Self-similar transmission patterns induced by magnetic field effects in graphene

Rodríguez-González, R.; Rodrı́guez-Vargas, I.; Díaz-Guerrero, D. S.; Gaggero‐Sager, L. M.

doi:10.1016/j.physe.2018.03.007

Cited by 5 publications

(3 citation statements)

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“…Here, it is important to mention that substrates with different degrees of interaction with the graphene sheet (different barrier heights) are needed in order to obtain the self-similar graphene structures. It is also reported that simpler complex graphene structures present self-similar physical properties 16 – 19 . 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.…”

Section: Introductionmentioning

confidence: 93%

“…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.…”

Section: Introductionmentioning

confidence: 99%

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Self-similar transport, spin polarization and thermoelectricity in complex silicene structures

Rodríguez-González

Gaggero‐Sager

Rodrı́guez-Vargas

2020

Sci Rep

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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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Section: Introductionmentioning

confidence: 93%

Section: Introductionmentioning

confidence: 99%

Self-similar transport, spin polarization and thermoelectricity in complex silicene structures

Rodríguez-González

Gaggero‐Sager

Rodrı́guez-Vargas

2020

Sci Rep

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“…Similarly, employing magnetic and electrostatic barriers, a novel self-similar graphene structure was investigated. The transmission coefficient has self-similar features, according to the authors [31].…”

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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