Orbital Hall Effect Accompanying Quantum Hall Effect: Landau Levels Cause Orbital Polarized Edge Currents

TL;DR

This paper demonstrates that the quantum Hall effect in two-dimensional systems also induces an orbital Hall effect, with orbital polarized edge states and a quadratic magnetic field dependence, revealing a new aspect of topological electronic behavior.

Contribution

It introduces the orbital Hall effect accompanying the quantum Hall effect, highlighting orbital polarization of edge states and their magnetic field dependence, a novel insight into topological phenomena.

Findings

Orbital Hall effect coexists with quantum Hall effect.

Orbital Hall resistivity scales quadratically with magnetic field.

Edge states are orbital polarized similar to quantum anomalous Hall systems.

Abstract

The quantum Hall effect emerges when two-dimensional samples are subjected to strong magnetic fields at low temperatures: Topologically protected edge states cause a quantized Hall conductivity in multiples of $e^2/h$. Here we show that the quantum Hall effect is accompanied by an orbital Hall effect. Our quantum mechanical calculations fit well the semiclassical interpretation in terms of "skipping orbits". The chiral edge states of a quantum Hall system are orbital polarized akin to a hypothetical orbital version of the quantum anomalous Hall effect in magnetic systems. The orbital Hall resistivity scales quadratically with the magnetic field making it the dominant effect at high fields.