Localization of large polarons in the disordered Holstein model

We solve the disordered Holstein model via the density-matrix renormalization group method to investigate the combined roles of electron-phonon coupling and disorder on the localization of a single charge or exciton. The parameter regimes chosen, namely the adiabatic regime, (h) over bar omega/4t(0) = omega' to = < 1, and the large polaron regime, lambda < 1, are applicable to most conjugated polymers. We show that as a consequence of the polaron effective mass diverging in the adiabatic limit (defined as a omega' -> 0 subject to fixed lambda) self-localized, symmetry-breaking solutions are predicted by the quantum Holstein model for infinitesimal disorder, in complete agreement with the predictions of the Born-Oppenheimer Holstein model. For other parts of the (omega', lambda) parameter space, however, self-localized Born-Oppenheimer solutions are not expected. If omega' is not small enough and lambda is not large enough, then the polaron is predominately localized by Anderson disorder, albeit more than for a free particle, because of the enhanced effective mass. Alternatively, for very small electron-phonon coupling (lambda << 1) the disorder-induced localization length is always smaller than the classical polaron size, 2/lambda, so that disorder always dominates. We comment on the implication of our results on the electronic properties of conjugated polymers.