Landau Level Gap Reduction at Abrupt Edges

TL;DR

This paper investigates how abrupt edges in a magnetic field influence Landau level gaps, revealing that sharp barriers cause significant gap reduction, which diminishes with smoother barriers unless the gradient exceeds a certain threshold.

Contribution

It demonstrates the conditions under which Landau level gap reduction occurs at edges, emphasizing the importance of barrier sharpness and gradient in magnetic systems.

Findings

Sharp barriers cause significant Landau level gap reduction.

Smoother barriers reduce the effect unless the gradient exceeds a critical value.

The effect varies with barrier shape and configuration.

Abstract

For an electron localized near a finite rectangular step potential under strong magnetic field we found a profound local reduction of the gap between neighbouring Landau levels. We investigate under what conditions the effect persists when the barrier gets smoother. The conclusion is that to get a substantial gap reduction the barrier gradient has to be larger than $\hbar\omega_c/a_L$ ($a_L$ is the magnetic length). The sensitivity of the gap reduction is illustrated using tilted and multiple step barriers and finite stripe configurations.