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

TL;DR

This paper investigates the resistivity and thermopower in strongly compensated semiconductors and topological insulators, revealing how compensation affects activation energy, Fermi level position, and the transition to variable range hopping conduction.

Contribution

It provides a detailed theoretical analysis of resistivity and thermopower in strongly compensated semiconductors, extending previous models to include the effects of compensation on Fermi level and conduction mechanisms.

Findings

Activation energy scales as 0.3 times the energy difference between conduction band bottom and Fermi level.

Peltier energy is approximately half of the activation energy, indicating smaller thermopower.

Transition from activated conduction to variable range hopping occurs at a characteristic temperature depending on compensation.

Abstract

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 $\Delta =0.3 (E_g/2)$, 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 $1-K$.