Ultrafast Dynamics of Polariton Cooling and Renormalization in an Organic Single Crystal

Transcription

1 Supporting Information Ultrafast Dynamics of Polariton Cooling and Renormalization in an Organic Single Crystal Microcavity under Non-Resonant Pumping Kenichi Yamashita, Uyen Huynh, Johannes Richter, Lissa Eyre, Felix Deschler, Akshay Rao, Kaname Goto, Takumi Nishimura, Takeshi Yamao, Shu Hotta, Hisao Yanagi, Masaaki Nakayama, and Richard H. Friend 1. Crystal structure of BP1T-CN The crystal structure of vapor-grown BP1T-CN crystal has been studied deeply in Ref. 29. It is in a triclinic form with P-1, a = 3.84, b = 16.15, c = Å, α = , β = 94.27, γ = 90.43, and Z = 2 (CCDC registration code ). Figure S1a shows molecular packing viewed from the direction perpendicular to the (100) plane. The top and bottom surfaces of as-grown crystal correspond to the (001) planes. The tilting angle of long molecular axis against the surface is as small as 22 º. This nearly in-plane molecular polarization causes efficient coupling of the transition dipole moment with the vertical cavity mode. As found in Fig. S1b the molecular axes of two molecules in a unit cell are almost parallel. This molecular packing structure also enhances the coupling strength. The photoluminescence quantum efficiency (PLQE) of this crystal was measured to be ~33 %. The large PLQE is owing to the in-plane polarized molecular packing and high emissivity from the top surface. S1

2 a c b b a c b Figure S1 Molecular packing in platelet-like BP1T-CN crystal. a Packing structure viewed from a direction perpendicular to (100) plane. Horizontal dashed lines schematically indicate the planes of top and bottom surfaces in the as-grown plate-like crystal. b Packing structure viewed from a direction perpendicular to (001) plane. The as-grown BP1T-CN crystal usually has facets of (001), (02-1), and (1-10) planes. 2. Fundamental properties for DBR and BP1T-CN bare crystal The microcavity used in this study is composed of a pair of distributed Bragg reflectors (DBRs), which were fabricated by rf-magnetron sputtering method. Figure S2a shows the transmittance T of bare DBRs deposited on quartz substrates. The reflectivity R corresponds to (1 T). The high reflectivity ranges of R > 98 % are nm ( ev) and nm ( ev) for the bottom and top DBR mirrors, respectively. Steady-state photoluminescence (PL, solid line) and absorption spectra of bare BP1T-CN crystal are shown in Fig. S2b. For the PL measurement a continuous wave laser diode with the wavelength S2

3 PL Intensity (arb. units) Absorbance (arb. units) Transmittance of 405 nm was used. The excitation density was as low as ~10 mw/cm 2. In the absorption spectrum an excitonic absorption feature can be seen at ~2.70 ev, which is the energy edge of singlet exciton state (S 1 ). If we assume that this exciton absorption peak can be approximated by a Lorentzian function, a full-width of half-maximum of ~72 mev. The peak energy (E exc ) agrees well with the fitting result of the polariton energy dispersion (see Sec. 5 in this Supplementary). Note that both the PL and absorption spectra strongly depend on the polarization direction. The data shown here were obtained for the polarization direction parallel to the in-plane transition dipole moment. See Ref. 31 for more information. a 1 Bottom DBR Top DBR 0.5 b 0 E ex Figure S2 Transmittance spectra of bare DBR and optical properties of bare BP1T-CN crystal. a Transmittance spectra of bottom and top DBRs (blue and red lines, respectively). The DBRs were dielectric thin film multilayers deposited on a silica substrate by magnetron sputtering method. b Steady-state PL (black curves) and absorption (red curves) spectra of bare BP1T-CN crystal. The data at the polarization directions parallel and orthogonal to the in-plane molecular orientation are shown by solid and dashed curves, respectively. S3

