Magnetic Kronig-Penney model for Dirac electrons in single-layer graphene

Abstract

The properties of Dirac electrons in a magnetic superlattice (SL) on graphene consisting of very high and thin (delta-function) barriers are investigated. We obtain the energy spectrum analytically and study the transmission through a finite number of barriers. The results are contrasted with those for electrons described by the Schrodinger equation. In addition, a collimation of an incident beam of electrons is obtained along the direction perpendicular to that of the SL. We also highlight the analogy with optical media in which the refractive index varies in space.

21 pages, 13 figures, to appear in New Journal of Physics

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Cited by in corpus (39)

• Gauge fields in graphene
• Magnetic Kronig-Penney model for Dirac electrons in single-layer graphene
• Strain Modulated Superlattices in Graphene
• Band structures of bilayer graphene superlattices
• Pseudomagnetic fields in graphene nanobubbles of constrained geometry: A molecular dynamics study
• Magnetic superlattice and finite-energy Dirac points in graphene
• Resonant valley filtering of massive Dirac electrons
• Tunable electronic transport and unidirectional quantum wires in graphene subjected to electric and magnetic fields
• Dirac-Kronig-Penney model for strain-engineered graphene
• Resonant modes in strain-induced graphene superlattices
• Tunneling of multi-Weyl semimetals through a potential barrier under the influence of magnetic fields
• Qualitative analysis of trapped Dirac fermions in graphene
• Conductance across strain junctions in graphene nanoribbons
• Transmission and conductance across junctions of isotropic and anisotropic three-dimensional semimetals
• Localization behavior of Dirac particles in disordered graphene superlattices
• General $\delta$-shell interactions for the two-dimensional Dirac operator: self-adjointness and approximation
• Magnetic scattering of Dirac fermions in topological insulators and graphene
• Bootstrapping the Kronig-Penney Model
• One-dimensional scattering of fermions on $\delta$-impurities
• Tunneling of Graphene Massive Dirac Fermions through a Double Barrier
• Electron transmission through a periodically driven graphene magnetic barrier
• A primer on twistronics: A massless Dirac fermion's journey to moiré patterns and flat bands in twisted bilayer graphene
• Tunnelling through finite graphene superlattices: resonance splitting effect
• Two-dimensional Dirac operators with general $\delta$-shell interactions supported on a straight line
• Resonant peak splitting for graphene superlattices with one-dimensional periodic potentials of square barriers
• Effect of Magnetic Field on Goos-Hänchen Shifts in Gaped Graphene Triangular Barrier
• Beating oscillation and Fano resonance in the laser assisted electron transmission through graphene δ- function magnetic barriers
• Gap opening of single-layer graphene under the continuum model
• Transmission through Biased Graphene Strip
• Variational Approach for the Effects of Periodic Modulations on the Spectrum of Massless Dirac Fermion
• Finite-gap twists of carbon nanotubes and an emergent hidden supersymmetry
• Klein Bound States in Single-Layer Graphene
• Transport Properties for Triangular Barriers in Graphene
• Emergent flat band lattices in spatially periodic magnetic fields
• Casimir energy for spinor fields with $\delta$-shell potentials
• Bound states for massive Dirac fermions in graphene in a magnetic step field
• The selection rule of graphene in a composite magnetic field
• Magnetically modulated superconductor-graphene-superconductor (SGS) Josephson junctions and their tunability
• Transmissions in gapped graphene exposed to tilting and oscillating barriers