Localization of large polarons in the disordered Holstein model

Abstract

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, $\ensuremath{\hbar}\ensuremath{\omega}/4{t}_{0}={\ensuremath{\omega}}^{\ensuremath{'}}<1$, and the large polaron regime, $\ensuremath{\lambda}<1$, are applicable to most conjugated polymers. We show that as a consequence of the polaron effective mass diverging in the adiabatic limit (defined as ${\ensuremath{\omega}}^{\ensuremath{'}}\ensuremath{\rightarrow}0$ subject to fixed $\ensuremath{\lambda}$) 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 (${\ensuremath{\omega}}^{\ensuremath{'}}$, $\ensuremath{\lambda}$) parameter space, however, self-localized Born-Oppenheimer solutions are not expected. If ${\ensuremath{\omega}}^{\ensuremath{'}}$ is not small enough and $\ensuremath{\lambda}$ 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 ($\ensuremath{\lambda}\ensuremath{\ll}1$) the disorder-induced localization length is always smaller than the classical polaron size, $2/\ensuremath{\lambda}$, so that disorder always dominates. We comment on the implication of our results on the electronic properties of conjugated polymers.