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In organic semiconductors working under ambient circumstance, there areremarkable quantum effects lack of comprehensive understanding, and an exoticcomposite particle named charge transfer (CT) exciton is normally regarded asthe key ingredient. Another essential substance is the phonons stemming fromintra- and inter-molecular vibrations, and the relevant diagonalelectron-phonon couplings give rise to spatial localization and theoff-diagonal couplings refer to the dispersion of electron wavefunctions. Inthis work, we first propose a toy model based upon the fracton physics tophenomenologically unveil the coherent motion of CT excitons followed byresonant phonons in the aggregates. Based on this model, a generic scenario ofhierarchical quantum effects is described in various material systems. Toexamine whether the fracton model can be applicable in practice, we calculatethe out-of-time-ordered correlator (OTOC), a quantum dynamic measurement of theentanglement entropy, of CT excitons by the adaptive time-dependent densitymatrix renormalization group algorithm. On the basis of three commonly-usedrealistic models in organic materials with two competing interactions takinginto account, we investigate the irreducible roles of CT excitons and aggregatephonons in the ultrafast charge transfer, the coherent polaron hopping, and thedissociation of triplet pairs, respectively. Our theory unifies the charge,exciton, spin and phonons into a single framework, which may help clarify thecomplicated and diverse quantum effects in organic semiconductors.

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