Metal-insulator transition in highly conducting oriented polymers

Abstract

We suggest that highly conducting oriented polymers with a fibril structure can be modeled by a regular lattice of disordered metallic wires with a random first-neighbor interwire coupling which mimics the cross links between fibrils. We determine the position of the metal-insulator transition (MIT) as a function of interwire cross-link concentration, interwire coupling $J$, and number $M$ of polymer chains in a wire. Two different approaches are used. The first one is based on the self-consistent diagrammatic theory of Anderson localization. In the second approach, we show that the MIT can be described by a nonlinear $\ensuremath{\sigma}$ model. For $M=1$, we find that a small value of $J$ favors the metallic state while a large value of $J$ induces localization in agreement with recent numerical calculations. When $M\ensuremath{\gg}1$, an increase of $J$ always favors a delocalization of the electronic states in agreement with a previous analytical analysis.