Thermoelectric properties in semimetals with inelastic electron-hole scattering

TL;DR

This paper provides a detailed theoretical analysis of thermoelectric effects in semimetals, highlighting how inelastic electron-hole scattering influences transport properties and thermoelectric efficiency, especially in uncompensated semimetals.

Contribution

It advances understanding by precisely treating inelastic electron-hole scattering beyond the relaxation time approximation and linking it to thermoelectric properties.

Findings

Seebeck coefficient depends on Coulomb screening length and Lorenz ratio.

Deviations from compensation increase the Seebeck coefficient.

Uncompensated semimetals can achieve high thermoelectric efficiency.

Abstract

We present systematic theoretical results on thermoelectric effects in semimetals based on the variational method of the linearized Boltzmann equation. Inelastic electron-hole scattering is known to play an important role in the unusual transport of semimetals, including the broad $T^2$ temperature dependence of the electrical resistivity and the strong violation of the Wiedemann-Franz law. By treating the inelastic electron-hole scattering more precisely beyond the relaxation time approximation, we show that the Seebeck coefficient when compensated depends on the screening length of the Coulomb interaction as well as the Lorenz ratio (the ratio of thermal to electric conductivity due to electrons divided by temperature). It is found that deviations from the compensation condition significantly increase the Seebeck coefficient, along with crucial suppressions of the Lorenz ratio. The result indicates that uncompensated semimetals with the electron-hole scattering have high thermoelectric efficiency when the phonon contribution to thermal conductivity is suppressed.