Relativistic particles in super-periodic potentials: exploring graphene and fractal systems

Abstract

In this article, we employ the transfer matrix method to investigate relativistic particles in super-periodic potentials (SPPs) of arbitrary order $n\in I^{+}$. We calculate the reflection and transmission probabilities for spinless Klein particles encountering rectangular potential barriers with super-periodic repetition. It is found that spinless relativistic particles exhibit Klein tunneling and a significantly higher degree of reflection compared to their non-relativistic counterparts. Additionally, we analytically explore the behavior of experimentally realizable massless Dirac electrons as they encounter rectangular potential barriers with a super-periodic pattern in a monolayer of graphene. In this system, the transmission probability, conductance, and Fano factor are evaluated as functions of the number of barriers, the order of super-periodicity, and the angle of incidence. Our findings reveal that the transmission probability shows a series of resonances that depend on the number of barriers and the order of super-periodicity. We extend our analysis to specific cases within the Unified Cantor Potentials (UCPs)-$\gamma$ system ($\gamma$ is a scaling parameter greater than $1$), focusing on the General Cantor fractal system and the General Smith-Volterra-Cantor (GSVC) system. For the General Cantor fractal system, we calculate the tunneling probability, which reveals sharp transmission peaks and progressively thinner unit cell potentials as $G$ increases. In the GSVC system, we analyze the potential segment length and tunneling probability, observing nearly unity tunneling coefficients when $\gamma \approx 1$, as well as saturation behavior in transmission coefficients at higher stages $G$.

15 pages, 13 figures

References in corpus (37)

• Electric Field Effect in Atomically Thin Carbon Films
• Two-Dimensional Gas of Massless Dirac Fermions in Graphene
• Experimental Observation of Quantum Hall Effect and Berry's Phase in Graphene
• Chiral tunneling and the Klein paradox in graphene
• Ultrathin epitaxial graphite: 2D electron gas properties and a route toward graphene-based nanoelectronics
• Hofstadter's butterfly in moire superlattices: A fractal quantum Hall effect
• Gate-induced insulating state in bilayer graphene devices
• Andreev reflection and Klein tunneling in graphene
• Selective transmission of Dirac electrons and ballistic magnetoresistance of \textit{n-p} junctions in graphene
• Evidence of Klein tunneling in graphene p-n junctions
• Anisotropic behaviors of massless Dirac fermions in graphene under periodic potential
• Transport measurements across a tunable potential barrier in graphene
• Zitterbewegung, chirality, and minimal conductivity in graphene
• Electric Field Modulation of Galvanomagnetic Properties of Mesoscopic Graphite
• Transfer matrix method for optics in graphene layers
• Klein tunneling in graphene: optics with massless electrons
• Quantized Transport in Graphene p-n Junctions in Magnetic Field
• Extra Dirac points in the energy spectrum for superlattices on single-layer graphene
• Emerging Zero Modes for Graphene in a Periodic Potential
• Dirac and Klein-Gordon particles in one-dimensional periodic potentials
• Fractional fractal quantum Hall effect in graphene superlattices
• Conductance of p-n-p graphene structures with 'air-bridge' top gates
• Landau Levels and Quantum Hall Effect in Graphene Superlattices
• Fabrication of Graphene p-n-p Junctions with Contactless Top Gates
• Dirac electrons in a Kronig-Penney potential: dispersion relation and transmission periodic in the strength of the barriers
• Impurity-assisted tunneling in graphene
• Supercriticality and Transmission Resonances in the Dirac equation
• Dirac-Kronig-Penney model for strain-engineered graphene
• Anyons and Fractional Quantum Hall Effect in Fractal Dimensions
• Periodic Landau gauge and Quantum Hall effect in twisted bilayer graphene
• Revealing Hofstadter Spectrum for Graphene in a Periodic Potential
• Super Periodic Potential
• Transport Anisotropy in One-dimensional Graphene Superlattice in the High Kronig-Penney Potential Limit
• Transport in graphene nanostructures with spatially modulated gap and potential
• Sub-Sharvin conductance and enhanced shot noise in doped graphene
• Tunneling from general Smith-Volterra-Cantor potential
• Two-dimensional hydrodynamic electron flow through periodic and random potentials

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