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Prototypical many-body signatures in transport properties of semiconductors

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 coefficient in systems, such as FeSb$_2$, FeAs$_2$, RuSb$_2$ and FeGa$_3$.