We compute the transmission probability through rectangular potential barriers and p-n junctions in the presence of a magnetic and electric fields in bilayer graphene taking into account contributions from the full four bands of the energy spectrum. For energy E higher than the interlayer coupling γ 1 (E > γ 1 ) two propagation modes are available for transport giving rise to four possible ways for transmission and reflection coefficients. However, when the energy is less than the height of the barrier the Dirac fermions exhibit transmission resonances and only one mode of propagation is available for transport. We study the effect of the interlayer electrostatic potential denoted by δ and variations of different barrier geometry parameters on the transmission probability.
We study the Goos-Hänchen like shifts for Dirac fermions in graphene scattered by double barrier structures. After obtaining the solution for the energy spectrum, we use the boundary conditions to explicitly determine the Goos-Hänchen like shifts and the associated transmission probability. We analyze these two quantities at resonances by studying their main characteristics as a function of the energy and electrostatic potential parameters. To check the validity of our computations we recover previous results obtained for a single barrier under appropriate limits.
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.
We study the electronic transport through np and npn junctions for AAA-stacked trilayer graphene. Two kinds of gates are considered where the first is a single gate and the second is a double gate. After obtaining the solutions for the energy spectrum, we use the transfer matrix method to determine the three transmission probabilities for each individual cone τ = 0, ±1. We show that the quasiparticles in AAA-stacked trilayer graphene are not only chiral but also labeled by an additional cone index τ . The obtained bands are composed of three Dirac cones that depend on the chirality indexes. We show that there is perfect transmission for normal or near normal incidence, which is a manifestation of the Klein tunneling effect. We analyze also the corresponding total conductance, which is defined as the sum of the conductance channels in each individual cone. Our results are numerically discussed and compared with those obtained for ABA-and ABC-stacked trilayer graphene.
The quantum Goos-Hänchen shifts of the transmitted electron beam through an AA-stacked bilayer graphene superlattices is investigated. We found that the band structures of graphene superlattices can have more than one Dirac point, their locations do not depend on the number of barriers. It was revealed that any n-barrier structure is perfectly transparent at normal incidence around the Dirac points created in the superlattices. We showed that the Goos-Hänchen shifts display sharp peaks inside the transmission gap around two Dirac points (E = V B + τ , E = V W + τ ), which are equal to those of transmission resonances. The obtained Goos-Hänchen shifts are exhibiting negative as well as positive behaviors and strongly depending on the location of Dirac points. It is observed that the maximum absolute values of the shifts increase as long as the number of barriers is increased. Our analysis is done by considering four cases: single, double barriers, superlattices without and with defect.
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