Abstract:A new self-similar multibarrier system is proposed and used to study transmission of Dirac electrons in graphene. Such system is based on the scaling of the length and energy of the barriers. The use of self-similar structures allows us to compare the transmission in graphene and gallium arsenide (GaAs). The transmission coefficient for charge carriers in graphene shows a surprising scaling behavior structure, which is not seen in GaAs. The scaling properties are established as a function of three parameters: … Show more
The Landauer-Büttiker conductivity of arbitrary uniaxial spatially dependent strain in an armchair graphene nanoribbon is studied. Due to the uniaxial character of the strain, the corresponding transfer matrix can be reduced to a product of 2 × 2 matrices. Then the conductivity and the Fano factor can be calculated from this product. As an example of the technique, sinusoidal space dependent strain fields are studied using two different strain wavelengths. For the bigger wavelength the conductivity is reduced when compared with the unstrained case, although both conductivities are almost the same in shape. Whereas, for the smaller wavelength case, the conductivity is strongly modified. In spite of this, for energies close to the Dirac point energy, the conductivity and the Fano factor are quite similar to their unstrained counterpart for the two strain wavelengths here studied.
The Landauer-Büttiker conductivity of arbitrary uniaxial spatially dependent strain in an armchair graphene nanoribbon is studied. Due to the uniaxial character of the strain, the corresponding transfer matrix can be reduced to a product of 2 × 2 matrices. Then the conductivity and the Fano factor can be calculated from this product. As an example of the technique, sinusoidal space dependent strain fields are studied using two different strain wavelengths. For the bigger wavelength the conductivity is reduced when compared with the unstrained case, although both conductivities are almost the same in shape. Whereas, for the smaller wavelength case, the conductivity is strongly modified. In spite of this, for energies close to the Dirac point energy, the conductivity and the Fano factor are quite similar to their unstrained counterpart for the two strain wavelengths here studied.
“…As we already mentioned, in previous works we have shown that graphene under appropriate nanostructuring can present self-similar characteristics 19 – 21 . To be specific, the transmission probability or transmittance sustains self-similar patterns with well defined rules.…”
Section: Resultsmentioning
confidence: 60%
“…As far as we know, materials such as SiO 2 , SiC, hBN, etc. could be used for this purpose 22–24 .Figure 1Self-similar multi-barrier structure 21 . ( a ) Potential or conduction band-edge profile of a Cantor-like multibarrier system.…”
Section: Resultsmentioning
confidence: 99%
“…Several works claim that the transmission probability sustains self-similar characteristics in Fibonacci and Thue-Morse superlattices 15 – 18 , but once again the scale factors that connect the transmission patterns are not derived. Recently, we have shown that the transmission properties of graphene subjected to self-similar and self-affine multi-barrier structures present self-similar characteristics 19 – 21 . Even more, we have determined the scale factors that connect the transmission patterns.…”
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 particular, self-similar graphene structures, in which only the length of the barriers is scaled according to the Cantor set rules, display self-similar characteristics in the transmission probability or transmittance. These self-similar structures can be generated by nanostructured substrates 16 – 18 and inhomogeneous magnetic fields 19 . As we have documented graphene is the only material that manifests a fractal complex behavior in the electron transport.…”
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.
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