Magnetic field barriers in graphene: an analytically solvable model

TL;DR

This paper presents an exactly solvable model for carrier dynamics in graphene under inhomogeneous magnetic fields, revealing spectral properties and transmission resonances with potential applications in graphene-based electronic devices.

Contribution

It introduces an analytically solvable model using supersymmetric quantum mechanics for magnetic barriers in graphene, detailing spectral evolution and resonance conditions.

Findings

Bound spectra characterized by a few bands for narrow barriers

Spectral evolution into Landau levels as barrier widens

Analytical formula for transmission coefficient and resonance conditions

Abstract

We study the dynamics of carriers in graphene subjected to an inhomogeneous magnetic field. For a magnetic field with an hyperbolic profile the corresponding Dirac equation can be analyzed within the formalism of supersymmetric quantum mechanics, and leads to an exactly solvable model. We study in detail the bound spectra. For a narrow barrier the spectra is characterized by a few bands, except for the zero energy level that remains degenerated. As, the width of the barrier increases we can track the bands evolution into the degenerated Landau levels. In the scattering regime a simple analytical formula is obtained for the transmission coefficient, this result allow us to identify the resonant conditions at which the barrier becomes transparent.