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 … Show more
“…In systems in which only the spatial coordinate or the energy axis are scaled (self-affine transformation) this connection between the scaling rules and the scale factors of the structure is not fulfilled, results that will be published elsewhere. This contrasts with the results obtained for the transmission probability, since in that case it is not necessary to scale both axis 20 . Other important characteristic of the system under study is that the scaling rules for the transmittance are also valid for oblique incidence, like in the case of simple Cantor-like structures 20 .…”
Section: Discussioncontrasting
confidence: 83%
“…The specific values of the rmsd for generations, heights of the main barrier, lengths of the system and the general scaling are 0.017274226, 0.01056703, 0.011058418 and 0.018950994, respectively. It is worth mentioning that even when we are dealing with a double average property the rmsds are acceptable and even better than the corresponding ones previously reported for the transmittance 20 .Figure 6Difference between non-scaled and scaled curves for ( a ) generations, ( b ) heights of barrier, ( c ) lengths of the system and ( d ) the combination (general scaling) of the preceding ones. The non-scaled and scaled curves correspond to the results presented in Figs 2, 3, 4 and 5.
…”
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.
“…In systems in which only the spatial coordinate or the energy axis are scaled (self-affine transformation) this connection between the scaling rules and the scale factors of the structure is not fulfilled, results that will be published elsewhere. This contrasts with the results obtained for the transmission probability, since in that case it is not necessary to scale both axis 20 . Other important characteristic of the system under study is that the scaling rules for the transmittance are also valid for oblique incidence, like in the case of simple Cantor-like structures 20 .…”
Section: Discussioncontrasting
confidence: 83%
“…The specific values of the rmsd for generations, heights of the main barrier, lengths of the system and the general scaling are 0.017274226, 0.01056703, 0.011058418 and 0.018950994, respectively. It is worth mentioning that even when we are dealing with a double average property the rmsds are acceptable and even better than the corresponding ones previously reported for the transmittance 20 .Figure 6Difference between non-scaled and scaled curves for ( a ) generations, ( b ) heights of barrier, ( c ) lengths of the system and ( d ) the combination (general scaling) of the preceding ones. The non-scaled and scaled curves correspond to the results presented in Figs 2, 3, 4 and 5.
…”
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.
“…6b we show the concrete results of applying Eq. (17). In some energy intervals the scaling works reasonable well, while in others, mainly at low energies, the coincidence between the scaled and reference curve is far from good.…”
2D materials open the possibility to study Dirac electrons in complex self-similar geometries. The two-dimensional nature of materials like graphene, silicene, phosphorene and transition-metal dichalcogenides allow the nanostructuration of complex geometries through metallic electrodes, interacting substrates, strain, etc. So far, the only 2D material that presents physical properties that directly reflect the characteristics of the complex geometries is monolayer graphene. In the present work, we show that silicene nanostructured in complex fashion also displays self-similar characteristics in physical properties. In particular, we find self-similar patterns in the conductance, spin polarization and thermoelectricity of Cantor-like silicene structures. These complex structures are generated by modulating electrostatically the silicene local bandgap in Cantor-like fashion along the structure. The charge carriers are described quantum relativistically by means of a Dirac-like Hamiltonian. The transfer matrix method, the Landauer–Büttiker formalism and the Cutler–Mott formula are used to obtain the transmission, transport and thermoelectric properties. We numerically derive scaling rules that connect appropriately the self-similar conductance, spin polarization and Seebeck coefficient patterns. The scaling rules are related to the structural parameters that define the Cantor-like structure such as the generation and length of the system as well as the height of the potential barriers. As far as we know this is the first time that a 2D material beyond monolayer graphene shows self-similar quantum transport as well as that transport related properties like spin polarization and thermoelectricity manifest self-similarity.
“…There is a surge of interest in exploring transport properties of the quasi‐periodic superlattices (refs. ). The quasi‐periodical SL can have different application areas, in particular as the convenient and effective energy filter for the quasiparticles.…”
Section: Introductionmentioning
confidence: 97%
“…Various types of the SL are considered: strictly periodic ones, disordered ones, lattices with defects, etc. Structures intermediate between the periodic and the disordered ones (in particular the quasi‐periodic lattices, such as the Fibonacci and the Thue‐Morse superlattices) occupy a notable place among the SL . This is determined by their unique properties, such as the self‐similarity, the Cantor nature of the energy spectrum, and others (see, e.g.,).…”
The focus of our work is to explore quasiparticle transmission through the quasi‐periodic superlattices based on the Lieb lattice, in which the fermion pseudo‐spin equals 1. We are the first to calculate and analyze the transmission spectra (quasiparticle transmission dependences on their energy) for such structures. The quasi‐periodic modulation is created with the help of the external electrostatic potential in the form of the rectangular barriers located along the axis of the superlattice. Our observations provide that the effective Fibonacci modulation is achieved by the alternation of the potential barriers heights in the various elements of the superlattice. For massless fermions, the quasi‐periodic modulation takes place under the conditions of the oblique incidence of the particles. For massive fermions, the quasi‐periodic modulation is observed both for the oblique and the normal incidence. Besides, we define the special importance of a super Klein tunneling band in the transmission spectra. The present study provides a thorough analysis of the transmission spectra dependence on the parameters of the problem. The conductivity of the structure considered is also analyzed. For a definite parameter set, the transmission spectra values for pseudospin‐1 fermions (Lieb lattice) and those of pseudospin‐1/2 (graphene) coincide. Our findings may have useful implications in the development of nanoelectronic devices based on the Lieb lattice.
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