Electronic states intrans-polyacetylene with bond-type impurities in the coherent-potential approximation

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Abstract
Disorder effects on the electronic states in trans-polyacetylene are investigated in the case of bond-type impurities which give rise to backward scatterings of electrons. The generalized Takayama–Lin-Liu–Maki model is studied with the help of the coherent-potential approximation (CPA). The dimerization of the lattice is assumed to be uniform and is represented by an order parameter Δ. The CPA gives equations for electron Green functions. They are solved numerically, while Δ is determined as to give minimum energy. We find three solutions at low impurity concentrations, one of which is stable solution, another is metastable, while the third is unstable. In the stable solution, which survives for higher impurity concentrations, impurity bands are not formed. In the metastable solution, the conduction and valence bands intrude into the gap region, indicating the development of impurity bands. Concentration dependences of the order parameters, energy gaps, and the critical concentration for the metastable solution are derived.