Eilenberger Equations in trans-Polyacetylene with Random Disorder

Abstract

Eilenberger equations are derived for trans-polyacetylene with random impurities. The Takayama-Lin-Liu-Maki model is generalized to include the impurity effect. Two types of disorders, namely, site-type and bond-type are studied. Since the original derivation, for dirty superconductors, does not work for the Peierls system, new derivation is given with the help of self-consistent argument. The equations are solved, using the assumption that dimerization pattern is uniform. It turns out there are no differences between the two types of disorders and we get exactly the same results as for the gapless superconductors with paramagnetic impurities. Electronic density of states and order parameter are calculated as functions of disorder parameter. They are compared with the results by Xu and Trullinger, obtained by supersymmetry arguments. Present method gives an overall agreement as far as the density of states is concerned. There is a difference in the order parameter.