Electrically tunable organic–inorganic hybrid polaritons with monolayer WS2

Exciton-polaritons are quasiparticles consisting of a linear superposition of photonic and excitonic states, offering potential for nonlinear optical devices. The excitonic component of the polariton provides a finite Coulomb scattering cross section, such that the different types of exciton found in organic materials (Frenkel) and inorganic materials (Wannier-Mott) produce polaritons with different interparticle interaction strength. A hybrid polariton state with distinct excitons provides a potential technological route towards in situ control of nonlinear behaviour. Here we demonstrate a device in which hybrid polaritons are displayed at ambient temperatures, the excitonic component of which is part Frenkel and part Wannier-Mott, and in which the dominant exciton type can be switched with an applied voltage. The device consists of an open microcavity containing both organic dye and a monolayer of the transition metal dichalcogenide WS2. Our findings offer a perspective for electrically controlled nonlinear polariton devices at room temperature.

Supplementary Figure 6: Peak and dispersion fitting a) Fitted transmission peaks with error bars superimposed on raw transmission data for different cavity mode energies. Each peak is fitted with a Lorentzian profile. b) Dispersion as given by Eq. 2 fitted to the peak positions presented in a. The fit is performed after obtaining three separate equations for UP, MP and LP from diagonalisation of Eq. 2 and proceeding with a non-linear least squares algorithm with shared parameters E f , E w , V f and V w . In the following section we describe the two mirrors forming the cavity and the absorbing material within. more details on the measurements are given in the next section. The first mirror consists of 10 pair DBR of SiO 2 , TiO 2 with refractive indices 1.45 and 2.05 respectively deposited on a 0.5 mm thick, flat Silica substrate. The stopband of this mirror is centered around λ = 637 nm and the reflectivity at that wavelength is 99.7%. The second, smaller mirror is produced by removing large areas of a flat silica substrate with a dicer to create a 200 × 300 µm 2 plinth made semi-reflective by thermally evaporating a 50 nm thick silver layer. To enable electrical control within the cavity, silver electrodes with a width and a spacing of 90 µm are thermally evaporated on top of the DBR. This process is facilitated by masking a region of the DBR with a laser processed foil defining the electrode shape. The thickness of these electrodes is similar to the thickness of the silver layer on the small opposing mirror, approximately 50 nm. The WS 2 flakes are grown as described in [S1] and transferred onto the dielectric mirror stack, which has a low refractive-index terminated layer to provide an anti-node of the electric field at the mirror surface and thus optimal coupling to the monolayer. This transfer is facilitated by spin-coating a thick layer of PMMA onto the as-grown WS 2 flakes on their native SiO 2 substrate. After etching the substrate away the PMMA stays connected with the WS 2 flakes and can be fished out and cut manually. The resulting PMMA section is then manually positioned over the DBR region holding the electrodes and baked at 100 • C for one hour. After this the PMMA is removed by putting the sample into an acetone bath for about 15 min. The distribution of WS 2 flakes relative to the electrodes is random, the average size of a WS 2 flake being 80 µm, with 90% of the flakes overlapping partially with the silver electrodes (see Fig. 1). The results presented above were obtained from a flake which was not in contact with the electrodes, thus ensuring purely electrostatic tuning. The electrodes have a length of ≈ 1 cm and were connected to thin wires with conducting silver paint at the respective ends. A cavity mode in the region of these electrodes would be spectrally broader and the number of round-trips would be reduced due to the additional absorption of the second silver interface. For the data that we present in the manuscript the effect that such broadening would have can be estimated: Given the cavity length of around 500 nm and the reflectivity of the silver mirror R = 0.95, we can equate an effective mode area A = πLλ 1−R ≈ 19.5 µm 2 , as derived in [S2]. This area translates to a mode radius of r ≈ 2.5 µm. Since the region of the sample from which we obtained the results is more than 15 µm from the next silver electrode, the effect from the electrode on the cavity mode is negligible.
The organic dye was introduced on the opposing mirror by dissolving J-aggregated 1,1 -diethyl-3,3 -di(4-sulfobutyl)-5,5 ,6,6 -tetrachlorobenzimidazolocarbocyanine (TDBC) in an aqueous solution with 5 weight percent gelatine. The solution was then spin coated onto the small silver mirror, giving a polymer, dye layer of approximately 300 nm. The j-aggregate exciton energy can be shifted in an electrical field through the Stark effect, but it requires field strengths of about 10 6 V/cm for a 20 nm shift (as determined through electroabsorption measurements -unpublished), whereas the field strengths that we obtained in our experiment were about 2.33 × 10 4 V/cm. Our data gives experimental evidence of this, since the Frenkel exciton energy remained unchanged (within the uncertainty of the Lorentzian lineshape fit) for any applied electric field.

B. Optical measurements
The small silver mirror is mounted on a three-dimensional piezo actuated stage, which makes electric positioning relative to the WS 2 flake possible. To initialise the cavity, white light from a light emitting diode is shone through the mirrors while reducing the separation. With the help of Fabry-Perot fringes visible for small mirror separations (L < 20 µm) both surfaces are made parallel within 150 µrad. Optical access to the sample is given by a standard ×10 objective lens and the collected light is focused on an Andor combined spectrograph/CCD for analysis. The electrodes were pairwise connected to a Keithley 2400 to apply voltages and monitor the current. Care was taken that for the datasets presented, the full voltage was applied and the respective current limits were not exceeded.

