Abnormal Seebeck effect in doped conducting polymers

The Seebeck effect or thermopower relates the temperature gradient to the electric voltage drop. Seebeck coefficient $α$ measures the transport entropy, which could either linearly increase with temperature $T$ like metallic conducting or decrease as $1/T$ like semiconducting behavior. It could become more complicated in the temperature dependence for a number of disordered systems but still in a monotonic way. However, several recent experiments reported the “abnormal” non-monotonic temperature dependence of the Seebeck coefficient in doped conducting polymers, for instance, first increasing and then decreasing. Through a one-dimensional tight-binding model coupled with the Boltzmann transport equation, we investigate theoretically the doping effect for the Seebeck coefficient. We find that the abnormal behavior comes from multi bands' contribution and a two-band model (conduction or valence band plus a narrow polaronic band) can address such an abnormal Seebeck effect, namely, if there exists (i) a small bandgap accessible for thermal activation between the two bands; and (ii) a large difference in the bandwidth between the polaronic band and the conduction band (or valence band), then the Seebeck coefficient increases with temperature first, then levels off, and finally drops down.