Unified definition of exciton coherence length for exciton-phonon coupled molecular aggregates

TL;DR

This paper introduces a unified, oscillator strength-based definition of exciton coherence length that accurately correlates with radiative efficiency in molecular aggregates, improving understanding of exciton behavior in various systems.

Contribution

It proposes a new, unified ECL definition based on oscillator strengths, addressing limitations of previous measures and demonstrating its effectiveness through numerical simulations.

Findings

ECL correlates monotonically with radiative efficiency

Two-dimensional aggregates can show maximum superradiance at finite temperature

The new ECL definition improves characterization of exciton coherence

Abstract

Exciton coherence length (ECL) is an essential concept to characterize the nature of exciton in molecular aggregates for photosynthesis, organic photovoltaics, and light-emitting diodes. ECL has been defined in a number of ways through the variance or purity of the electronic reduced density matrix. However, we find that these definitions fail to present a monotonic relationship with respect to the exciton radiative decay efficiency as it should be when exciton-phonon couplings are taken into accounts. We propose a unified definition of ECL by virtue of sum rule of oscillator strengths. Using the numerically accurate time-dependent matrix product states formalism applied to Frenkel-Holstein models for molecular aggregates in both one- and two-dimensional system, we find our ECL definition exhibits a monotonic relationship with respect to the radiative efficiency and can serve as an efficient and unified description for exciton coherence. We further predict that the two-dimensional aggregates can display maximum superradiance enhancement (SRE) at finite temperature, different from the previous knowledge of SRE-$1/T$ behavior.