Comprehending robust quantum effects in organic semiconductors: Charge-transfer excitons, aggregate phonons and fractons

In organic semiconductors working under ambient circumstance, there are remarkable quantum effects lack of comprehensive understanding, and an exotic composite particle named charge transfer (CT) exciton is normally regarded as the key ingredient. Another essential substance is the phonons stemming from intra- and inter-molecular vibrations, and the relevant diagonal electron-phonon couplings give rise to spatial localization and the off-diagonal couplings refer to the dispersion of electron wavefunctions. In this work, we first propose a toy model based upon the fracton physics to phenomenologically unveil the coherent motion of CT excitons followed by resonant phonons in the aggregates. Based on this model, a generic scenario of hierarchical quantum effects is described in various material systems. To examine whether the fracton model can be applicable in practice, we calculate the out-of-time-ordered correlator (OTOC), a quantum dynamic measurement of the entanglement entropy, of CT excitons by the adaptive time-dependent density matrix renormalization group algorithm. On the basis of three commonly-used realistic models in organic materials with two competing interactions taking into account, we investigate the irreducible roles of CT excitons and aggregate phonons in the ultrafast charge transfer, the coherent polaron hopping, and the dissociation of triplet pairs, respectively. Our theory unifies the charge, exciton, spin and phonons into a single framework, which may help clarify the complicated and diverse quantum effects in organic semiconductors.