Local spin Hall conductivity

TL;DR

This paper derives a local expression for the spin Hall conductivity in two-dimensional systems, enabling analysis of inhomogeneous regions like interfaces and surfaces, which was previously challenging.

Contribution

It introduces a novel local formulation of spin Hall conductivity applicable to heterogeneous and bounded 2D systems, extending beyond traditional periodic calculations.

Findings

Applicable to systems with open and periodic boundaries

Enables local analysis of spin Hall effects in inhomogeneous regions

Provides a theoretical foundation for studying interfaces and surfaces

Abstract

The spin Hall conductivity is usually calculated for periodic solids, while the knowledge of local contributions from inhomogeneous regions like interfaces or surfaces would be desirable. In this work we derive a local expression for the spin Hall conductivity of two-dimensional systems in analogy to the local anomalous Hall conductivity discussed recently. Our approach is applicable to heterogeneous fully bounded systems and nanoribbons with both open and periodic boundary conditions.