Fig. 3: Transient ballistic motion of excitons.

a–b Temperature dependence of diffusivity as the first derivative, \(D(t)=\frac{d{R}^{2}(t)}{2dt}\), for DAB-1 (a), and OA-1 (b). The orange and purple shaded areas represent the time windows used to extract \({D}_{\max }\) and \({D}_{s}\), respectively. The standard deviations are calculated from multiple separate measurements at each temperature. c Comparison of diffusivity between DAB-1, DAB-2 and OA-1 at 7 K using transient PL microscopy, plotted as unitless \(D(t)/J{a}^{2}\). These results provide evidence for coherent exciton transport within \({L}_{0}\) by validating the existence of a distinct peak \({D}_{\max }\). The color circles indicate \({D}_{\max }\). The error bars represent standard deviation calculated from multiple separate measurements. d Simulated diffusivity with increasing \(\varGamma\) (blue to red) with \(\Delta /J=1.0\), plotted as unitless \(D/J{a}^{2}\). Here a larger \(\varGamma\) is correlated to a higher temperature and the terms dephasing rate and temperature are used interchangeably within the HSR model. e Simulated diffusivity for selected \(\Delta /J\) values with \(\varGamma=0\) and initialized as a Gaussian distribution with standard deviation of 10 lattice spacings, plotted as unitless \(D/J{a}^{2}\). f Illustration of the relationship between \(\Delta /J\) and \({L}_{0}\). During \({t}_{\max },\) excitons propagate ballistically within the coherent length \({L}_{0}\).