Subdiffusive exciton motion in systems with heavy-tailed disorder

Abstract

We study the transport of collective excitations (Frenkel excitons) in systems with static disorder in the transition energies, not limiting ourselves to Gaussian transition energy distributions. Instead, we generalize this model to the wider class of Lévy stable distributions, characterized by heavy tails. Phonon-assisted scattering of excitons, localized by the disorder, leads to thermally activated exciton motion. The time evolution of the second moment of the exciton distribution is shown to be sublinear, thus indicating that the exciton dynamics in such systems is not diffusive, but rather subdiffusive instead. The heavier the tail in the transition energy distribution is, the larger are the deviations from the diffusive regime. This from fluctuations of site energies larger than the exciton band width (outliers). We show that the occurrence of subdiffusive transport for heavy-tailed disorder distributions can be understood from the scattering rate distributions, which possess a (second) peak at zero scattering rate.

Regimes of Exciton Transport in Molecular Crystals in the Presence of Dynamic Disorder

“…In the opposite limit of slow fl uctuations one should consider a distribution of hopping rates between distinct pairs of molecules, as done for example in ref. [ 21 ] .…”

“…The limit of J fluctuations that are faster than any other timescale can be studied in the classical Haken-Strobl-Reineker model, [19,20] whereas the limit of J fluctuations slower than any other timescale is a particular case of exciton transport in a statically disordered system. [21] For weak fluctuations, i.e. if their amplitude is much smaller than their average value, one can adopt exciton-polaron band renormalization theories.…”

Visualization of exciton transport in ordered and disordered molecular solids

“…Such anomalous diffusion is characteristic of particles diffusing in a disordered potential and is observed in a wide range of physical systems from protein diffusion in cells to charge diffusion in semiconductors 30 , but to our knowledge has not previously been observed in excitonic systems. Recent theoretical work has predicted that subdiffusive transport of excitons can occur in energy disordered systems with excitonic energy trap levels at the low energy tail of the exciton distribution 31 . In tetracene we attribute the subdiffusive transport to the excitons becoming trapped in lowerenergy molecular sites, which decreases the hopping rate for a subpopulation of excitons.…”

Dynamics of the Excitonic Coupling in Organic Crystals

“…In this limit, it is also not possible to decouple electronic and nuclear motions assuming that the latter are much faster as done for example in the Haken-Strobl-Reineker model [7,8]. Similarly it is not possible to assume that the fluctuation is slow enough to discuss the transport as an incoherent sequence of hopping events in a disordered landscape [9].…”

“…Crucially, the characteristic timescale for the fluctuations determines the transport mechanism. The limit of J fluctuations that are faster than any other timescale is studied in the classical Haken-Strobl-Reineker model [7,8], while the limit of J fluctuations slower than any other timescale is a special case of exciton transport in a statically disordered medium [9]. Away from these two limits it is very difficult to develop analytical theories that incorporate the effect of phonons on the excitonic coupling (nonlocal exciton-phonon coupling).…”