Quantization of edge currents along magnetic barriers and magnetic guides

TL;DR

This paper studies the quantization and stability of edge conductance in particles influenced by magnetic barriers and guides, demonstrating quantization, stability under perturbations, and establishing a sum rule.

Contribution

It proves the quantization and stability of edge conductance for magnetic barriers and guides, extending understanding of magnetic effects on edge currents.

Findings

Quantization of edge conductance in magnetic barriers and guides

Stability of quantized conductance under magnetic perturbations

A sum rule relating different edge conductances

Abstract

We investigate the edge conductance of particles submitted to an Iwatsuka magnetic field, playing the role of a purely magnetic barrier. We also consider magnetic guides generated by generalized Iwatsuka potentials. In both cases we prove quantization of the edge conductance. Next, we consider magnetic perturbations of such magnetic barriers or guides, and prove stability of the quantized value of the edge conductance. Further, we establish a sum rule for edge conductances. Regularization within the context of disordered systems is discussed as well.