Metallic transitions of soliton lattice in conducting polymers randomly doped

Metallic transitions are theoretically investigated for a chain of trans-polyactylene with an assumption of random impurity distributions, effects of excess charges by the dopants being represented by the introduction of the soliton lattice. Harigaya and Terai carried out a computer simulation work to find that the energy gap vanishes at the right impurity concentration. The energy gap was defined by the difference between the lowest energy among the lowest unoccupied states of a sample ensemble and the highest energy among the highest occupied states. Each sample has a non-vanishing energy gap. The purpose of this work is to see if their result can be reproduced using one of the traditional methods for random systems. The soliton lattice is represented by a modified order parameter with two adjustable parameters. One of them is associated with an amplitude variation and the other with a variation in the spatial periodicity. The method gives a set of selfconsistent conditions for the parameters. Numerical solutions show that they are satisfied fairly well, leading to the electronic density of states. We find that the gap vanishes at the right impurity concentration for a reasonable strength of the impurity potential. The order parameter still persists, indicating a gapless Peierls system.