Charge Kondo Effect in Thermoelectric Properties of Lead Telluride doped with Thallium Impurities

We investigate the thermoelectric properties of PbTe doped with a small concentration $x$ of Tl impurities acting as acceptors and described by Anderson impurities with negative on-site (effective) interaction. The resulting charge Kondo effect naturally accounts for a number of the low temperature anomalies in this system, including the unusual doping dependence of the carrier concentration, the Fermi level pinning and the self-compensation effect. The Kondo anomalies in the low temperature resistivity at temperatures $T\leq 10\, {\rm K}$ and the $x$-dependence of the residual resistivity are also in good agreement with experiment. Our model also captures the qualitative aspects of the thermopower at higher temperatures $T>300\, {\rm K}$ for high dopings ($x>0.6%$) where transport is expected to be largely dominated by carriers in the heavy hole band of PbTe.