Ab initio Informed Tight Binding Theory of Axis-dependent Conduction Polarity in Goniopolar Materials

We have recently shown that NaSn₂As₂ exhibits opposite conduction polarities along in-plane and cross-plane directions, defined as “goniopolarity”. On the lowest level of theory, we can show that this novel phenomenon originates from a special topology of the Fermi surface, which is essentially determined by the nature of the bonding states in this layered crystal. In this paper, we present an improved fundamental understanding of goniopolarity based on a novel formulation of goniopolarity within the tight-binding model. The tight-binding matrix elements are calculated from GW calculations based on Density Functional Theory (DFT) via maximally localized Wannier functions. Considering a minimum-basis set with sp³ orbitals for both Sn and As, , the 64 hopping integrals are evaluated. Within our model, we provide a new tight-binding based formulation for both Seebeck and Hall coefficients for NaSn₂As₂ and can show that critical ratios of hopping and on-site matrix elements exist that pose limits for goniopolarity to appear in materials. Based on that, additional candidate materials for goniopolarity can be proposed, and the design space for goniopolar materials in general will be defined.