Supporting information for: Strong exciton-photon coupling with colloidal. nanoplatelets in an open microcavity

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1 Supporting information for: Strong exciton-photon coupling with colloidal nanoplatelets in an open microcavity Lucas C. Flatten,, Sotirios Christodoulou,, Robin K. Patel, Alexander Buccheri, David M. Coles, Benjamin P. L. Reid, Robert A. Taylor, Iwan Moreels, and Jason M. Smith, Department of Materials, University of Oxford, Oxford OX1 3PH, United Kingdom Nanochemistry Department, Istituto Italiano di Tecnologia, Via Morego 30, IT Genova, Italy Department of Physics, Clarendon Laboratory, University of Oxford, OX1 3PU, UK Department of Physics, University of Genoa, Via Dodecaneso 33, IT Genova, Italy Fax: +44 (0) Materials Synthesis of CdSe nanoplatelets emitting around 515 nm: In a three-neck round bottom flask 170 mg of Cadmium Myristate, 24 mg of Selenium powder (99.999%) and 15 ml Octadecene (ODE) were introduced and degassed under vacuum for 30 min at 120 C. Then the temperature was raised gradually up to 240 C under Argon flow. When the solution turns orange (around 210 C) 90 mg of Cadmium Acetate were swiftly added to the reaction. After 10 min of the reaction time the heating mantle was removed and 2.5 ml of Oleic Acid were S1

2 injected. When the solution had cooled down to 80 C 15 ml of Hexane were added. The CdSe nanoplatelets were then separated by selective precipitation. Figure 1a shows a TEM micrograph of dispersed platelets. While platelets towards the edges of the agglomeration tend to lay flat on the substrate, other platelets are stacked and lay sideways. The platelets have an average length of L x = 32.5 ± 2.5 nm, a width of L y = 8.2 ± 0.9 nm and a thickness of L z = 1.36 nm, obtained by taking the inter-plane distance along the 100 direction (13.6 Å) and 4.5ML of CdSe. Fig. 1b shows the photoluminescence and absorbance lineshape of the platelets. Methods The substrate for both sides of the cavity is fused silica. On one side the material is removed with a dicer to form a free standing plinth (Fig. 1f in main text). The plinth and the plain substrate are then coated with a semi-transparent 50 nm silver layer via thermal evaporation. Now the nanoplatelets are dispersed on the main mirror by dropcasting. In the process of drying residual oleic acid acting as a passivating ligand helps in creating a homogeneous film (see Fig. 1d-e in main text). To form a tunable microcavity the two mirrors are mounted opposite each other, one on a Thorlabs kinematic mount, the other onto a ring piezo-actuator. The mirrors are then brought close to each other ( 10 µm) and made parallel with the help of fabry-perot fringes visible in a transmission experiment with a light emitting diode. The angular detuning after this procedure is less than 400 µrad. The piezo-actuator allows for a length tunability of 16 µm and is driven by a Keithley Optical access to the sample is given by a standard 10 ojective lens and the collected light is focused on an Andor combined spectrograph/ccd with a 300 grooves/mm grating. For the photoluminescence experiment the sample is excited with a continuous wave GaN diode laser with λ = 405 nm at power densities around ρ exc = 1000 W cm 2. S2

3 Elementary analysis in CdSe NPL The concentration of the CdSe NPL has been determined with inductively coupled plasma optical emission spectrometry (ICP-OES). Two measurements of the same sample has been performed and the average has been used to determine the concentration of the CdSe NPL. The results can be summarized in the following table : Table S1: Results of inductively coupled plasma optical emission spectrometry (ICP-OES) analysis of CdSe nanoplatelet solution. Element Avg Stddev %RSD Cd ppm Se ppm Cd ppm Se ppm Cd ppm Se ppm The concentration of the CdSe NPL has been determined using the Selenium atoms because the solution has an excess of cadmium oleate. Additional cavity spectra To give a more comprehensive overview of the open cavity system and the obtained spectra, we include several additional figures which we present in this chapter. Fig. S1 shows transmission spectra corresponding to vertical slices through Fig. 2a for different cavity lengths, demonstrating the avoided level crossing about the hh (Fig. S1a) and lh exciton energy (Fig. S1b). The latter one is not fully resolved, as the exciton and cavity linewidth exceed the Rabi splitting slightly (see values in main text.) We have fitted each peak with a sum of two Lorentzian lineshapes and plotted the central position and linewidth for the hh anticrossing in Fig. S2a. For reference to the previously presented raw transmission data in Fig. 2, we have superposed the same theoretical polariton dispersion on this dataset, to show the agreement. The polariton properties are given by a S3

