Edge currents in the absence of edges

TL;DR

This paper studies a charged particle in a magnetic field interacting with a periodic obstacle array, revealing continuous spectrum bands and transport phenomena despite Landau level degeneracy.

Contribution

It demonstrates the existence of continuous spectrum bands and transport in a system with Landau levels, analyzing band functions and probability currents.

Findings

Landau levels are infinitely degenerate eigenvalues.

Between Landau levels, the system exhibits absolutely continuous spectrum bands.

The system shows transport along the obstacle array.

Abstract

We investigate a charged two-dimensional particle in a homogeneous magnetic field interacting with a periodic array of point obstacles. We show that while Landau levels remain to be infinitely degenerate eigenvalues, between them the system has bands of absolutely continuous spectrum and exhibits thus a transport along the array. We also compute the band functions and the corresponding probability current.