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

TL;DR

This paper compares how Gaussian and Lorentzian diagonal disorder affect the localization of one-dimensional Frenkel excitons, revealing differences in localization length, state structure, and energy dependence, especially in the Lifshits tail region.

Contribution

It provides a detailed analysis of the distinct localization properties and state structures induced by Gaussian versus Lorentzian disorder in 1D Frenkel excitons, highlighting the absence of exchange narrowing in Lorentzian disorder.

Findings

Lorentzian disorder lacks exchange narrowing, affecting localization length distribution.

Different local state structures are observed for Gaussian and Lorentzian disorders near the band edge.

Lorentzian disorder produces strongly localized low-energy exciton states with energy-dependent properties.

Abstract

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.