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Localization of Large Polarons in the Disordered Holstein Model

We solve the disordered Holstein model via the DMRG 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, $\hbarω/4t_0 = ω' < 1$, and the `large' polaron regime, $λ< 1$, are applicable to most conjugated polymers. We show that as a consequence of the polaron effective mass diverging in the adiabatic limit (defined as $ω' \to 0$ subject to fixed $λ$) 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 ($ω'$, $λ$) parameter space, however, self-localized Born-Oppenheimer solutions are not expected. If $ω'$ is not small enough and $λ$ 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-nuclear coupling ($λ\ll 1$) the disorder-induced localization length is always smaller than the classical polaron size, $2/λ$, so that disorder always dominates. We comment on the implication of our results on the electronic properties of conjugated polymers.