Edge Modes Waves in Superlattices in Quantum Hall Effect Regime

TL;DR

This paper investigates edge wave propagation in superlattices of 2D electron gases under quantum Hall conditions, deriving boundary relations and dispersion characteristics, revealing non-dispersive modes and a Meissner-like effect.

Contribution

It introduces a novel theoretical framework for edge wave modes in superlattice structures, including boundary charge-current relations and dispersion analysis, extending previous models.

Findings

Edge modes have no dispersion at any frequency.

Derived boundary relations similar to London equations.

Identified a Meissner-like effect at the boundary.

Abstract

The wave propagation of edge modes in a superlattice of 2D electron Gases in quantum Hall regime is investigated. After introducing surfaces charge and current densities at the edge, the Maxwell equations are solved for waves running along the boundary. The constitutive relations expressing the edge charge and current densities in terms of the fields at the boundary are derived. One of them is similar to the London equation for superconductor currents. The dispersion relation and wave polarizations for the momenta region $w/c<k$ are also obtained for propagation along the borderlines of the electron gases. It follows that the modes have no dispersion at any frequency. The static limit solutions complete the definition at the boundary of the formerly determined interior field configurations showing a Meissner like effect. The results underline that various of the current theoretical approaches to edge excitations could be appropriate for superlattice structures but can fail to describe standard planar samples.