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

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In the recent paper we explained why the maximum bulk resistivity of topological insulators (TIs)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 Fermi level is pinned in the middle of the gap the activation energy of resistivity Δ=0.3 (Eg/2), where Eg is the semiconductor gap. In this paper, we consider strongly compensated n-type semiconductor. We find position of the Fermi level μ calculated from the bottom of the conduction band and the activation energy of the resistivity Δ as a function of compensation K, and show that Δ= 0.3 (Ec-μ) holds at any 1-K ≪ 1. At the same time Peltier energy (heat) Π is even smaller: Π≃ 0.5Δ= 0.15(Ec - μ). We also show that at low temperatures the activated conductivity crosses over to variable range hopping (VRH) and find the characteristic temperature of VRH, TES, as a function of 1-K.