Electronic Transport Calculation using Fermi Surface Geometry and Topology

The topology and geometry of the Fermi surface can be used to calculate transport properties. Haldane showed that the non-quantized anomalous Hall conductivity is purely a Fermi surface property. We show that the geometrical properties of the Fermi surface are fully described by a 3D discrete manifold. Using DFT and maximally localized Wannier functions, a tight-binding model was obtained and used to construct the Fermi surface as a discrete mesh. Geometric properties such as spin and Berry phase are resolved on the Fermi surface and the extrinsic and intrinsic conductivity are calculated as a surface integral over the Fermi surface. We demonstrate our approach works for the s-orbital tight-binding and the 2x2 Weyl semimetal models, iron, and platinum. Our results indicate that this method provides a robust and efficient way to calculate transport properties of various model Hamiltonians and real materials.