4 3. Dispersions of group refractive index and phase refractive index Figure S3a shows a PL spectrum of BP1T-CN crystal slab with a thickness d of ~5 μm. In this measurement, the crystal was placed on a bottom DBR and not covered by a top mirror; i.e. it was a half-vcsel structure. Interference fringes caused by the Fabry-Pérot (FP) resonance between the bottom reflector and the top surface reflection were clearly observed. The group refractive index n g as a function of the wavelength λ can be estimated by substituting the mode separation Δλ of the FP resonance peaks into the following equation. n g λ2 2Δλd (S1) Closed circles in Fig. S3b show the n g spectra estimated from (S1). The horizontal axis reveals the energy (E = 2πħc λ). Generally the n g spectrum is represented by the following equation using the phase refractive index n p. n g = n p [1 ( λ n p dn p dλ )] (S2) The n p can be also regarded as the material refractive index and is approximated by the Sellmeier dispersion formula of n p = ε + Aλ2 λ 2 λ 0 2. (S3) Substituting (S3) into (S2), we can obtain a fitting function for the n g obtained experimentally. The fitting result is shown by the dashed curve in Fig. S3b. The fitting parameters of Sellmeier coefficient A, high-frequency dielectric constant ε, and resonant wavelength λ 0 were calculated to be 0.557, 6.57, and 427 nm, respectively. Figure S3c shows an energy dispersion of n p reproduced from (S3) with the obtained fitting parameters. In the next section, we use the estimated n g value at the energy of each LPB modes to obtain the modeled quality factor and the lifetime of cavity photon. S4

5 Phase Index Group Index PL Intensity (arb. units) a 10 b c Figure S3 Refractive index dispersion of BP1T-CN single crystal. a Photoluminescence spectrum of the single crystal on a bottom DBR. Interference fringes caused by the FP resonance can be clearly seen. b Closed circles show group refractive index, which was obtained from the mode separations of FP resonances. Dashed curve shows the fitting result using (S2) and (S3). c Phase refractive index calculated from the fitting result of group refractive index dispersion. 4. Spectral linewidth and polariton lifetimes Polariton lifetimes in the BP1T-CN microcavity can be evaluated from linewidths of steady-state transmission spectra. Figure S4 shows the results of Lorentzian fits of the LPB transmission peaks. Full width of half-maximum (FWHM) is now denoted as ΔE. Then the polariton lifetime τ pol can be written as follows S1. τ pol = ħ ΔE = 1 γ pol (S4) S5

6 Transmittance (arb. units) Here ħ is Planck constant and γ pol is a damping constant of the polariton. Decay times of cavity photon are estimated from the device parameters of microcavity. Using the reflectivities of bottom and top DBRs (R 1 and R 2 ), the group refractive index n g, and cavity length L, decay time of cavity photon, τ ph (= 1 γ ph ), and the quality factor Q of empty cavity can be estimated as follows. Q = ωτ ph = n g ωl c ln(1 R 1 R 2 ) (S5) Here c is velocity of light and ω is the angular frequency. L is a fixed parameter to be 510 nm. γ pol and γ ph satisfy the following relation with a dephasing constant of exciton, γ exc. γ pol = C 2 γ ph + X 2 γ exc (S6) Here C 2 and X 2 show fractions of photonic and excitonic natures, respectively, in a polariton state. These are known as the Hopfield coefficients. From (S6) the exciton decoherence times τ exc (= 1 γ exc ) were estimated for the LBP 2 and LPB 3 modes as summarized in Table S1. This estimation is not good for the LPB 1 mode probably due to the underestimation of the reflectivity for top DBR. As shown in Fig. S2a, the energy of LPB 1 mode (~2.29 ev) is in the vicinity of stop-band edge of the top DBR. Therefore the actual reflectivity at this energy position is very sensitive to the deposition condition. In particular, the reflectance spectrum is possible to be slightly blue-shifted when the reflector has an interface with the organic crystal instead of the air. a b c Peak Position = ev FWHM = mev Peak Position = ev FWHM = mev Peak Position = ev FWHM = mev LPB 1 LPB 2 LPB Figure S4 Lorentzian fits of LPB transmission peaks. Transmission data (open circles) were S6

