Metal-insulator transition in highly conducting oriented polymers

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 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 much greater than 1, an increase of J always favors a delocalization of the electronic states in agreement with a previous analytical analysis.