Transmittance and Fractality in a Cantor-Like Multibarrier System

We investigate the transmission properties of quasiperiodic or aperiodic structures based on graphene arranged according to the Cantor sequence. In particular, we have found self-similar behaviour in the transmission spectra, and most importantly, we have calculated the scalability of the spectra. To do this, we implement and propose scaling rules for each one of the fundamental parameters: generation number, height of the barriers and length of the system. With this in mind we have been able to reproduce the reference transmission spectrum, applying the appropriate scaling rule, by means of the scaled transmission spectrum. These scaling rules are valid for both normal and oblique incidence, and as far as we can see the basic ingredients to obtain self-similar characteristics are: relativistic Dirac electrons, a self-similar structure and the non-conservation of the pseudo-spin. This constitutes a reduction of the number of conditions needed to observe self-similarity in graphene-based structures, see Díaz-

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“…2). The fundamentals of Schrödinger electrons can be found elsewhere, 30 and some minor details can be seen Fig. 3.…”

Section: Methodsmentioning

confidence: 99%

Self-similar transmission properties of aperiodic Cantor potentials in gapped graphene

et al. 2016

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“…They also show that the selfaffinity is a novel geometric property that is inherited to physical measurable properties of the model. It is worth mentioning that this scaling features in transmission had not been found, as far as we know, in non-relativistic systems for other kinds of systems [27][28][29].…”

Section: -P2mentioning

confidence: 92%

Scaling behavior in the transmission coefficient for a self-affine multi-barrier system using graphene

Díaz-Guerrero

Gaggero‐Sager

Rodrı́guez-Vargas

et al. 2015

EPL

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By means of a deposited or epitaxial graphene model, we study the transmission coefficient as a function of the incident electron's energy, for a multi-barrier system which is finitely self-affine (i.e., it is self-similar but with different scaling ratios in the x and energy axis) and has mirror symmetry with respect to the center of the structure. The main result is the scaling behavior in the transmission coefficient (which in fact resembles the form of the multi-barrier structure) and the appearance of a scaling relation between curves of different parameter values. This system is finitely self-affine as the number of scaled pieces is finite and the scaling is only made in the energy axis. In order to study the transmission properties of the proposed structure, we consider first different “generations” of its construction, we compute their transmission coefficient curves and then search for some resemblance of the geometric properties of the multi-barrier structure in the form of scaling relations between transmission curves. We find that not only such scaling relations exist, but they are surprisingly simple. In fact they are simple enough to write down a closed algebraic expression that describe them. We thought that this is due to the finite self-affinity property and that it could be used as a basic model to analyze more complicated multi-barrier profiles.

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“…Several recent works have highlighted self-similar structures in graphene and reported self-similar behavior in transmission spectra and conductance. For instance, the Cantor-like multibarrier system was studied, and it was demonstrated that the set of transmittance maxima exhibits a fractal structure [24][25][26].…”

Section: Introductionmentioning

confidence: 99%

Quantum transport in novel self-similar structure based on graphene

Miniya,

Oubram,

Gaggero-Sager

2023

Phys. Scr.

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A new self-similar graphene structure with different construction parameters is created to investigate the scalability of transmission coefficient. The transfer matrix formalism is used to calculate transmission spectra for generations of the self-similar structure. Two cases are analyzed: In the first case, the barriers were created by substrates, which induce a gap in the graphene. In the second case, the barriers were created by electric fields that can produce a displacement of the Dirac cones. We find that both cases show self-similarity patterns in their transmission spectra, which can be demonstrated through analytical equations called scaling rules, those rules connecting the generations of the structure. It results when the height of the barriers (V 0) is scaled or not, it gives different scaling rules, which shows that V 0 can be a revealing factor to find alternatives to scaling the transmission coefficient. Scaling rules can be useful because one can determine the transmission coefficient of generation i + 1 only by knowing a generation i.

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Transmittance and Fractality in a Cantor-Like Multibarrier System

Cited by 7 publications

References 13 publications

Self-similar transmission properties of aperiodic Cantor potentials in gapped graphene

Self-similar transmission properties of aperiodic Cantor potentials in gapped graphene

Scaling behavior in the transmission coefficient for a self-affine multi-barrier system using graphene

Quantum transport in novel self-similar structure based on graphene

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