4 Figure S1: a) Cavity transmission spectra for decreasing cavity length from bottom to top, corresponding to vertical slices through the data presented in Fig. 2 in the main text. Each spectrum is fitted with two superposed Lorentzian lineshapes to obtain the position and the linewdith of the polariton states. A clear anticrossing about the heavy hole exciton energy can be observed. b) Equivalent data for the light hole exciton transition, demonstrating that the splitting is not fully resolvable given the linewidths of exciton and cavity mode. weighted average of the properties of its constituents, ie. the polariton linewidth is the sum of the excitonic linewidth times the excitonic coefficient (β 2, γ 2 in main text) and photonic linewidth multiplied by α 2 (Γ pol = Γ exc β 2 +Γ cav α 2 ). The cavity mode linewidth for the silver cavity we have used is Γ cav 35 mev at an energy of 2.23 ev (see Fig. S2b) and broadens as the reflectivity of silver decreases for higher energies. S4

5 Figure S2: a) Polariton dispersion about the heavy hole exciton energy as obtained by the fits shown in Fig. S1. The vertical extent of the shaded area around the datapoints corresponds to the fitted linewidth of the Lorentzian lineshape. b) Transmission spectrum at a cavity length L = 1.66 µm, where the cavity mode energy is far from both exciton energies. The fit shows a HWHM of Γ = 35 mev, corresponding to a cavity Q-factor of Q = 64. Figure S3: The cavity linewidth as a function of the cavity length for longitudinal mode number q = 6 (yellow continuous line). The blue dashed line shows the dependence on the silver mirror reflectivity only, the red dashed dotted line the effect of the mirror separation. S5

6 The linewidth of a cavity mode composed of two mirrors with reflectivity R and separation L is given by: S1 Γcav = 1 R R 1 n c L (1) Here n c is the effective refractive index within the cavity. With the wavelength dependent refractive index of silver taken from S2 and the mode energy dependence on the cavity length E cav = qhc 2L we can plot Γ cav as a function of the cavity length for the longitudinal mode index q = 6 (see Fig. S3). The graph shows the steep increase in cavity linewidth for cavity lengths below 1.3 µm and demonstrates that the above reported linewidth is compatible with the theory. The reason for the poor resolution of the lh coupling is thus a combination of the reduced reflectivity of the silver mirror for the energy above 2.5 ev and a weaker oscillator strength and broader linewidth of the lh exciton in comparison with the hh exciton. Reasons for this are additional relaxation paths from lh to the lower energy hh-exciton (comp. with S3 Suppl. Materials, Sect. E). Fig. S4 shows additional PL spectra derived from the data presented in Fig. 3a. By scaling each frame with the corresponding inverse of the square of the photonic coefficient α, we obtain the normalised polariton population (Fig. Fig. S4a). We note that before scaling the PL intensity to obtain the polariton population, we subtract the uncoupled exciton emission (i.e. the PL spectrum at shortest cavity length). Fig. S4b displays a selection of cavity spectra for decreasing cavity length from bottom to top, corresponding to vertical slices through the data presented in Fig. 3a. Each spectrum is fitted with a sum of two Lorentzian lineshapes (red), one at the position of the lower polariton state (blue line) and one for the uncoupled exciton emission at an energy of 2.4 ev. The latter one is kept fixed (in all three parameters amplitude, width and position) for all fits. The data presented in Fig. 3b is obtained by taking the area of the LP state (blue line), scaling it by the respective inverse of the square of the photonic coefficient α and plotting it against the energy of the LP state. Note that the shift in peak position which results from this scaling is small ( 5 mev). S6

7 Figure S4: a) Normalised polariton population obtained from experimental data presented in Fig. 3a by scaling each frame with the corresponding inverse of the square of the photonic coefficient α. We note that before scaling the PL intensity to obtain the polariton population, we subtract the uncoupled exciton emission (i.e. the PL spectrum at shortest cavity length). b) Selection of cavity spectra for decreasing cavity length from bottom to top, corresponding to vertical slices through the data presented in Fig. 3a. Each spectrum is fitted with a sum of two Lorentzian lineshapes (red), one at the position of the lower polariton state (blue line) and one for the uncoupled exciton emission at an energy of 2.4 ev. The latter one is kept fixed (in all three parameters amplitude, width and position) for all fits. The data presented in Fig. 3b is obtained by taking the area of the LP state (blue line, numerical values for A given to the left of each frame), scaling it by the respective inverse of the square of the photonic coefficient α and plotting it against the energy of the LP state. Measuring the dipole moment In the following we show how to obtain the dipole moment of a single nanoplatelet. The Rabi splitting for an ensemble of N randomly aligned dipoles with transition dipole moment µ is given as: S4 hω = 1 ( ) 1 2 hω 3 µ 2 N ε 0 n 2 eff V eff (2) S7

