Transport properties through graphene-based fractal and periodic magnetic barriers

We investigate the transmission of electrons in a single layer graphene system subjected to nanoscale magnetic barriers and wells arranged in the Cantor pre-fractal and the finite periodic distribution. We find that the angular threshold and angular asymmetry of the transmission spectra are closely related to the ratio between the magnitude of the vector potential and the incident energy (|A|/E), which also determine the number and width of the resonant domains for the finite periodically magnetic modulation and the splitting features for the pre-fractal distribution. For the finite periodically magnetic modulation, the position, magnitude, and interval of the oscillatory domains in the conductance spectra are determined by the value |A|. However, due to the disorder of the pre-fractal distribution, the oscillation of the conductance spectrum is less regular compared to the corresponding one of the finite periodic distribution. We also find that the conductance approaches the classical limit in the high-Fermi-energy region but exceeds it in the low-Fermi-energy region, and the critical point of the two regions is negatively correlated with the magnitude of the vector potential.