controlled by the number of emitters (N) that collectively couple to the cavity, their oscillator strength (f), and the cavity mode volume (Vm) as Ω ∝

f N

Vm

.

For typical Fabry-Pérot cavities the large mode volumes are challenging for applications requiring miniaturization and/or operation on the single emitter level in low-energy optoelectronic devices.8 As an alternative to that, 2D plasmonic crystals supporting hybrid photonic-plasmonic nanocavities have been recently used to investigate and exploit strong lightmatter coupling.9–14 Plasmonic crystals represent a class of structures formed by periodically patterned metallic structures, e.g. nanoparticle or nanohole arrays, and combine the advantages of high quality factors of conventional photonic cavities and the nanoscale field localization of plasmons. The characteristic period of these structures is comparable to the wavelength of the plasmon resonances (e.g. local plasmon resonances, LPRs) that allows the diffractive or waveguide coupling to create surface lattice resonances (SLRs) or quasi-guided modes, respectively. In order to tailor the dissipation rate and field confinement, the photon-plasmon composition of the final modes is varied via the periodicity and size or shape of the metallic nanostructures.15


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With regard to suitable materials, strong light-matter interaction at room temperature requires a large exciton binding energy, and hence is limited to large bandgap inorganic semiconductors, e.g., GaN5,16 and ZnO,17 monolayered MoS218 or MoSe219 or in organic materials with their strongly bound Frenkel excitons.2,3 Recently, we reported that semiconducting single-walled carbon nanotubes (SWCNTs)20 in microcavities also show strong light-matter coupling and thus formation of the exciton-polaritons at room temperature. Their unique optoelectronic properties offer a number of key advantages. First, SWCNTs exhibit a small Stokes shift and narrow excitonic transitions (~20-40 meV),21 which is a result of their large exciton oscillator strength.22,23 Second, the high exciton binding energy (~300 meV)24 and exceptional charge transport properties of SWCNTs25 as well as their chirality-dependent excitonic transition energies26 offer the opportunity for broadly tunable electrically-pumped polariton devices at room temperature. Finally, as narrow-bandgap semiconductors (first excitonic transition: Eex ~ 0.5-1.3 eV) SWCNTs are also attractive candidates for emission in the telecommunication wavelength range and for the investigation of the ultrastrong coupling regime, for which Rabi splitting is comparable to the uncoupled transition energies.27–30 The full potential of ultrastrong coupling is still unexplored, but it is considered to lead to new intriguing phenomena such as quantum vacuum radiation31 and quantum phase transitions.32 The integration of SWCNTs with plasmonic crystals may also present an important step toward the long standing goal of achieving an electrically-pumped carbon-based (plasmon)-exciton polariton laser. It was recently reported that an admixture of the plasmonic component in the compound plasmon-exciton polaritons (PEPs) reduces their effective mass and facilitates room temperature quantum condensation because the critical temperature for condensation is inversely proportional to the effective mass.12,33


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Previously, we demonstrated that in the weak coupling regime semiconducting (6,5) SWCNTs coupled to plasmonic crystals can be turned into broadband tunable emitters by exploiting the Purcell effect1. Here, we explore the evolution of plasmon-exciton interactions in the strong coupling regime by increasing the number of SWCNTs coupled to square lattice plasmonic crystals. Using the coupled-oscillator model we describe experimentally observed angle-dependent reflectivity and photoluminescence (PL) data. We find a coupling strength of up to ~120 meV, which corresponds to light-matter interaction approaching the ultrastrong coupling regime. Thin films of polymer-wrapped (6,5) SWCNTs21 were deposited on plasmonic crystals. The plasmonic crystals were composed of periodic arrays of gold nanodisks (NDs) with square symmetry, a pitch of a=670 nm and a total area of 100×100 µm2. To vary the number of SWCNTs coupling to the nanocavities of our plasmonic crystals, we drop-cast different amounts of a highly concentrated toluene dispersion of polymer-wrapped (6,5) SWCNTs onto the ND arrays. This procedure yielded SWCNTs layers with final thicknesses between 100 and 300 nm (see Supporting Information for details). In order to ensure the homogeneity of the dielectric environment that is required for the far-field coupling of the LPRs,1,34 the SWCNT layers were covered with poly(methyl methacrylate) producing final thickness of the SWCNTs/PMMA layer of 250-350 nm. The final composition of our samples is illustrated in Figure 1a. To verify that even SWCNTs that were located 300 nm away from the NDs efficiently couple to the nanocavities of the ND array and thus will contribute to the expected collective coupling, we simulated the 3D mode profile of the SLRs (at λ=1035 nm) as shown in Figure 1b. Although the field intensity is largest close to the NDs, there are regions with substantial field intensity extending up to 300 nm in the Y-direction. The extended field penetration into the surrounding