7 obtained at the incident angle of 0 º. Spectral resolution of the measurement was ~0.1 nm (~0.5 mev). Results of fitting analyses are plotted by red solid lines. The results for a LPB 1, b LPB 2, and c LPB 3 modes are shown. Table S1 Estimation of lifetimes. The group index was obtained from the mode separation of FP resonant peaks (see Sec. 3) and the Hopfield coefficients were obtained from a fitting analysis of polariton energy dispersion using a coupled oscillator model (see Sec. 5). LPB 1 LPB 2 LPB 3 (Experimental) Peak energy (ev) Linewidth (mev) Polariton lifetime (fs) (Model) Reflectivity of bottom mirror Reflectivity of top mirror 0.9 (probably underestimated) Group index Quality factor Photon lifetime (fs) (Estimation) Hopfield coefficient C 2 at θ = 0 º Hopfield coefficient X 2 at θ = 0 º Exciton decoherence time (fs) Coupled oscillator model Coupling between the cavity photon mode and exciton transition dipole moment is often described by the coupled oscillator model using a phenomenological Hamiltonian H shown as follows. H = [ E ph iγ ph V ] (S7) V E exc iγ exc Here V is the coupling parameter between the photon and exciton. The exciton energy E exc is treated as constant because of the large effective mass of the Frenkel exciton. E ph is energy of the S7

8 cavity photon mode, which depends on in-plane wavevector k as shown below. E ph (k ) = ħc n eff ( mπ L )2 + k 2 (S8) m is an integer number corresponding to the cavity mode number. n eff is the effective refractive index, which corresponds to a weighted refractive index in the DBR/BP1T-CN/DBR structure and is determined by the electric field distribution of the cavity photon mode. This equation can be transformed to an expression as a function of observation angle θ ) E ph (θ) = mπħc (1 sin2 θ n eff L n eff (S9) θ is zero at the normal incidence. The energies of polariton modes are obtained by solving an eigenvalue problem for H. As the result the upper and lower polariton energies E ± pol are written as E ± pol = (E ph+e exc ) i(γ ph +γ exc )± [(E ph E exc ) i(γ ph γ exc )] 2 +4V 2 2. (S10) γ ph and γ exc were assumed to be constant for θ. The Rabi splitting energy ħω Rabi at E ph = E exc is then represented as ħω Rabi = 4V 2 (γ ph γ exc ) 2. (S11) We used the experimental results of angular dependent transmission measurement (see Figs. S5a and S5b) for the fitting analysis with the equation (S10). A set of three 2 2 Hamiltonians, which shows just a one-to-one coupling between cavity photon mode and the exciton mode, was considered S2. The results of analysis are summarized in Fig. S5c. The polariton energies agree well with the experimental values. In these analyses the Hopfield coefficients are also given as the eigenvectors of H. Other fitting parameters are summarized in Table S2. The exciton energy E exc also agrees well with the experimental result (see Fig. S2). ħω Rabi was estimated to be ~188 mev. The term of (γ ph γ exc ) is insignificant in this microcavity system, which can be expected from the lifetimes shown in Table S1 as ~10 mev at maximum. Thus we roughly estimated the coupling parameter V to be ~95 mev. S8

9 Hopfield coefficients for LPB Polariton Transmittance (arb. units) a b θ = 54 º θ = 0 º c UPB 1 UPB 2 UPB LPB 2 LPB LPB C 2 X C 2 X X 2 C Angle (degree) Angle (degree) Angle (degree) Figure S5 Angular dependent transmission measurements and analyses using coupled oscillator model. a Transmission spectra depending on incident angle θ and b contour map for the transmission data. The incident light is S-polarized. This polarization direction is parallel to that of S9

10 in-plane transition dipole moment. c Results of the fitting analyses using the coupled oscillator model. Closed circles and dashed curves in the upper figures show energies of polariton modes obtained in the experiment and the analyses, respectively. The lower figures show the Hopfield coefficients for the LPB modes obtained in the analyses. Table S2 Fitting parameters obtained in the analyses with coupled oscillator model. The analyses were performed for respective polariton modes. In these analyses the exciton energy E exc and Rabi splitting energy ħω Rabi were treated as the global parameters. The Hopfield coefficients were also obtained in the analyses, which are shown in Fig. S5 as a function of incident angle. LPB 1 LPB 2 LPB 3 Effective index n eff Exciton energy E exc (ev) Mode number m Rabi splitting energy ħω Rabi (mev) Control experiment: Comparison of dispersion curves between BP1T-CN cavity and passive cavity To make sure the strong coupling formation in the BP1T-CN microcavity, we fabricated a passive cavity sample, in which photopolymer was used as the cavity layer instead of the active crystal. A pair of DBRs was used for the top and bottom reflectors. The photopolymer layer was fabricated by the spin-coating of UV curable resin (PAK-01CL, Toyo Gosei) and the UV exposure (see Fig. S6a). The thickness of cavity was approximately 1 μm. The angular dependent transmission spectrum was performed for the passive cavity sample as shown in Fig. S6b. Four or five cavity photon modes were observed in an energy range of ev. In this range the DBR used has moderate transmittance ( , see dashed curve) to observe the transmitted cavity photon mode. Figure S6c shows the energy dispersions of selected two cavity photon modes (closed circles and triangles). S10

