Resonant tunneling through double barrier graphene systems: A comparative study of Klein and non-Klein tunneling structures

Abstract

We study the resonant tunneling effects through double barrier graphene systems (DBGSs). We have considered two types of DBGSs in order to take into account or rule out Klein tunneling effects: (1) the well-known and documented electrostatic-barrier structures (EBSs) created by means of electrostatic probes that act perpendicularly to the graphene sheet; and (2) substrate-barrier structures (SBSs) built sitting the graphene layer on alternating substrates, such as SiO2 and SiC, which are capable of non-open and open an energy bandgap on graphene. The transfer matrix approach is used to obtain the transmittance, linear-regime conductance, and electronic structure for different set of parameters such as electron energy, electron incident angle, barrier, and well widths. Particular attention is paid to the asymmetric characteristics of the DBGSs, as well as to the main differences between Klein and non-Klein tunneling structures. We find that: (1) the transmission properties can be modulated readily changing the energy and angle of the incident electrons, the widths of the well and barrier regions; (2) the linear-regime conductance is easily enhancing, diminishing, and shifted changing from symmetric to asymmetric DBGSs configuration overall in the case of non-Klein tunneling structures; (3) the conductance shows an oscillatory behavior as function of the well width, with peaks that are directly related to the opening and opening-closure of bound-state subbands for EBSs and SBSs, respectively. Finally, it is important to mention that electrostatic DBGSs or substrate DBGSs could be more suitable depending on a specific application, and in the case of non-Klein tunneling structures, they seem possible considering the sophistication of the current epitaxial growth techniques and whenever substrates that open an energy bandgap on graphene, without diminishing the carrier's mobility, be experimentally discovered.

Non-conventional graphene superlattices as electron band-pass filters

“…1c) the potential barriers are induced by substrates with different degree of interaction with the graphene sheet. A possibility to generate the potential barriers could be the so-called heterostructured SiO 2 /SiC substrates 35 . In the SiO 2 regions the Dirac cone structure of pristine graphene is preserved, while in the SiC regions the interaction between the graphene sheet and the substrate results in a bandgap opening 36 .…”

Fibonacci quasiregular graphene-based superlattices: Quasiperiodicity and its effects on the transmission, transport and electronic structure properties

“…We consider this kind of barriers because they are opposite, one (electrostatic case) in which Klein tunneling is presented and the other (substrate case) in which it is ruled out. Following the lines of our previous works [51][52][53], the main concern of this study is to find out how aperiodic modulation affects the intrinsic oscillatory nature of the linear-regime conductance in graphene as well as how these oscillations are correlated with the energy level structure, and what is the role played by Klein tunneling.…”

Angle-dependent bandgap engineering in gated graphene superlattices

“…51,52 The basic information needed to apply this methodology is the dispersion relation, wave vectors and wave functions in the barrier and well regions as well as in the semi-infinite left and right regions. 53,54 In the well and semi-infinite regions the dispersion relation and wave functions comes as:…”

“…53,54 Once these quantities are known, we can apply the continuity conditions of the wave function along the superlattice axis as well as the consevation of the transversal momentum (k y = q y ), and define the transmission probability in terms of the so-called transfer matrix,…”