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medium is a distinct property of hybrid photonic-plasmonic SLRs compared to purely localized LPRs.35 Figure 1c shows the absorbance spectra of three SWCNTs films with different thicknesses. The spectra are dominated by the E22 and E11 transitions of (6,5) SWCNTs at λ=575 nm and λ=1000 nm, respectively, confirming the presence of mainly a single SWCNT species. The linewidth of the E11 transition is only 48 meV. The E11 absorbance increases superlinearly with the thickness of the SWCNT layer (see Supporting Information Figure S1), indicating a densification of the SWCNT layer during the successive drop-casting process, which is favorable for improving coupling to the nanocavities. The emission of our SWCNT layers is also dominated by the exciton transitions of (6,5) SWCNTs (linewidth γex=47 meV; see photoluminescence-excitation map in Supporting Information Figure S2). The scanning electron micrograph of the electron-beam lithographically fabricated NDs (area 100×100 µm2) in Figure 1d illustrates the square symmetry of the array and shape of NDs (slightly elliptic, with diameter 160-180 nm). The square lattice was selected as it represents one of the simplest cases of a 2D periodic structure facilitating interpretation of the band structure of plasmon-exciton polaritons. The corresponding first Brillouin zone is shown in the inset of Figure 1d, where the three high-symmetry points (Γ, X, M) are indicated. The pitch of the ND array was chosen such that the spectral position of the Γ-point was at approximately λ=1005 nm (λ ≈ surrounding medium refractive index × pitch) and thus at the minimum detuning with the E11 transitions of the (6,5) SWCNTs at 1000-1010 nm. The theoretical dispersion relations of the plasmonic crystal along Γ-М and Γ-Х direction are shown in Figure 1e. The polar angle scale (i.e., sin(θ)) is used for direct correlation with the experimental angle-dependent optical


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response. The dispersion shows that the nanocavity modes are related to the (±1,0) and orthogonal (0,±1) Rayleigh anomalies (RAs). The corresponding relation is given by:36

2n  (k sin( ) cos( )  i  2 ) 2  (k sin( ) sin( )  j  2 ) 2 0 0  a a

(1)

, where k0 is the free space wavevector, n the refractive index in the region surrounding the ND array, and i, j are the RAs orders, e.g. 0,±1,±2, and so forth. The azimuthal angles for the Γ-М and Γ-Х directions are φ=0 and φ=π/4, respectively. As one can see, some modes are degenerate, e.g. (0, ±1) for the Γ-Х direction and the pairs (-1, 0), (0,-1) and (+1,0), (0,+1) for the Γ-М direction. Upon coupling of the LPRs supported by the gold NDs to these diffraction orders the hybrid photonic-plasmonic SLRs appear. The corresponding energy exchange leads to the renormalization of the final nanocavity modes. In order to investigate the band structure of the SLRs, we performed angle-resolved reflectance measurements of a sample without SWCNTs for φ=0 and φ=π/4 (Figure 1f). We used a Fourier imaging configuration where the orientation of the entrance slit of the spectrometer defined the plane of detection and thus the azimuthal angle (see Supporting Information for details). The dispersion extracted from the reflectivity data (i.e. maximum intensity for each angle of detection) was fitted to a coupled-oscillator model (dotted white lines), taking into account the dispersion of the RAs and spectral position of the LPRs along the shorter or longer axis of the NDs (see Methods and Supporting Information Figure S3). For the Γ-point and thus the in-plane wavevector component k||=0 both curves split and form a photonic stop band that indicates coupling between two RAs and lifting of the degeneracy.37,38 We note that for the coupled-oscillator model used to fit SLRs dispersion, we only used data for the lower SLR branch (L-SLRs). No reliable experimental data can be extracted for the upper SLR branch (U-SLRs) due to the Fano-like interaction between broad LPRs and narrow RAs,


