Electrostatic and magnetic fields in bilayer graphene

Abstract

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.

Double Barriers and Magnetic Field in Bilayer Graphene

“…These peaks can be attributed to the bound states formed in the double barrier structure [19]. That are correlated to the transmission gap and show a suppression due to cloak effect around E = V 3 , as it was the case for the single barrier [20]. In Figure 5 we show the different channels associated with the four transmissions as a function of the transverse wave vector k y and energy E. The height of the potential is set to V 2 = V 4 = 2.5 γ 1 and V 3 = 0 γ 1 .…”

“…) the transmission is zero and there are no resonances in the low regime energy E < V 3 . While resonances occur at non-normal incidence, which is equivalent to the case of a single barrier [20]. In the regime of energy V 3 < E < V 2 = V 4 , it is clearly seen that the peaks are due to the bound electron states [19].…”

“…We notice that the Dirac fermions exhibit transmission resonance in T + + channel in the region E < V 2 − γ 1 where the electrons propagate via α + . The cloak effect [24] appears in the region V 2 − γ 1 < E < V 2 for nearly normal incidence in the T + + , T + − and T − + channels, while for non-normal incidence it does not appear [18][19][20]. Introducing asymmetric double barrier structure in the presence of the magnetic field will break this equivalence such that T + − = T − + .…”

“…Recall that our eigenspinors can be obtained in similar way as we have done in [20] dealing with the same system but scattered by single barrier potential. To go further, it is convenient to use the matrix formalism such that the wave function in each region, denoted by the integer j, can then be writhen as…”

“…Based on previous investigations of Dirac fermions in bilayer graphene and in particular the work [18] in our recent work [19,20] we developed a theoretical framework to deal with bilayer graphene in the presence of a perpendicular electric and magnetic fields for single barrier. Our theoretical model is based on the well established tight binding Hamiltonian of graphite [21] and adopted the Slonczewski-Weiss-McClure parametrization of the relevant intralayer and interlayer couplings [22] to model the bilayer graphene system.…”