Local equilibrium charge and spin currents in two-dimensional topological systems

TL;DR

This paper investigates local charge and spin currents in two-dimensional topological systems under equilibrium and nonequilibrium conditions, revealing how magnetic fields and spin-orbit interactions influence these currents.

Contribution

It provides general expressions for local electronic currents in topological systems, enabling analysis of charge, spin, valley, and orbital currents under various conditions.

Findings

Magnetic fields induce equilibrium charge currents in the quantum Hall regime.

Spin-orbit interaction generates local equilibrium spin currents in the quantum spin Hall regime.

The developed framework allows comprehensive analysis of local currents in topological materials.

Abstract

We study the equilibrium and nonequilibrium electronic transport properties of multiprobe topological systems using a combination of the Landauer-B\"uttiker approach and nonequilibrium Green's functions techniques. We obtain general expressions for both nonequilibrium and equilibrium local electronic currents that, by suitable projections, allow one to compute charge, spin, valley, and orbital currents. We show that external magnetic fields give rise to equilibrium charge currents in mesoscopic system and study the latter in the quantum Hall regime. Likewise, a spin-orbit interaction leads to local equilibrium spin currents, that we analyze in the quantum spin Hall regime.