We devise a methodology for charge, heat, and entropy transport driven by carriers with finite lifetimes. Combining numerical simulations with analytical expressions for low temperatures, we establish a comprehensive and thermodynamically consistent phenomenology for transport properties in semiconductors. We demonstrate that the scattering rate (inverse lifetime) is a relevant energy scale: It causes the emergence of several characteristic features in each transport observable. The theory is capable to reproduce, with only a minimal input electronic structure, the full temperature profiles measured in correlated narrow-gap semiconductors. In particular, we account for the previously elusive low-$T$ saturation of the resistivity and the Hall coefficient, as well as the (linear) vanishing of the Seebeck and Nernst coefficients in systems such as ${\mathrm{FeSb}}_2, {\mathrm{FeAs}}_2, {\mathrm{RuSb}}_2$, and ${\mathrm{FeGa}}_3$.

• Received 14 December 2021
• Accepted 9 February 2022

DOI:https://doi.org/10.1103/PhysRevB.105.085139