Double Barriers and Magnetic Field in Bilayer Graphene

TL;DR

This paper investigates how Dirac fermions transmit through double barriers in bilayer graphene under a magnetic field, revealing resonance behaviors, absence of Klein tunneling at normal incidence, and effects of magnetic and electrostatic parameters.

Contribution

It provides a comprehensive analysis of transmission probabilities considering full four-band spectrum and boundary conditions, highlighting new resonance phenomena and the impact of magnetic fields in bilayer graphene.

Findings

Transmission resonances occur below the barrier height.

No Klein tunneling at normal incidence in AB-stacked bilayer graphene.

Magnetic field and barrier parameters significantly influence transmission.

Abstract

We study the transmission probability in an AB-stacked bilayer graphene of Dirac fermions scattered by a double barrier structure in the presence of a magnetic field. We take into account the full four bands of the energy spectrum and use the boundary conditions to determine the transmission probability. Our numerical results show that for energies higher than the interlayer coupling, four ways for transmission probabilities are possible while for energies less than the height of the barrier, Dirac fermions exhibits transmission resonances and only one transmission channel is available. We show that, for AB-stacked bilayer graphene, there is no Klein tunneling at normal incident. We find that the transmission displays sharp peaks inside the transmission gap around the Dirac point within the barrier regions while they are absent around the Dirac point in the well region. The effect of the magnetic field, interlayer electrostatic potential and various barrier geometry parameters on the transmission probabilities are also discussed.