Quasilinear dispersion in electronic band structure and high Seebeck coefficient in CuFeS2-based thermoelectric materials

The earth-abundant natural mineral chalcopyrite $\mathrm{CuFe}{\mathrm{S}}_{2}$ is a potential $n$-type thermoelectric material because of its large Seebeck coefficient at high carrier concentrations. For a long time, the large Seebeck coefficient of $\mathrm{CuFe}{\mathrm{S}}_{2}$ has been attributed to a large electron effective mass, but the reasons for this and the unusual carrier concentration dependent behavior have rarely been discussed. Here, we systematically investigated the special transport behavior of $\mathrm{CuFe}{\mathrm{S}}_{2}$ and found the classical parabolic band model to be inadequate in explaining it. Our experimental and theoretical studies indicate that there are two flat electronic pockets at the \ensuremath{\Gamma} and $Z$ points of the Brillouin zone near the conduction band edge of $\mathrm{CuFe}{\mathrm{S}}_{2}$ that dominate the charge transport. These electronic pockets result from nonparabolic quasilinearly dispersing bands that give rise to a linear wave vector dependent energy ($E\ensuremath{\sim}k$) and a carrier density dependent effective mass (${m}^{*}\ensuremath{\sim}{m}_{0}{n}^{1/3}$). Such a strong carrier concentration dependent carrier effective mass results in the high Seebeck coefficient of $\mathrm{CuFe}{\mathrm{S}}_{2}$ compound under a large carrier density. The work demonstrates that quasilinearly dispersing bands can give strongly enhanced Seebeck coefficient, and could be useful in optimizing the properties of thermoelectric materials.