Qualitative analysis of magnetic waveguides for two-dimensional Dirac fermions

TL;DR

This paper investigates how magnetic fields can confine two-dimensional Dirac fermions in waveguides, providing criteria for their band structure based on magnetic field behavior, applicable even when analytical solutions are unavailable.

Contribution

It introduces practical criteria for Dirac fermion confinement in magnetic waveguides, enhancing understanding of their band structures in complex systems.

Findings

Criteria for existence or absence of energy bands based on magnetic field behavior

Application of results to systems with magnetic fields from wires or strips

Insights into confinement without analytical solutions

Abstract

We focus on the confinement of two-dimensional Dirac fermions within the waveguides created by realistic magnetic fields. Understanding of their band structure is of our main concern. We provide easily applicable criteria, mostly depending only on the asymptotic behavior of the magnetic field, that can guarantee existence or absence of the energy bands and provide valuable insight into the systems where analytical solution is impossible. The general results are employed in specific systems where the waveguide is created by the magnetic field of a set of electric wires or magnetized strips.