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

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.