Magnetic transport in laterally coupled layers

TL;DR

This paper investigates magnetic transport in a system of two coupled layers with a perpendicular magnetic field, analyzing spectral properties and the effects of layer geometry on transport characteristics.

Contribution

It introduces a detailed spectral analysis of coupled layered systems with different geometries, revealing the conditions for flat bands and their properties.

Findings

Spectrum includes absolutely continuous and flat bands.

Flat bands occur only when layer widths are commensurate.

Layer geometry significantly influences spectral features.

Abstract

We discuss magnetic transport in the system of two adjacent hard-wall layers exposed to a homogeneous field perpendicular to the layer plane and coupled laterally through a strip-shaped window in the common boundary. We show that the spectrum is a combination of absolutely continuous and flat bands, the latter being present only if the widths of the two layers are commensurate, and derive their properties. We also analyze the one-sided geometry in which the barrier separating the two layers is a halfplane.