Metal-insulator transition in doped conjugated polymers: Effects of long-ranged Coulomb potentials

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Abstract
The metal-insulator transition in doped conjugated polymers is investigated for charged impurities that are represented as long-ranged potentials. The impurity positions are randomly selected. The change in the number of electrons is determined by the number of impurities. Physical quantities are derived from a sufficiently large number of samples, each of which is described by a finite-size Su-Schrieffer-Heeger Hamiltonian with the impurity potentials. It is shown that the electronic gap can disappear above a certain concentration even as the dimerization patterns persist. The present results well explain the appearance of the metallic Pauli susceptibility, its magnitude, and the critical concentration, characteristic of the metal-insulator transition observed in experiments. The persistence of dimerization is also consistent with results of experiments in which highly doped samples are used. A comparison with a previous study using short-ranged site-type impurity models is given. It is found that the agreement is excellent, which indicates that the main results do not depend on whether the impurity potentials are short or long ranged.