Magnetic strip waveguides

TL;DR

This paper studies the spectral properties of a 2D charged particle in a magnetic field with a finite strip, deriving conditions for spectrum continuity and analyzing the number of spectral gaps, supported by numerical simulations.

Contribution

It introduces new sufficient conditions for absolute continuity of the spectrum in the local Iwatsuka model and examines the finiteness of spectral gaps.

Findings

Derived two new conditions for spectrum absolute continuity.

Showed that the number of spectral gaps is generally finite.

Numerically analyzed the case of zero magnetic field in the strip.

Abstract

We analyze the spectrum of the "local" Iwatsuka model, i.e. a two-dimensional charged particle interacting with a magnetic field which is homogeneous outside a finite strip and translationally invariant along it. We derive two new sufficient conditions for absolute continuity of the spectrum. We also show that in most cases the number of open spectral gaps of the model is finite. To illustrate these results we investigate numerically the situation when the field is zero in the strip being screened, e.g. by a superconducting mask.