Electronic states in doped conducting polymers: Numerical simulation of disordered systems

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Abstract
In order to substantiate the applicability of the coherent-potential approximation (CPA) to conducting polymers with randomly distributed impurities, the Su-Schrieffer-Heeger model is generalized by including the effects of the impurities and solved numerically. The lattice configurations, electronic levels, and wave functions are determined for each impurity distribution. The size of lattice dimerization and electronic density of states are determined and averaged over a large number of impurity distributions, which are selected independently and randomly. The study is confined to systems with one electron per site that we have studied previously using the CPA. Two types of impurities as well as three doping mechanisms are considered. It turns out that the magnitude of lattice dimerization agrees remarkably well with the CPA result for all impurity types and doping mechanisms under consideration. The density of states shows a characteristic tail at the edge of a band where the CPA predicts an impurity band at lower concentrations. Such a tail never occurs in regimes where the CPA does not predict such bands. Quasilocalization is found in the wave functions of the states at the band edges. It is closely associated with the characteristic structure of the density of states. The usefulness of the CPA is thus established for the Peierls system as far as gross qualitative properties are concerned.