Electron transmission through different non-conventional (non-uniform barrier height) gated and gapped graphene superlattices (GSLs) is studied. Linear, Gaussian, Lorentzian and Pöschl-Teller superlattice potential profiles have been assessed. A relativistic description of electrons in graphene as well as the transfer matrix method have been used to obtain the transmission properties. We find that it is not possible to have perfect or nearly perfect pass bands in gated GSLs. Regardless of the potential profile and the number of barriers there are remanent oscillations in the transmission bands. On the contrary, nearly perfect pass bands are obtained for gapped GSLs. The Gaussian profile is the best option when the number of barriers is reduced, and there is practically no difference among the profiles for large number of barriers. We also find that both gated and gapped GSLs can work as omnidirectional band-pass filters. In the case of gated Gaussian GSLs the omnidirectional range goes from −50° to 50° with an energy bandwidth of 55 meV, while for gapped Gaussian GSLs the range goes from −80° to 80° with a bandwidth of 40 meV. Here, it is important that the energy range does not include remanent oscillations. On the light of these results, the hole states inside the barriers of gated GSLs are not beneficial for band-pass filtering. So, the flatness of the pass bands is determined by the superlattice potential profile and the chiral nature of the charge carriers in graphene. Moreover, the width and the number of electron pass bands can be modulated through the superlattice structural parameters. We consider that our findings can be useful to design electron filters based on non-conventional GSLs.
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