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)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 $Δ=0.3 (E_g/2)$, where $E_g$ 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 $Δ= 0.3 (E_c-μ)$ holds at any $1-K \ll 1$. At the same time Peltier energy (heat) $Π$ is even smaller: $Π\simeq 0.5Δ= 0.15(E_c - μ)$. We also show that at low temperatures the activated conductivity crosses over to variable range hopping (VRH) and find the characteristic temperature of VRH, $T_{ES}$, as a function of $1-K$.

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