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which results in extremely weak reflectivity for the U-SLRs. This also led to the slight discrepancies (~10 nm at Γ-point) in the fitted curves for the Γ-М and Γ-Х directions. On introducing the SWCNTs to these nanocavities the excitons effectively couple to the upper and lower SLRs (U-/L-SLRs) and form upper, middle and lower plasmon-exciton polaritons (U-/M-/L-PEP) as illustrated in Figure 2a. To demonstrate this experimentally, we performed angle-resolved reflectivity and PL measurements on ND array coated with SWCNT layers of different thicknesses (see Supporting Information for details). Additionally, the transverse-electric (TE) or transverse-magnetic (TM) light polarization were selected to discriminate the spectral features as depicted in Figure 2b. Figure 2c and 2d present the angle- and polarization-resolved PL for samples with SWCNT layers of different thicknesses (h=100, 200 and 300 nm) for φ=0 and φ=π/4, respectively (see Supporting Information Figure S4 for the reflectivity data). The common dispersionless spectral feature at λ=1000-1020 nm corresponds to the excitonic emission of the SWCNTs with an increased Stokes shift for thicker layers. This signal corresponds to the share of SWCNTs not coupled to the nanocavities. In order to estimate coupling strength between excitons and SLRs (white dotted lines in Figure 2c and 2d), we extracted PL maxima and fitted those to the eigenvalues of the effective Hamiltonian12:

 E ex  H  VU  SLR V  L  SLR

VU  SLR EU  SLR(θ ) VU-L

V L  SLR   VU-L  E L  SLR( ) 

(2)

, where the diagonal terms Eex, EU-SLR(θ) and EL-SLR(θ) correspond to the uncoupled exciton, the upper and the lower SLRs states, respectively. The off-diagonal terms VU-SLR and VL-SLR represent exciton-SLRs coupling energies and are used as the fitting parameters. In order to allow the fit to converge, we also included an additional coupling term VU-L reflecting interaction


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between U-SLR and L-SLR. Although its value increases for thicker SWCNT films (up to ~80 meV) and thus seems to be affected by the excitons, the mechanism of this coupling is not clear yet as the direct exciton-SLRs coupling is already included as VU-SLR and VL-SLR. The resulting dispersion curves for the M-PEP and L-PEP show a reasonably good fit (Figure 2c, 2d, left and middle, white solid lines). For the sample with the thinnest SWCNT layer (Figure 2c, 2d, left) only the L-PEP branch can be resolved due to the weak far-field response of the U-SLRs as discussed above. The same applies to the reflectivity data (see Supporting Information Figure S4). However, for the thicker SWCNT layers (Figure 2c, 2d, middle and right), the MPEP, which originates from splitting of the U-SLR, is also visible, while the U-PEP remains undetectable. In addition, the TE-polarized M-PEPs at φ=π/4 show an apparent bending behavior for |sin(θ)|>0.4. This data is not taken into account during the fitting procedure, since it originates from the (±1,±1) RAs that are clearly visible in this range of the uncoupled state (indicated with red arrows in Figure 2d). It is also important to note that the U-SLR for TE polarization at φ=0 and TE/TM at φ=π/4 as well as the associated U-PEP and M-PEP at sin(θ)=0 are optically inactive due to the symmetry of the field distribution around the NDs38,39. However, they can be changed from dark to bright by varying the ND shape and pitch of the array10. The same effect also prevents observation of these states in TM polarization for all angles of detection. This behavior has an important implication for lasing because it corresponds to the reduction of radiative losses as highlighted recently.33 We note that our model does not include nontrivial spectral features (indicated with white arrows in Figure 2c, middle and right) for the TE-polarized M-PEP at large angles (that is |sin(θ)|>0.3) and thus these data points were excluded from the fit. These features are more pronounced in a sample with the larger exciton-SLRs detuning, i.e. ND array pitch a=830 nm


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(see Supporting Information Figure S5). As for their origin we have to take into account that this branch-like feature is optically inactive at small angles as is the TE-polarized M-PEP. A closer look also reveals that it is convex (i.e. d2λ/d2k0.1Eex). Although the ultrastrong coupling regime was not reached completely and no new effects were observed, further increase of the coupling strength may reveal interesting phenomena. This could be achieved, for example, via the incorporation of SWCNTs with a larger diameter and thus smaller transition energies or by aligning the carbon nanotubes in one direction41,42 and thus increasing their effective density. The need of a large number of SWCNTs for the observation of collective strong light-matter coupling explains the lack of corresponding effects in previous reports dealing with single SWCNTs or relatively thin films coupled to microcavities.43–47 In summary, we have shown the progressive increase from the weak to the strong and up to the ultrastrong coupling regime between (6,5) SWCNTs and plasmon polaritons supported by a periodic gold nanodisk array. Aside from exploring SWCNTs as a promising material for strong light-matter coupling at room temperature, our hybrid plasmon-exciton polariton structures could be easily integrated in the optoelectronic devices (e.g. light-emitting field-effect transistors)48 and possibly lead to electrically-pumped polariton lasing. The appearance of spatial coherence between emitters (e.g. SWCNTs) coupled to plasmonic crystals10 may potentially enable observation of the plasmonic Dicke effect49 and generation of entanglement between emitters.50 Finally, the development of practical quantum technologies and low-power/energy


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optoelectronic components requires a strong coupling regime at the single emitter-photon level, and thus will take advantage of SWCNTs with their large oscillator strength and high charge carrier mobilities.

