Non-conventional graphene superlattices as electron band-pass filters

Abstract

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.

Gaussian and Gaussian-pulsed-like Fermi velocity graphene structures

“…In short, to have electron passbands in GPL-FVGSLs a precise control of θ, η, PF, and N is needed. Here, it is also important to mention that the passbands of GPL-FVGSLs are similar to the ones of gapless non-conventional (Gaussian) graphene superlattices [19]. In both cases, there are residual oscillations that impede perfect flat transmission minibands.…”

“…In fact, after PF = 0.4 there are only three broad transmission minibands, see figures 2(d)-(f). The remaining aspect that we have to find out it is if the GPL profile can provide perfect or nearly perfect flat transmission bands or passbands as in the case of semiconductor and gapped graphene superlattices [1,2,19]. To do so, we can fix the angle of incidence and plot the transmission coefficient as a function of ξ max .…”

“…The studies of Gaussian superlattices in 2D materials are not the exception. There are various reports analyzing different properties of Gaussian superlattices in monolayer graphene [16][17][18][19][20]. For instance, the electronic band gap and the transport properties of graphene superlattices with a Gaussian electrostatic potential were studied [16].…”

“…In addition, by comparing the transmission of Gaussian and uniform magnetic graphene superlattices, it was deduced that the position of minibands and minigaps are insensitive to the variation of the strength of the Gaussian barriers. The passband filtering characteristics of gapless and gapped nonconventional graphene superlattices were also studied [19]. Gaussian, Lorentzian, Linear and Pöschl-Teller profiles were assessed.…”

Filtering electrons by mode coupling in finite semiconductor superlattices

“…From the experimental point of view, Gómez et al 19 modified the model by considering the Gaussian potential profile of barriers only, which was then verified with GaAs/Al x Ga 1−x As superlattices in experiments 20 . In addition, Gaussian superlattices can also be formed by electrostatic gating 21 . However, the doping level of barriers and the mass of nanoscale electrodes challenge the experiments of non-conventional superlattices.…”