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Anisotropic Scattering in Goniopolar Metal NaSn$_2$As$_2$

Recent experimental discoveries in axis-dependent conduction polarity, or goniopolarity, have observed that the charge carriers can conduct like either electrons or holes depending on the crystallographic direction they travel along in layered compounds such as NaSn$_2$As$_2$. To elucidate this unusual transport behavior, we present an ab initio study of electron scattering in such systems. We study different microscopic scattering mechanisms in NaSn$_2$As$_2$ and present the electron-phonon scattering time distribution on its Fermi surface in momentum space, the anisotropy of which is proposed to be the origin of the axis-dependent conduction polarity. Further, we obtain the overall anisotropic lifetime tensors in real space at different electron chemical potentials and temperatures and discuss how they contribute to the macroscopic thermopower. While we find that the contribution of the in-plane and cross plane lifetimes exhibits a similar trend, the concave portion of the Fermi surface alters the electron motion significantly in the presence of a magnetic field, thus flipping the conduction polarity as measured via the Hall effect. Our calculations and analysis of NaSn$_2$As$_2$ also suggests the strong possibility of hydrodynamic electron flow in the system. Finally, our work has implications for anisotropic electron lifetimes in a broad class of goniopolar materials and provides key, general insights into electron scattering on open Fermi surfaces.