Discrete Quantum Geometry and Intrinsic Spin Hall Effect

TL;DR

This paper introduces a numerical method to analyze the quantum geometry of the Fermi surface using a 3D discrete quantum manifold, enabling precise calculations of intrinsic Hall effects even near singularities.

Contribution

The paper presents a novel discrete quantum geometric approach that accurately computes spin-resolved Hall conductivities and local Fermi surface properties, overcoming previous singularity issues.

Findings

Accurately computes anomalous and spin Hall conductivities in Weyl semimetals.

Demonstrates robustness near Fermi level singularities.

Validates method with ab-initio calculations of zincblende GaAs.

Abstract

We show that the quantum geometry of the Fermi surface can be numerically described by a 3-dimensional discrete quantum manifold. This approach not only avoids singularities in the Fermi sea, but it also enables the precise computation of the intrinsic Hall conductivity resolved in spin, as well as any other local properties of the Fermi surface. The method assures numerical accuracy when the Fermi level is arbitrarily close to singularities, and it remains robust when Kramers degeneracy is protected by symmetry. The approach is demonstrated by calculating the anomalous Hall and spin Hall conductivities of a 2-band lattice model of a Weyl semimetal and a full-band ab-initio model of zincblende GaAs.