11 Transmission Intensity (arb. units) DBR Transmittance at 0 degree As compared with the BP1T-CN microcavity (open circles), the passive cavity sample showed more sensitive dispersion against the incident angle θ. These dispersions can be represented well by (S9) rather than (S10), and thus they are of as passive cavity without the strong coupling. The dispersion curves of the BP1T-CN microcavity, on the other hand, cannot be accounted for without a strong coupling formation. In addition, n eff estimated to be is much larger than that of the passive cavity (n eff ~ 1.3). From these facts, it is apparent that the BP1T-CN microcavity is in the strong coupling regime. a b 0.4 c DBR Silica plate 0 θ = 22 º Ta 2 O 5 /SiO Photopolymer LPB 3 LPB 2 BP1T-CN microcavity Ta 2 O 5 /SiO 2 LPB 1 Silica plate 2.2 Passive cavity θ = 0 º Passive cavity Angle (degree) Figure S6 Angular dispersion measurement for a passive cavity sample. a A schematic of sample structure of the passive cavity consisting of a photopolymer layer and a pair of DBRs. b Angular dependent transmission spectrum of the passive cavity sample. Each spectrum is shifted vertically for clarity. Dashed curve shows a transmittance spectrum of the DBR used. c Energy dispersions of transmission modes for the passive cavity. Closed circles and triangles show the transmission peak energies of the passive cavity. Solid curves exhibit results of fitting analyses using (S9). The energy dispersions in the BP1T-CN single crystal microcavity are also shown for comparison (open circles). S11

12 7. TRPL results and polariton population dynamics TRPL results shown in Figs. 3 and S7 can be accounted for by a simple rate equation model including a stimulated cooling process. In the mean-field approximation a Gross-Pitaevskii equation with the wavefunction of condensed polariton, Ψ LP, can be written as 3,35 iħ Ψ LP t = { ħ2 2 2m LP + iħ 2 [W(n R) 1 τ LP ] + gn LP + g n R } Ψ LP, (S12) where m LP is the effective mass of lower polariton branch around k ~ 0. n R is the exciton density in the reservoir state. n LP is the polariton density around k ~ 0 and corresponds to Ψ LP (t) 2. W(n R ) is the rate of stimulated cooling from the reservoir state to the polariton energy minimum. Here we assume W(n R ) to be linearly depending on n R as described in Ref. 13. The term of gn LP + g n R represents the blue shift of condensate energy. From (S12) the rate equation for n LP can be derived as dn LP dt = Wn R n LP n LP τ LP + f n R τ R. (S13) Here the additional last term means the spontaneous cooling from the reservoir state with a coupling constant f. τ R is the lifetime of exciton reservoir state. Meanwhile the rate equation for n R can be written as dn R dt = P(t) n R τ R Wn R n LP. (S14) P(t) shows the temporal profile for exciton injection by the pumping pulse, and for the presented case, it can be written by a Gaussian function with the pulse width of 80 fs. The hot excitons generated by the pumping pulse are assumed to relax to the reservoir state quickly. Results of the numerical simulation for n LP are shown in Fig. 3c in the main article and the physical parameters used in the simulation are summarized in Table S3. τ LP of ~130 fs agrees well with that obtained in the steady state measurements (see Table S1). We could reproduce the experimentally observed PL kinetics with the superpositions of the calculated date under the belowand above-threshold condition. W under the below- and above-threshold condition are and cm 3 s -1, respectively. These values are the same order with that reported in a recent S12

