One-dimensional excitonic systems with diagonal L\'{e}vy disorder: A detailed study of the absorption spectra and the disorder scaling of localization length

TL;DR

This paper investigates how Levy alpha-stable disorder affects excitonic systems, revealing novel localization and spectral broadening effects, with analytical and numerical insights across different disorder regimes.

Contribution

It provides a comprehensive analysis of Levy alpha-stable disorder impacts on exciton localization and absorption spectra, including analytical descriptions and numerical validation.

Findings

Heavy-tailed Levy disorder causes exchange broadening of spectra.

Localization length exhibits nontrivial scaling with disorder strength.

Outliers induce short localization segments affecting spectral features.

Abstract

We present a detailed study of the effects of L\'evy $\alpha$-stable disorder distributions on the optical and localization properties of excitonic systems. These distributions are a generalization of commonly studied Gaussian randomness ($\alpha = 2$). However, the more general case ($\alpha < 2$) includes also heavy-tailed behavior with a divergent second moment. These types of distributions give rise to novel effects, such as exchange broadening of the absorption spectra and anomalous localization of the excitonic states, which has been found in various excitonic systems. We provide a thorough examination of the localization behavior and the absorption spectra of excitons in chains with L\'evy $\alpha$-stable diagonal disorder. Several regimes are considered in detail: (i) weak disorder and small systems, where finite size effects become significant; (ii) intermediate disorder and/or larger systems for which exciton states around the exciton band edge spread over a number of monomers, and (iii) strong disorder where the exciton wave functions resemble the individual molecular states. We propose analytical approaches to describe the disorder scaling of relevant quantities for these three regimes of localization, which match excellently with numerical results. We also show the appearance of short localization segments caused by outliers (monomers having transition energies larger than the exciton band width). Such states give rise to an additional structure in the absorption spectrum, density of states, and in the nontrivial disorder scaling of the absorption band width.