Anomalously small resistivity and thermopower of strongly compensated semiconductors and topological insulators

In the recent paper, we explained why the maximum bulk resistivity of topological insulators (TIs) such as Bi2Se3 is so small [B. Skinner, T. Chen, and B. I. Shklovskii, Phys. Rev. Lett. 109, 176801 (2012)]. Using the model of completely compensated semiconductor we showed that when the Fermi level is pinned in the middle of the gap the activation energy of resistivity is Delta = 0.3(E-g/2), where E-g is the semiconductor gap. In this paper, we consider a strongly compensated n-type semiconductor. We find the position of the Fermi level mu calculated from the bottom of the conduction band E-c and the activation energy of resistivity Delta as a function of compensation K, and show that Delta = 0.3(E-c - mu) holds at any 0 < 1 - K <= 1. In the same range of relatively high temperatures, the Peltier energy (heat) Pi is even smaller: Pi similar or equal to Delta/2 = 0.15(E-c - mu). We also show that at low temperatures, the activated conductivity crosses over to variable range hopping (VRH) and find the characteristic temperature of VRH, T-ES, as a function of K. DOI: 10.1103/PhysRevB.87.165119