13 paper of an organic cavity polariton 13. τ R of ~20 ps might be too short to be the exciton lifetime. But this is also possible because, in this time scale, bimolecular exciton annihilation is the dominant process for this material 29. a θ = 0 o LPB 3 LPB 2 LPB 1 b θ = 10 o c θ = 20 o Figure S7 Contour plots of ultrafast TRPL. The detection angles are a θ = 0 º, b θ = 10 º, and c θ = 20 º. The emission intensities are normalized by the highest values. S13

14 Table S3 Parameters used in numerical simulation of polariton population dynamics. Parameters Values Pumping pulse wavelength (nm) 400 Pumping pulse energy (μj/cm 2 ) 200 Pumping pulse width (fs) 80 Reservoir exciton lifetime τ R (ps) 20 Polariton lifetime τ LP (ps) 0.13 Reservoir to polariton scattering rate W (cm 3 s -1 ) (for below threshold calc.) (for above threshold calc.) Coupling constant f Control experiment: Ultrafast TRPL measurement of BP1T-CN crystal without cavity We performed the ultrafast TRPL measurement also for the bare BP1T-CN crystal without cavity and compared the result with that for the microcavity sample. Figure S8 shows the result for the bare crystal. The pumping wavelength and fluence were 400 nm and ~510 μj/cm 2, which is enough higher than for the measurement condition for the microcavity sample (200 μj/cm 2 ). The time-resolved PL spectrum shown in Fig. S8a is similar to the steady state PL (see Fig. S2b). In early time shown in Fig. S8b, the profile of PL intensity does not show a ultrafast component of ~1 ps that was found in the microcavity sample. As shown in Fig. S8c, the decay profile is expressed by a double-exponential function with time constants of ~50 ps and ~1.4 ns. It was revealed in ref. 29 that the amplified spontaneous emission and normal PL decay for the BP1T-CN single crystal have decay time constants of ~100 and ~900 ps, respectively, and almost agree with the current result. The emission decay of ps is reasonable for the ASE, 36,37 and thus we can conclude that the ultrafast emission component of < ~1 ps observed for the microcavity sample does not originate from the used material but is induced by equipping the cavity. S14

15 PL Intensity (arb. units) PL Intensity (arb. units) PL Intensity (arb. units) a b c Bare Crystal Delay (ps) Delay (ps) Figure S8 Ultrafast TRPL spectroscopy for a bare BP1T-CN crystal without cavity. a Time-resolved PL spectrum. The PL intensity was integrated in a temporal region of ps. b TRPL kinetics in an early time. The PL intensity was spectrally integrated between 490 and 560 nm. c TRPL kinetics in a longer time scale. The red curve shows a double-exponential fitting function with time constants of ~50 ps and ~1.4 ns. 9. TT results and polariton renormalization dynamics Transient transmission (TT) measurement can be performed with an experimental setup for the conventional transient absorption. The TT signal is described in the form of ΔT/T(E), which is defined as ΔT/T(E) = T pump (E) T no pump (E), (S15) T no pump (E) and enables the sensitive detection of the photo-induced change in the transmission signal. Here T pump (E) and T no pump (E) are time-resolved transmission spectra under the optical pumping and without the pumping, respectively. The derivative-like spectral feature of ΔT/T(E) (see Fig. 4a in the main article) means a slight blue-shift of the transmission peak. Examples of the raw data for T pump (E) and T no pump (E) spectra are shown in Fig. S9. One can find that the Lorentzian spectral profiles can approximate the T no pump (E) transmission spectrum. By using a Lorentzian function as the modelled T no pump (E) spectrum in the equation of (S15), therefore, we could S15

16 Transmission (arb. units) reproduce the T pump (E) spectra as a function of the delay time. The peak energy and the full width of half-maximum of the modelled T no pump (E) spectrum are 2.48 ev and 30 mev, respectively. The examples of the reproduced T pump (E) spectra are shown in Fig. 4b in the main article. The intensity is normalised by the maximum value of the T no pump (E) spectrum (T 0 ). Figures S10a and S10b show contour plots of ΔT/T(E) signal for the LPB 2 mode. Figures S10c and S10d show the contour plots for the reproduced T pump (E) signal intensity normalized by T 0 (denoted as T/T 0 for simplicity). The peak energy and peak intensity show drastic changes just after the pumping (< ~1 ps) and then gradually recover to their original positions. Temporal evolutions of the maximum intensity T max T 0 and the shift energy ΔE are summarized in Figs. 4c and 4d. As well as the LPB 2 mode, the LPB 1 mode also showed the similar divertive-like spectral feature as shown in Fig. S11. Although the details of the analyses are not presented here, we have confirmed that the underlying physics is the same. w/o pump w punp, (ps) Figure S9 An example of raw transmission data obtained in TT measurement. Closed and open circles show T no pump (E) and T pump (E) spectra, respectively. S16

