Quantum hopping in metallic polymers

Highly conducting polymers such as polyaniline and polypyrrole in a metallic state have unusual frequency-dependent conductivity, including multiple zero crossing of the dielectric function. A low-frequency electromagnetic response in terms of a Drude metal is provided by an extremely small fraction of the total number of conduction electrons ∼0.1% but with extremely high mobility or anomalously long scattering time ∼10-13 s. We show that a network of metallic grains connected by resonance quantum tunneling has a Drude-type response for both the high- and low-frequency regimes and behaves as a dielectric at intermediate frequency in agreement with experimental observations. The metallic grains in polymers represent crystalline domains of well-packed chains with delocalized electrons embedded in the amorphous media of poor chain order. Intergrain resonance tunneling occurs through the strongly localized states in the amorphous media