Transmission properties of multilayered Period Doubling and Silver-Mean graphene structures
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Transmission properties of multilayered Period Doubling and Silver-Mean graphene structures G. Rodríguez-Arellano, D. P. Juárez-López, J. Madrigal-Melchor, R. Pérez-Álvarez, J. C. Martínez-Orozco and I. Rodríguez-Vargas Unidad Académica de Física, Universidad Autónoma de Zacatecas, Calzada Solidaridad Esquina con Paseo La Bufa S/N, 98060 Zacatecas, Zac., Mexico ABSTRACT We present the propagation properties of Dirac-electrons in multilayered PeriodDoubling (MPDGS) and Silver-Mean (MSMGS) graphene structures. The multilayered graphene structures are built arranging breaking and non-breaking symmetry substrates such as SiC and SiO2 following a given quasirregular substitution rule locating on them a graphene sheet. We have implemented the Transfer Matrix technique to calculate the transmittance of these multilayered graphene structures. This technique allows us to analyze readily the main differences of the transmission properties between MPDGS and MSMGS. INTRODUCTION It is well known that some features of the aperiodic order appear in different parts of nature. Aperiodic order or order without periodicity has emerged to properly describe an increasing number of complex systems [1]. From the technological standpoint the aperiodic or quasiperiodic multilayer structures have attracted a lot of attention due to the peculiar characteristics of their electronic spectra: fragmentation, selfsimilarity, critical wave function and fractality [2]. These characteristics are the result of interplay between the short-range and longrange effects in these systems. The most promising applications of quasiregular multilayers have been as electronic and optic filters, specifically their most spectacular result in the field of nonlinear optics with the generation of second and third harmonics [3]. Among the most studied quasiregular structures we can find Fibonacci and Thue-Morse, which sustain the mentioned characteristics irrespective, in most cases, of the elementary excitation considered. There are also other, less investigated, quasiregular structures that could be of practical interest due to their distinctive transmission properties. For instance, Period-Doubling and Rudin-Shapiro dielectric structures shown suitable transmission characteristic for microcavity resonators and optical filters, respectively [4]. On the other hand, the advent of new materials opens new possibilities from both the fundamental and the technological standpoints. This is the case of graphene due to its outstanding properties and superb conditions for multiple technological applications [5-7]. From the fundamental view point graphene serves as natural bridge between condensed matter physics and high energy physics offering the possibility of: 1) test relativistic effects in top-table experiments [8] and open new fields in physics as Relativistic Condensed Matter Physics, term that is begin coined in the community. From the technological standpoint the opportunities are unprecedented taking into account that graphene gather excellent thermal, electronic an
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