1212.4183 (Tianran Chen et al.)

Anomalously small resistivity and thermopower of strongly compensated
semiconductors and topological insulators    [PDF]

Tianran Chen, B. I. Shklovskii

In the recent paper we explained why the maximum bulk resistivity of topological insulators (TIs)is so small \cite{Brian2012}. 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 $\Delta =0.3 (E_g/2)$, where $E_g$ is the semiconductor gap. In this paper, we consider strongly compensated $n$-type semiconductor. We find position of the Fermi level $\mu$ calculated from the bottom of the conduction band and the activation energy of the resistivity $\Delta$ as a function of compensation $K$, and show that $\Delta = 0.3 (E_c-\mu) $ holds at any $1-K \ll 1$. At the same time Peltier energy (heat) $\Pi$ is even smaller: $\Pi \simeq 0.5\Delta = 0.15(E_c - \mu)$. 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 $1-K$.

View original: http://arxiv.org/abs/1212.4183