Magnetic Kronig-Penney model for Dirac electrons in single-layer graphene

TL;DR

This paper analytically investigates the energy spectrum and transmission of Dirac electrons in a magnetic superlattice on graphene, revealing beam collimation and optical analogies, with implications for electronic device control.

Contribution

It introduces a magnetic Kronig-Penney model for Dirac electrons in graphene, providing analytical solutions and exploring novel electron collimation effects.

Findings

Analytical energy spectrum for Dirac electrons in magnetic superlattice

Beam collimation along the superlattice direction

Optical media analogy with spatially varying refractive index

Abstract

The properties of Dirac electrons in a magnetic superlattice (SL) on graphene consisting of very high and thin (delta-function) barriers are investigated. We obtain the energy spectrum analytically and study the transmission through a finite number of barriers. The results are contrasted with those for electrons described by the Schrodinger equation. In addition, a collimation of an incident beam of electrons is obtained along the direction perpendicular to that of the SL. We also highlight the analogy with optical media in which the refractive index varies in space.