Attracting Solitons and a first Order Lock-In Transition: Metallic Polyacetylene and the Spin-Peierls System

Abstract

The problem of a one-dimensional fermion system whose density is at or near to that of a half-filled band is of recent experimental and theoretical interest. For fermions with chemical potential μ and density ρ (measured from the half-filled band level) the relation ρ(μ) at zero temperature defines the lock-in phase transition. In the spin-Peierls problem [1] the magnetization is mapped into p of spinless fermions and the external magnetic field into μ. In a recent experiment [2] on a spin-Peierls system a first-order lock-in transition was observed. On the other hand, when doping polyacetylene [3], the experiment controls ρ — the doping level, and not the chemical potential. If the lock-in transition is first order it implies that for ρ smaller than some ρ* the system will phase separate into regions with either ρ=0 or ρ=ρ*. The system will then appear as metallic particles embedded in an insulating medium. This is indeed consistent with: a) infrared absorption data [4] which shows metallic absorption coexistent with the semiconducting gap, b) the appearance of metallic type magnetic susceptibility [5] below the threshold for the metallic d.c. behaviour and c) temperature dependence of the conductivity which is consistent with percolation between metallic particles [6].