Transmission and Goos-H\"anchen like Shifts through a Graphene Double Barrier in an Inhomogeneous Magnetic Field

TL;DR

This paper investigates electron transport in graphene with a double barrier and inhomogeneous magnetic field, revealing magnetic barriers' ability to confine Dirac fermions and linking transmission with Goos-H"anchen like shifts.

Contribution

It introduces a detailed analysis of magnetic barriers in graphene, showing their unique confinement properties and correlation with Goos-H"anchen shifts, which differ from electrostatic barriers.

Findings

Transmission is forbidden for certain energy ranges.

Magnetic barriers can confine Dirac fermions.

Transmission properties correlate with Goos-H"anchen like shifts.

Abstract

We studied the transport properties of electrons in graphene as they are scattered by a double barrier potential in the presence of an inhomogeneous magnetic field. We computed the transmission coefficient and Goos-H\"anchen like shifts for our system and noticed that transmission is not allowed for certain range of energies. In particular, we found that, in contrast to the electrostatic barriers, the magnetic barriers are able to confine Dirac fermions. We also established some correlation between the electronic transmission properties of Dirac fermions with the Goos-H\"anchen like shifts, as reflected in the numerical data.