Extended states in random dimer gated graphene superlattices.

Ordered and disordered semiconductor superlattices represent structures with completely opposed properties. For instance, ordered superlattices exhibit extended Bloch-like states, while disordered superlattices present localized states. These characteristics lead to higher conductance in ordered superlattices compared to disordered ones. Surprisingly, disordered dimer superlattices, which consist of two types of quantum wells with one type always appearing in pairs, exhibit extended states. The percentage of dissimilar wells does not need to be large to have extended states. Furthermore, the conductance is intermediate between ordered and disordered superlattices. In this work, we explore disordered dimer superlattices in graphene. We calculate the transmission and transport properties using the transfer matrix method and the Landauer-Büttiker formalism, respectively. We identify and discuss the main energy regions where the conductance of random dimer superlattices in graphene is intermediate to that of ordered and disordered superlattices. We also analyze the resonant energies of the double quantum well cavity and the electronic structure of the host gated graphene superlattice (GGSL), finding that the coupling between the resonant energies and the superlattice energy minibands gives rise to the extended states in random dimer GGSLs.

Gaussian and Gaussian-pulsed-like Fermi velocity graphene structures.

Gaussian and Gaussian-related structures are quite attractive due to its versatility to modulate the electronic transport, including its possibility as electron filters. Here, we show that these non-conventional profiles are not the exception when dealing with Fermi velocity barriers in monolayer graphene. In particular, we show that Gaussian Fermi velocity graphene barriers (G-FVGBs) and Gaussian-pulsed-like Fermi velocity graphene superlattices (GPL-FVGSLs) can serve as electron band-pass filters and oscillating conductance structures. We reach this conclusion by theoretically studying the transmission and transport properties of the mentioned structures. The study is based on the continuum model, the transfer matrix method and the Landauer-Büttiker formalism. We find nearly flat transmission bands or pass bands for G-FVGBs modulable through the system parameters. The pass bands improve as the maximum ratio of Fermi velocities (ξmax) increases, however its omnidirectional range is reduced. These characteristics result in a decaying conductance (integrated transmission) withξmax. The integrated transmission remains practically unaltered with the size of the system due to the saturation of the electron pass band filtering. In the case of GPL-FVGSLs the GPL profile results in regions of high transmission probability that can merge as flat transmission minibands if the pulse fraction and the superlattice parameters are appropriately tuned. The GPL profile also results in conductance (integrated transmission) oscillations that can be multiplied or reduced in number by adjusting the pulse fraction as well as the superlattice parameters.

Self-similar conductance patterns in graphene Cantor-like structures.

Graphene has proven to be an ideal system for exotic transport phenomena. In this work, we report another exotic characteristic of the electron transport in graphene. Namely, we show that the linear-regime conductance can present self-similar patterns with well-defined scaling rules, once the graphene sheet is subjected to Cantor-like nanostructuring. As far as we know the mentioned system is one of the few in which a self-similar structure produces self-similar patterns on a physical property. These patterns are analysed quantitatively, by obtaining the scaling rules that underlie them. It is worth noting that the transport properties are an average of the dispersion channels, which makes the existence of scale factors quite surprising. In addition, that self-similarity be manifested in the conductance opens an excellent opportunity to test this fundamental property experimentally.