Transport properties of graphene under periodic and quasiperiodic magnetic superlattices

We study the transmission of Dirac electrons through the one-dimensional periodic, Fibonacci, and Thue-Morse magnetic superlattices (MS), which can be realized by two different magnetic blocks arranged in certain sequences in graphene. The numerical results show that the transmission as a function of incident energy presents regular resonance splitting effect in periodic MS due to the split energy spectrum. For the quasiperiodic MS with more layers, they exhibit rich transmission patterns. In particular, the transmission in Fibonacci MS presents scaling property and fragmented behavior with self-similarity, while the transmission in Thue-Morse MS presents more perfect resonant peaks which are related to the completely transparent states. Furthermore, these interesting properties are robust against the profile of MS, but dependent on the magnetic structure parameters and the transverse wave vector.