Abstract
Magnetic field effects have been instrumental to unveil several exotic phenomena in two-dimensional (2D) materials. Here, we show that graphene exhibits self-similar transport once the material is nanostructured with a magnetic field in complex fashion. In specific, when magnetic barriers are arranged according to the Cantor set rules. In this study, the charge carriers are described as quantum relativistic particles through an effective low-energy Hamiltonian. The transmission, transport and thermoelectric properties are computed with the transfer matrix method, the Landauer–Büttiker formalism and the Cutler–Mott formula, respectively. Self-similarity is reflected in the conductance spectra and Seebeck coefficient for different structural parameters such as generation number, the intensity of the magnetic field, the height of the barrier and the total length of the system. Moreover, well-defined scaling rules, which described fairly good the scalability between self-similar patterns, are obtained. We also compare the self-similar patterns of magnetic complex structures with the corresponding ones to magnetic-electric complex structures, finding better scalability for the former. It is worth mentioning that as far as we have corroborated the breaking symmetry associated to the magnetic field is paramount for the self-similar transport. So, magnetic complex structures constitute an excellent option to corroborate the peculiar phenomenon of self-similar transport.
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