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

TL;DR

This paper explores the self-similar transmission spectra of aperiodic Cantor-structured graphene, establishing scalable rules for spectral features based on fundamental parameters, applicable to both normal and oblique incidences.

Contribution

It introduces and validates scaling rules for transmission spectra in Cantor-structured graphene, simplifying the observation of self-similarity with fewer conditions.

Findings

Self-similar transmission spectra observed in Cantor graphene structures.

Established scaling rules for generation, barrier height, and length.

Rules valid for both normal and oblique incidence.

Abstract

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 D\'iaz-Guerrero et al. [D. S. D\'iaz-Guerrero, L. M. Gaggero-Sager, I. Rodr\'iguez-Vargas, and G. G. Naumis, arXiv:1503.03412v1, 2015].