Localization properties of one-dimensional Frenkel excitons: Gaussian versus Lorentzian diagonal disorder

We compare localization properties of one-dimensional Frenkel excitons with Gaussian and Lorentzian uncorrelated diagonal disorder. We focus on the states of the Lifshits tail, which dominate the optical response and low-temperature energy transport in molecular J-aggregates. The absence of exchange narrowing in chains with Lorentzian disorder is shown to manifest itself in the disorder scaling of the localization length distribution. Also, we show that the local exciton level structure of the Lifshits tail differs substantially for these two types of disorder: In addition to the singlets and doublets of localized states near the bare band edge, strongly resembling those found for Gaussian disorder, for Lorentzian disorder two other types of states are found in this energy region as well, namely multiplets of three or four states localized on the same chain segment and isolated states localized on short segments. Finally, below the Lifshits tail, Lorentzian disorder induces strongly localized exciton states, centered around low energy sites, with localization properties that strongly depend on energy. For Gaussian disorder with a magnitude that does not exceed the exciton bandwidth, the likelihood to find such very deep states is exponentially small.Comment: 9 two-column pages, 4 figures, to appear in Phys. Rev.

Excitons in Molecular Aggregates with L\'evy Disorder: Anomalous Localization and Exchange Broadening of Optical Spectra

We predict the existence of exchange broadening of optical lineshapes in disordered molecular aggregates and a nonuniversal disorder scaling of the localization characteristics of the collective electronic excitations (excitons). These phenomena occur for heavy-tailed L\'evy disorder distributions with divergent second moments - distributions that play a role in many branches of physics. Our results sharply contrast with aggregate models commonly analyzed, where the second moment is finite. They bear a relevance for other types of collective excitations as well