8 Here hω is the exciton energy, n eff is the effective refractive index within the cavity and V eff is the electric field mode volume. The factor 1 3 is obtained by evaluating the integral: < µ Ê > = 1 4π = µ 2 2π 0 π 0 π dφ sin(θ)dθ cos 2 (θ)µ 0 sin(θ) cos 2 (θ)dθ = 1 (3) 3 µ We have measured the thickness of the drop casted nanoplatelet film with an AFM to d = (693 ± 77)nm (see Fig. S5a). We deduce the effective refractive index n eff = 1.3 in accordance with our TMM calculations by taking the weighted average of the refractive index of the film and air within the cavity (n film = 1.5, mainly composed of oleic acid). To compute V eff, we take the expression for the effective mode volume for a planar cavity from S5 as V eff = πl2 λ 1 R 560λ3 = 75 µm 3 (4) with λ = 2πc ω = 511 nm and the mirror reflectivity R = Now, the only missing parameter is the number of platelets N coupled to the mode. To obtain it, we first measure the average size of nanoplatelets on the basis of a TEM micrograph L x = 32.5±2.5 nm, L y = 8.2±0.9 nm and L z = 1.36±0.05 nm. We then obtain the concentration of selenium atoms in solution by inductively coupled plasma optical emission spectroscopy (ICP-OES), from which we infer a concentration of c NPL sol To compare this volume concentration of platelets in solution c NPL sol = ± µm. to the volume concentration in a dried film c NPL film, we measure the weight difference m = 6.24 mg of a drop of V sol = (10 ± 0.18) µl before and after evaporation V dry of the solvent hexane with the known density of ρ hex = mg ml. Note that the uncertainty in the volume pipetted (σ V = 1.8%) dominates the end result. With this we find the volume concentration of platelets in the dried film c NPL film as: c NPL film = c NPL sol V sol = c NPL sol V dry V sol V sol m ρ hex = c NPL sol = 18.9 ± 6.9 µm (5) S8

9 With the platelet dimensions (V NPL = L x L y L z ) above this concentration translates into a volume fraction f V of platelets in the film of (N A is the Avogadro number): f V = c film N A V NPL = (0.5 ± 0.2)% (6) For the number of platelets coupled to the cavity mode this equates to : N = V eff L dcnpl film N A = πlλ 1 R dcnpl film N A = (3.9 ± 1.5) 10 5 (7) Taking this value and using hω = (65.9 ± 1.4) mev we solve Eq. 2 for µ and obtain: µ = 3 ( ε0 n 2 eff V ) 1 2 eff hω = (1.92 ± 0.37) C m = (575 ± 110) D (8) 2 hω N Note that the value for µ is independent of the exact choice for the mode volume (and thus the mirror reflectivity) since: µ = 3 ( ε0 n 2 eff V ) 1 2 eff hω = 3 2 hω N ( ε 0 n 2 eff = 3 2 hωc NPL film N A ) 1 2 ( L d ( ε0 n 2 eff V ) 1 2 eff hω L 2 hω V eff dc NPL film N A ) 1 2 hω (9) Assuming a two level system with energy difference E = hω and transition dipole moment µ, the radiative lifetime τ of the heavy-hole exciton can be expressed as: S4 τ = 3πɛ 0 hc 3 ω 3 µ 2 (10) With µ as found above this expression results in τ = (1.3 ± 0.5) ps. Similarly the oscillator strength f of the transition can be expressed as: f = 2mω 3 h µ2 = (280 ± 107) (11) S9

10 where m is the reduced mass of the exciton. These results confirm the giant oscillator strength associated with the large exciton coherence area reported previously. S3 Figure S5: a) Atomic Force Microscope image of NPL film close to the edge. b) SEM micrograph of NPL film at an angle of 60 to the silver mirror. References (S1) Savona, V.; Andreani, L. C.; Schwendimann, P.; Quattropani, A. Solid State Commun. 1995, 93, (S2) Rakić, A. D.; Djurišić, A. B.; Elazar, J. M.; Majewski, M. L. Appl. Opt. 1998, 37, (S3) Naeem, A.; Masia, F.; Christodoulou, S.; Moreels, I.; Borri, P.; Langbein, W. Phys. Rev. B 2015, 91, (S4) Fox, M. Quantum Optics: An Introduction; OUP Oxford, (S5) Ujihara, K. Jpn. J. Appl. Phys. 1991, 30, L901 L903. S10