The temperature dependence of the conductivity in the critical regime of the metal-insulator transition in conducting polymers

The metal-insulator (M-I) transition in conducting polymers is particularly interesting; critical behaviour has been observed over a relatively wide temperature range in a number of systems, including polyacetylene (CH)(x), polypyrrole (PPy), poly(p-phenylenevinylene) (PPV), and polyaniline (PANI). In each case, the metallic, critical, and insulating regimes near the M-I transition have been identified from plots of W = (Delta ln sigma/Delta ln T) versus T: in the metallic and insulating regimes W(T) exhibits positive and negative temperature coefficients, respectively, while in the critical regime W(T) is temperature independent. Thus, in the critical regime, the conductivity follows a power law, sigma(T) = AT(beta), where beta is the critical exponent which is predicted by scaling theory to be between one-third and unity. In conducting polymers, the critical regime is easily tunable by varying the extent of disorder, or by applying external pressure and/or magnetic fields. The transitions from metallic to critical behaviour and from critical to insulating behaviour have been induced with a magnetic field, and that from insulating to critical and then to metallic behaviour with increasing external pressure. The detailed evolution of sigma(T) in the critical regime at low temperatures can be observed in W(T) plots as the system is changed from metal to insulator. Although W(T) is temperature independent for a wide range of temperatures below 50 K, beta systematically increases from values less than one-third on the metallic side towards unity as the system is moved toward the insulating side.