Local exciton ground states in disordered polymers

Abstract

Exciton localization in conjugated polymers with weak conformational disorder is investigated via the Anderson model with Gaussian off-diagonal disorder, $\ensuremath{\sigma}$. We show that a small fraction of the low-energy eigenstates are spatially localized, nonoverlapping, and space filling. We term these states ``local exciton ground states'' (LEGS). The LEGS exhibit an almost Gaussian density of states, an average localization length $L\ensuremath{\sim}{\ensuremath{\sigma}}^{\ensuremath{-}2/3}$, and an inhomogeneous optical linewidth $\ensuremath{\sim}{\ensuremath{\sigma}}^{4/3}$. Their transition dipole moments scale with their localization length in a way consistent with a lowest energy excitation confined to a region $\ensuremath{\sim}O(L)$. The length scale over which the LEGS are confined is an effective low-energy conjugation length or spectroscopic segment. The appendix describes an efficient and accurate technique for calculating the density of states of the Anderson model.