Smooth electron waveguides in graphene

Abstract

We present exact analytical solutions for the zero-energy modes of two-dimensional massless Dirac fermions fully confined within a smooth one-dimensional potential V(x)= - α/cosh(βx), which provides a good fit for potential profiles of existing top-gated graphene structures. We show that there is a threshold value of the characteristic potential strength α/β for which the first mode appears, in striking contrast to the non-relativistic case. A simple relationship between the characteristic strength and the number of modes within the potential is found. An experimental setup is proposed for the observation of these modes. The proposed geometry could be utilized in future graphene-based devices with high on/off current ratios.

8 Pages including 4 figures, an appendix and two additional figures added, references updated

References in corpus (28)

• The electronic properties of graphene
• Energy Band Gap Engineering of Graphene Nanoribbons
• Chiral tunneling and the Klein paradox in graphene
• Room-Temperature Quantum Hall Effect in Graphene
• Electronic States of Graphene Nanoribbons
• Andreev reflection and Klein tunneling in graphene
• A self-consistent theory for graphene transport
• Quantum interference and Klein tunneling in graphene heterojunctions
• Veselago Lens for Electrons: Focusing and Caustics in Graphene p-n Junctions
• Measurement of Scattering Rate and Minimum Conductivity in Graphene
• Quantum-limited shot noise 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
• Transport measurements across a tunable potential barrier in graphene
• Electronic transport and quantum Hall effect in bipolar graphene p-n-p junction
• Quantum dots in graphene
• Klein Backscattering and Fabry-Perot Interference in Graphene Heterojunctions
• Quantum Goos-Hanchen effect in graphene
• Random resistor network model of minimal conductivity in graphene
• Conductance of p-n-p graphene structures with 'air-bridge' top gates
• Quantum criticality and minimal conductivity in graphene with long-range disorder
• Nonlinear screening and ballistic transport in a graphene p-n junction
• Fabrication of Graphene p-n-p Junctions with Contactless Top Gates
• Effect of disorder on a graphene p-n junction
• Guided modes in graphene waveguides
• Mesoscopic conductance fluctuations in graphene
• Dirac electrons in graphene-based quantum wires and quantum dots
• Coherent Graphene Devices: Movable Mirrors, Buffers and Memories

Cited by in corpus (69)

• Gate-controlled Guiding of Electrons in Graphene
• Spatially resolved edge currents and guided-wave electronic states in graphene
• On a solution of the Schrodinger equation with a hyperbolic double-well potential
• Zero-energy states in graphene quantum dots and rings
• Quasi-exact solution to the Dirac equation for the hyperbolic secant potential
• Guiding of Electrons in a Few Mode Ballistic Graphene Channel
• Introduction to Graphene Electronics -- A New Era of Digital Transistors and Devices
• Band gap in graphene induced by vacuum fluctuations
• Excitons in narrow-gap carbon nanotubes
• One-dimensional Coulomb problem in Dirac materials
• Semiclassical theory of potential scattering for massless Dirac fermions
• Massless Dirac fermions in two dimensions: Confinement in nonuniform magnetic fields
• Searching for confined modes in graphene channels: the variable phase method
• Dirac electron in graphene under supersymmetry generated magnetic fields
• Absorptive pinhole collimators for ballistic Dirac fermions in graphene
• Visualization of phase-coherent electron interference in a ballistic graphene Josephson junction
• Super-geometric electron focusing on the hexagonal Fermi surface of PdCoO${}_2$
• Optimal traps in graphene
• Two-dimensional Dirac particles in a Pöschl-Teller waveguide
• Guiding Dirac fermions in graphene with a carbon nanotube
• Bound states in a hyperbolic asymmetric double-well
• Super-Klein tunneling of Dirac fermions through electrostatic gratings in graphene
• Energy states of the Hulthen plus Coulomb-like potential with position-dependent mass function in external magnetic fields
• Supersymmetric twisting of carbon nanotubes
• Qualitative analysis of trapped Dirac fermions in graphene
• Localization of massless Dirac particles via spatial modulations of the Fermi velocity
• On zero energy states in graphene
• An analysis of the zero energy states in graphene
• Generalized Dirac Oscillators with position-dependent mass
• Chiral interface states in graphene $p$-$n$ junctions
• Localization of Dirac-like excitations in graphene in the presence of smooth inhomogeneous magnetic fields
• Electron collimation at van der Waals domain walls in bilayer graphene
• Bound states of the two-dimensional Dirac equation for an energy-dependent hyperbolic Scarf potential
• Pair states in one-dimensional Dirac systems
• Conditional electron confinement in graphene via smooth magnetic fields
• Bipolar electron waveguides in graphene
• Phosphorene pnp junctions as perfect electron waveguides
• Zero-energy vortices in Dirac materials
• Self-similar Charge Transport in Gapped Graphene
• A new coupling mechanism between two graphene electron waveguides for ultrafast switching
• Coherent states for graphene under the interaction of crossed electric and magnetic fields
• Guided modes and terahertz transitions for two-dimensional Dirac fermions in a smooth double-well potential
• New solutions for graphene with scalar potentials by means of generalized intertwining
• mKdV equation approach to zero energy states of graphene
• Schrödinger-type 2D coherent states of magnetized uniaxially strained graphene
• Optical valley separation in two-dimensional semimetals with tilted Dirac cones
• Mapping borophene onto graphene: Quasi-exact solutions for guiding potentials in tilted Dirac cones
• Trapping charge carriers in low-dimensional Dirac materials
• Complex Supersymmetry in Graphene
• Zero Energy States for a Class of Two-Dimensional Potentials in Graphene
• Generalized harmonic confinement of massless Dirac fermions in (2+ 1) dimensions
• Zeta Functions of the Dirac Operator on Quantum Graphs
• Eigenvalues of a one-dimensional Dirac operator pencil
• Dirac fermions in armchair graphene nanoribbons trapped by electric quantum dots
• Design of graphene waveguide: Effect of edge orientation and waveguide configuration
• Klein Bound States in Single-Layer Graphene
• Manipulating electron waves in graphene using carbon nanotube gating
• Perfectly Conducting Graphene Electronic Waveguide with Curved Channels
• Dirac equation with complex potentials
• Darboux partners of Heun-class potentials for the two-dimensional massless Dirac equation
• Physical Properties of Zener Tunnelling Nano-devices in Graphene
• Lorentzian quantum wells in graphene: the role of shape invariance in zero-energy states trapping
• Solvable Two-dimensional Dirac Equation with Matrix Potential: Graphene in External Electromagnetic Field
• The selection rule of graphene in a composite magnetic field
• Ballistic guided electrons against disorder in graphene nanoribbons
• Observation of angle-dependent transmission of Dirac electrons in graphene hetero junctions
• Designer gapped and tilted Dirac cones in lateral graphene superlattices
• Confinement in bilayer graphene via intra- and inter-layer interactions
• Zero energy states of Dirac equation in $(2+1)$-dimensional curved spacetime