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Gapless bilayer graphene (GBG), like monolayer graphene, is a material systemwith unique properties, such as anti-Klein tunneling and intrinsic Fanoresonances. These properties rely on the gapless parabolic dispersion relationand the chiral nature of bilayer graphene electrons. In addition, propagatingand evanescent electron states coexist inherently in this material, giving riseto these exotic properties. In this sense, bilayer graphene is unique, since inmost material systems in which Fano resonance phenomena are manifested anexternal source that provides extended states is required. However, from anumerical standpoint, the presence of evanescent-divergent states in theeigenfunctions linear superposition representing the Dirac spinors, leads to anumerical degradation (the so called $\Omega$d problem) in the practicalapplications of the standard Coefficient Transfer Matrix ($K$) method used tostudy charge transport properties in Bilayer Graphen based multi-barriersystems. We present here a straightforward procedure based in the hybridcompliance-stiffness matrix method ($H$) that can overcome this numericaldegradation. Our results show that in contrast to standard matrix method, theproposed $H$ method is suitable to study the transmission and transportproperties of electrons in GBG superlattice since it remains numerically stableregardless the size of the superlattice and the range of values taken by theinput parameters: the energy and angle of the incident electrons, the barrierheight and the thickness and number of barriers. We show that the matrixdeterminant can be used as a test of the numerical accuracy in realcalculations.

Hybrid matrix method for stable numerical analysis of the propagation of Dirac electrons in gapless bilayer graphene superlattices