Unified Definition of Exciton Coherence Length for Exciton–Phonon Coupled Molecular Aggregates

Abstract

Exciton coherence length (ECL) characterizes the spatial extent of coherently delocalized excited states of molecular aggregates. Constructive/destructive superpositions of coherent molecular dipoles lead to superradiance/subradiance, where the radiative rate is enhanced/suppressed compared to that of a single molecule. Longer ECLs correspond to faster/slower radiative rates for superradiant/subradiant aggregates. However, previous ECL definitions fail to produce monotonic relationships when exciton–phonon coupling is considered, even for simple 1D exciton–phonon systems. This problem is exacerbated for 2D aggregates with both constructive and destructive superpositions. In this Letter, we propose a novel ECL definition by virtue of sum rule for oscillator strengths, ensuring a bijective and monotonic relationship between ECL and radiative rate for both 1D/2D superradiant and subradiant aggregates. Using numerically accurate time-dependent matrix product states, we study large-scale, exciton–phonon coupled 2D aggregates and predict the existence of maximum superradiance at finite temperature, in contrast to the previously believed 1/T law. Our results provide new insights into the design and optimization of efficient light emitting materials.