Superradiance from Two Dimensional Brick-Wall Aggregates of Dye Molecules: The Role of Size and Shape for the Temperature Dependence

Aggregates of interacting molecules can exhibit electronically excited states that are coherently delocalized over many molecules. This can lead to a strong enhancement of the fluorescence decay rate which is referred to as superradiance (SR). To date, the temperature dependence of SR is described by a $1/T$ law. Using an epitaxial dye layer and a Frenkel-exciton based model we provide both experimental and theoretical evidence that significant deviations from the $1/T$ behavior can occur for brick-wall-type aggregates of finite size leading even to a maximum of the SR at finite temperature. This is due to the presence of low energy excitations of weak or zero transition strength. These findings are relevant for designing light-emitting molecular materials.

Figure 1

(a) Enhancement factor ${\eta }_{\mathrm{SR}}$ of the superradiance as a function of temperature. The open circles show experimental data for a monolayer of PTCDA on the KCl (100) surface. Note the maximum of ${\eta }_{\mathrm{SR}}^{\max }=50$ at $T\approx 16\mathrm{K}$. The dashed line is calculated for a geometric distribution of aggregates sizes with an average size of $⟨N_x\times N_y⟩=12.4\times 12.4$ molecules (cf. Fig. 3) determined from the LEED Profile. The solid line was multiplied by an additional factor of 1.2 adapting the theoretical curve to the experimental situation (for details see the Supplemental Material [28]). Inset top: Hard sphere model of a $3\times 2$ aggregate of PTCDA molecules on the KCl (100) surface. The transition dipole moment $\overrightarrow{\mu }$ is depicted for the top left molecule. Inset bottom: Experimental and fitted LEED profile of the PTCDA (1,0) spot using the above mentioned geometric aggregate size distribution. More details are given in the SI. (b) Fluorescence (FL) spectra normalized at the 0-0 transition ($19600{\mathrm{cm}}^{-1}$) at 6 and 56 K illustrating the enhancement of the 0-0 transition with respect to the vibronic peaks due to superradiance.

Figure 2

Left: Temperature dependence of the enhancement factor ${\eta }_{\mathrm{SR}}$, according to Eq. (3) for different aggregates of $N_x\times N_y$ molecules. Right: Stick spectra of the transition strengths of the lowest eigenstates corresponding to the respective aggregates. The energies are referenced versus the excitation energy $\epsilon$ of the single molecule. The eigenstates are marked by filled ($\mathrm{TS}>0$) or open circles ($\mathrm{TS}=0$). The inset illustrates the normalized wave function of the lowest state ($k=1$). The values of the real coefficients $c_{nk}$ are plotted with red and blue color indicating positive and negative values, respectively. Note that the two wave functions at the top are symmetric, while the lower is antisymmetric leading to $\mathrm{TS}=0$ for the $k=1$ state.

Figure 3

(a) The maximum of the enhancement factor ${\eta }_{\mathrm{SR}}^{\max }$ for aggregates of different size $N_x\times N_y$. The blue overlayed isolines refer to the geometric aggregate size distribution used for the calculated ${\eta }_{\mathrm{SR}}(T)$ curve presented in Fig. 1. (b) The corresponding temperature $T_{\max }$. The regions where the three cases A, B, and C apply are indicated and separated by blue lines. For further details see text.