Electron transport and Goos-Hanchen shift in graphene with electric and magnetic barriers: optical analogy and band structure

TL;DR

This paper investigates how combined electric and magnetic barriers influence electron transport and band structure in graphene, revealing significant effects on transmission, reflection, and potential applications in graphene electronics.

Contribution

It extends the optical analogy to include scalar potentials, showing their profound impact on electron transmission and band structure in graphene with magnetic barriers.

Findings

Scalar potential significantly alters electron transmission.

Quantum Goos-Hänchen shift is calculated for total reflection.

Combined barriers modify the band structure near the Dirac point.

Abstract

Transport of massless Dirac fermions in graphene monolayers is analyzed in the presence of a combination of singular magnetic barriers and applied electrostatic potential. Extending a recently proposed (J Phys. Cond. Matt. Vol 21, 292204 (2009)) analogy between the transmission of light through a medium with modulated refractive index and electron transmission in graphene through singular magnetic barriers to the present case, we find the addition of a scalar potential profoundly changes the transmission. We calculate the quantum version of the Goos-H\"anchen shift that the electron wave suffers upon being totally reflected by such barriers. The combined electric and magnetic barriers substantially modify the band structure near the Dirac point. This affects transport near the Dirac point significantly and has important consequences for graphene-based electronics.