17 a b c d Figure S10 Results of TT spectroscopy and the analyses. These are results for the LPB 2 mode. a and b Contour plots of experimentally observed ΔT/T signal shown by long and short time scales. c and d Temporal evolution of transmission amplitude of the LPB 2 mode, T pump (E)/T 0, which were reproduced from the ΔT/T signal. b and d are shown also in the main article as Figs. 4e and 4f. S17

18 T/T T/T a b ev 0.02 LPB 1 LPB (ps) ev Delay (ps) c Figure S11 TT spectroscopy for LPB 1 mode of BP1T-CN microcavity. a Time-resolved ΔT/T spectra. The derivative-like signal is attributed to the shift of transmission peak energy by the optical pumping. b Temporal evolution of the ΔT/T signal amplitude detected at various energies. c Contour plot of the ΔT/T signal for LPB 1 mode. 10. Control experiment: TT measurement of a cavity without strong coupling To make sure the observed ultrafast ΔT/T signal is a real signal from the BP1T-CN microcavity, we performed a control measurement for an empty cavity sample without the strong coupling. The empty cavity had passive matrix (a piece of resin) as the cavity layer and the DBRs which are the same with that used in the BP1T-CN cavity. As shown in Fig. S12a, a defect mode was observed in the transmission spectrum of probe light around 2.3 ev. We measured ΔT/T spectrum for this S18

19 Transmission (arb. units) passive cavity under the pumping fluence of ~220 μj/cm 2, which is higher fluence condition than that in the measurements for BP1T-CN microcavity. However no ΔT/T signal was observed as shown in Fig. S12b. This result makes sure that the ultrafast ΔT/T signal observed in the BP1T-CN microcavity is not a coherent artifact that is occasionally observable in conventional ultrafast measurement. a Empty Cavity b Figure S12 TT spectroscopy for a passive cavity sample as a control experiment. a Transmission spectrum of probe light pulse used for the TT measurements. b Contour plot of ΔT/T result. It was confirmed that no signal was observable for the passive cavity. 11. Control experiment: TT measurement of BP1T-CN crystal without cavity We also performed another control measurement that was TT measurement for a bare BP1T-CN crystal. A slab single crystal with a thickness of ~500 nm was placed on a silica substrate. The measurement was performed with a broad band probe pulse made by the same setup. Other experimental conditions were the same with the case of microcavity sample. As shown in Fig. S13a, a broad photo-induced absorption band was observed. This signal shows the excited state absorption, and the timescale of this signal (~100 ps) is similar to that for the slow component observed in the microcavity sample (compare Fig. S13b and Fig. S10a). This fact ensures that the exciton population results in the slow component. On the other hand, no signal corresponding to the fast component was observed in the bare crystal sample as shown in Fig. S13c. S19

20 T / T Normailzed T / T Normailzed T / T a b c 0 Bare Crystal (ps) ,000 1,000-1, Wavelength (nm) at 600 nm Delay (ps) at 600 nm Delay (ps) Figure S13 TT spectroscopy for a BP1T-CN bare crystal. a TT spectrum of BP1T-CN crystal with a thickness of ~500 nm depending on delay time. b Decay profile of normalized TT signal detected at 600 nm. c The early-time decay profile of TT signal. References in Supplementary S1) Liu, J.-M. Photonics Devices, P (Cambridge University Press, Cambridge, 2005). S2) Richter, S., Michalsky, T., Fricke, L., Sturm, C., Franke, H., Grundmann, M. & Schmidt-Grund R. Maxwell consideration of polaritonic quasi-particle Hamiltonians in multi-level systems. Appl. Phys. Lett. 107, (2015). S20