Supplementary Note 2. Components of hybrid polariton system
In the following we present a characterisation of the individual components of the hybrid system. Fig. 2a shows transmission spectra of a microcavity with only a WS 2 flake for different cavity lengths. As the cavity length is decreased from left to right, the cavity mode energy increases and traverses the exciton energy. As both components strongly couple to each other, an avoided level crossing with characteristic Rabi splitting is visible. The coloured, dashed lines show the dispersion of the lower and upper polariton branch. Fig. 2b shows the photonic and excitonic fractions of the resulting polariton states, which are known as the Hopfield coefficients, as introduced in the main text. We have published a study on the properties of this open cavity polariton system [S3]. A strongly coupled system on the basis of organic dyes is well known in the literature [S4, S5]. Fig. 4 shows the Rabi splitting for a fixed cavity length as a function of the concentration of the dye TDBC. When plotted as a function of the square root of the concentration the linear relationship is visible. By varying the concentration of TDBC in the aquaeous solution it is possible to optimise the hybridisation between WS 2 and organic excitons. Fig. 5a shows transmission spectra of a hybrid microcavity system with a lower concentrated TDBC layer compared to the data presented before in the manuscript. Symbols and lines are defined as previously in the main text. As the strength of the interaction between dye and cavity mode is reduced, the photonic fraction in the middle polariton branch is increased and the hybridisation between both excitons only occurs marginally (β 2 = γ 2 ≈ 10% for a cavity length of L = 0.455 µm). By variation of the concentration of the dye it is thus possible to control the composition of the polariton branches, in particular the middle polariton branch. When relying on the photonic part of a polariton state for detection, a reduced overlap between both excitons is desirably -hence the choice of concentration in the main text. For applications, where the exciton hybridisation is the only important parameter, a larger dye concentration might be desirable.

Supplementary Note 3. Electrical control of WS2 absorption profile
The occurence of trion (or charged exciton) states in atomically flat TMDCs has been reported previously [S6, S7]. By applying an electric field to deplete a region of the material from electrons, it is possible to change the Fermi level and thus the spectral weight and position of both the neutral exciton (X 0 ) and charged exciton (X − ) states [S6, S8-S10]. Such electrical control can thus be used to vary the absorption profile. Fig. 3 shows the absorbance of the WS 2 for different applied voltages. As the Fermi level is raised for increasing positive biases the spectral weight of the absorption profile shifts towards the charged exciton X − .
As Fig. 2(a) in Ref. [S9] shows, the trion can be quenched by applying a negative gate voltage. The zero bias level of weight in neutral and charged exciton is dependent on the intrinsic doping of the WS 2 flake, which is thought to be a result of the growth and transfer method. On our CVD grown samples we see variations of X − contribution on one flake and even larger variations when comparing multiple flakes. In general the X/X − ratio found for our sample is similar to bias values between -30 V and 0 V in Fig. 2(a) in Ref. [S9]. To demonstrate the strong coupling to a cavity mode we chose a region with minimal trion contribution (as visible in the absorption lineshape in Fig. 1 d) for negative applied voltages). The reasoning behind this was, that with more trionic contribution the polariton linewidth increases, the asymmetry between upper and lower polariton branch increases and the splitting is less obvious.

Supplementary Note 4. Fitting procedure and error propagation
Each transmission data set is aquired and analysed by the following procedure: The sequence of transmission spectra is aquired by sweeping the voltage of the piezo microactuator, varying the cavity length. The actual cavity length for each frame is obtained by fitting a Lorentzian profile to the unperturbed cavity mode for either the same longitudinal mode (with index q = 4 and for energies below E =1.85 meV or the the next one (with index q + 1 = 5, if the q = 4 mode has energies above E =1.85 meV). The value of q can be obtained for each dataset from the free spectral range, which then allows the absolute cavity length to be expressed as L cav = qhc 2E , where E is the mode energy. Each frame is fitted with Lorentzian lineshape peaks to obtain the position of the individual polariton branches (Fig. 6a). The analytic form of the three equations for UP, MP and LP is found by diagonalising Eq. 2. The three expressions are simultanuously fitted to the obtained peaks with a nonlinear least squares algorithm (Fig. 6b). In a first round, the four parameters (E f , E w , V f , V w ) are shared in the fitting procedure and obtained as parameters after the fit. In a second round the parameters governing the position and the interaction strength of the dye (E f , V f ) are fixed to a common value obtained by averaging their respective values from the first round. The covariance matrix M cov is obtained for each fit. Through diagonalisation of Eq. 2 we obtain the eigenvectors, whose components represent the mixing coefficients after proper normalisation. The respective values for point A and B of these values is directly obtained by plugging in the parameters found above. The uncertainty for each of the coefficients is obtained by constructing the Jacobian J f ij = ∂fi ∂xj , where f i is the respective expression for the polariton fraction and x j is one of the parameters found above. The uncertainties u can now be calculated from u = diag(JM cov J t ).
Supplementary Note 5. Electrical control on different WS2 flake Complementary to the data set shown in the main text, we include another dataset showing the electrical control of the hybridisation. Fig. 7a-d show transmission spectra at a different point on the sample for different applied voltages. The symbols and lines are defined as in the main text and the figure caption. Fig. 7e-h show the photonic (blue, continuous), Wannier-Mott (purple, dashed) and Frenkel-excitonic (red,dashed) fractions of the three polariton branches corresponding to the dispersion shown to the left in a-d. Fig. 8 presents the summary of the electrically controlled hybridisation analogous to Fig. 3 in the main text for the second dataset.