ASSOCIATED CONTENT Supporting Information. Sample fabrication, characterization and theoretical analysis. Dependence of the SWCNTs layer absorbance at E11 on the thickness variation, photoluminescence excitation map of SWCNTs layer, local plasmon resonances of elliptical gold nanodisk, angle- and polarization-resolved reflectivity spectra, representative results for a sample with a=830 nm pitch, 3D-FDTD calculation of local field enhancement, summary of all coupling terms indicating transition from weak to ultrastrong coupling regime. This material is available free of charge via the Internet at http://pubs.acs.org.


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AUTHOR INFORMATION Corresponding Author * E-mail: [email protected]. * E-mail: [email protected].

Author Contributions The manuscript was written through contributions of all authors. Y.Z designed the experiments, carried out sample characterization and performed theoretical analysis. A.G. prepared monochiral SWCNTs dispersions, designed and built the angle-resolved optical setup and helped with measurements. J.Z. conceived and supervised the project. All authors have given approval to the final version of the manuscript.

ACKNOWLEDGMENT This research was financially supported by the European Research Council under the European Union's Seventh Framework Programme (FP/2007-2013)/ERC Grant Agreement No. 306298 (EN-LUMINATE). The authors thank Bernd Hähnlein and Jörg Petzold (TU Ilmenau) for help with sample preparation and Malte C. Gather (University of St Andrews) for discussions and advice on angle-resolved measurements.


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Garcia-Vidal, F. J.; Gómez-Rivas, J. arXiv 2016, 1066.06866v1. (34) Auguié, B.; Bendaña, X.; Barnes, W. L.; García de Abajo, F. Phys. Rev. B 2010, 82, 155447. (35)

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Figure 1. (a) Schematic of sample layout consisting of a glass substrate, gold nanodisk array, a layer of random (6,5) SWCNTs and a PMMA film. (b) Field intensity enhancement distribution at λ=1035 nm around a single gold nanodisk (diameter 170 nm) in a periodic array with 670 nm pitch. (c) Absorption spectra of SWCNTs layers with thickness of 100 (black line), 200 (blue) and 300 nm (red). (d) Scanning electron micrograph of a periodic array of gold nanodisks (670 nm pitch and diameter 160−180 nm). The inset shows the Brillouin zone of the plasmonic crystal with a square lattice. (e) Theoretical band structure of the plasmonic crystal with pitch a=670 nm in an environment with refractive index n=1.5. (f) Experimental angle-resolved reflectivity of plasmonic crystal without SWCNTs including fitted dispersion curves of upper and lower surface lattice resonances (U-SLRs/L-SLRs; white lines).


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Figure 2. (a) Schematic illustration of plasmon-exciton polariton creation (U-PEP, M-PEP and L-PEP) via interaction of excitons with surface-lattice resonances (U-SLR and L-SLR). (b) Scheme of detection configuration probing the band structure of the plasmon-exciton polaritons (φ=0 and φ=π/4 for Г-Х and Γ-М, respectively). Angle- and polarization-resolved photoluminescence spectra with increasing thickness of the SWCNTs layer (100, 200 and 300 nm, from left to right) for (c) φ=0 and (d) φ=π/4. Dispersion curves of uncoupled SLRs and exciton states (white dotted lines) were used to fit the experimental maxima in the coupledoscillator model yielding the plasmon-exciton polaritons branches (solid lines). White and red arrows indicate secondary spectral features and (±1,±1) Rayleigh anomalies, respectively.


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Figure 3. Summary of plasmon-exciton polariton dispersion curves (U-/M-/L-PEPs) with experimental data points used for the fits (evenly spaced data was excluded for clarity) for (a) φ=0 and (b) φ=π/4.


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Figure 4. Coupling strength between excitons and upper surface lattice resonance as a function of the square root of the effective absorbance (i.e. taking into account the E11 absorbance and volume-averaged coupling efficiency) for TE (black) and TM (red) polarized light and detection at φ=0 (open symbols) and φ=π/4 (solid). Transition regions of weak-to-strong and strong-toultrastrong coupling regime are indicated with horizontal, dashed lines. Least squares fit to the values are presented with dotted lines. For representation of all coupling strengths see Supporting Information S7.


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Table of Contents Graphic


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Figure 1 170x101mm (300 x 300 DPI)


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Figure 2 170x115mm (300 x 300 DPI)


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Figure 3 170x47mm (300 x 300 DPI)


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Figure 4 85x58mm (300 x 300 DPI)


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