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The transmission coefficients (TCs) and angularly averaged conductance for quasi-particle transport are studied for a bilayer graphene superlattice arranged according to the Fibonacci sequence. The transmission is found to be symmetric around the superlattice growth direction and highly sensitive to the direction of the quasi-particle incidence. The transmission spectra are fragmented and appear in groups due to the quasiperiodicity of the system. The average conductance shows interesting structures sharply dependent on the height of the potential barriers between two graphene strips. The low-energy conductance due to Klein transmission is substantially modified by the inclusion of quasi-periodicity in the system.

The well-known asymmetric Fano resonances that results from the quantum interference between the discrete and the continuum states are noted for the first time in the ballistic transmission spectrum of the bilayer graphene tunneling structures. This unconventional tunneling transmission, in stark contrast to the monolayer graphene and to the conventional heterostructures, arises due to the quadratic dispersion of the chiral charge carriers. If the Klein tunneling (the phenomenon for normal incidence) is an unusual characteristic of the massless chiral particles, then the Fano tunneling (the phenomenon for low glancing incidence) would be the specialty for the massive chiral particles. The characteristic features of the Fano line shape are found to be highly sensitive to the direction of incidence of the charge carriers, the applied homogeneous electric field, and to the barrier height. The sharp anti-resonance at the center of the tunneling band arising due to the destructive interference between the electron and the holelike states could probably be responsible for the high negative differential conductance (NDC) in the bilayer graphene. The tunneling conductance in the double barrier structure exhibits a resonant peak with a sharp NDC region for the Fermi energy less than or equal to half of the barrier height. The present findings might have great implications in the preparation of NDC-based devices using bilayer graphene nanostructures.

The kinetic transport of electrons through graphene magnetic barriers is studied theoretically in presence of an external time harmonic scalar potential. The transmission coefficients are calculated in the framework of the non-perturbative Floquet theory using transfer matrix method. The time dependent scalar potential is found to suppress the usual Fabry-Perot oscillations occurring in the transmission through a constant vector potential barrier (corresponding to two oppositely directed δ-function magnetic barriers). Two types of asymmetric Fano resonances (FR) are noted and are discussed for the narrow barrier structure. One of them arises due to the oscillatory mode while the other due to the evanescent mode of the electron wave inside the barrier. In contrast, the oscillating field favours the transmission for rectangular magnetic barrier structure and also exhibits the FR due to the presence of bound state inside the barrier. The characteristic Fano line shape can be tuned by varying the amplitude of the oscillating potential. The detection of such FRs' offers an efficient tool for the identification of the quasi-bound and evanescent extended states inside the barrier not reported in the literature so far, for the case of graphene magnetic barrier structures.

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