Searching for confined modes in graphene channels: the variable phase method
arXiv:1112.4034 · doi:10.1103/PhysRevB.86.075464
Abstract
Using the variable phase method, we reformulate the Dirac equation governing the charge carriers in graphene into a nonlinear first-order differential equation from which we can treat both confined-state problems in electron waveguides and above-barrier scattering problems for arbitrary-shaped potential barriers and wells, decaying at large distances. We show that this method agrees with a known analytic result for a hyperbolic secant potential and go on to investigate the nature of more experimentally realizable electron waveguides, showing that, when the Fermi energy is set at the Dirac point, truly confined states are supported in pristine graphene. In contrast to exponentially-decaying potentials, we discover that the threshold potential strength at which the first confined state appears is vanishingly small for potentials decaying at large distances as a power law, but nonetheless further confined states are formed when the strength and spread of the potential reach a certain threshold.
10 pages, 3 figures. V2: abstract expanded, 13 references added, typos corrected
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- Current-Voltage Characteristics of Weyl Semimetal Semiconducting Devices, Veselago Lenses and Hyperbolic Dirac Phase
- 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
- Optimal traps in graphene
- Magnetic quantum dots and rings in two dimensions
- Super-Klein tunneling of Dirac fermions through electrostatic gratings in graphene
- 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
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- An analysis of the zero energy states in graphene
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- Chiral interface states in graphene - junctions
- Zero-energy vortices in Dirac materials
- Self-similar Charge Transport in Gapped Graphene
- Guided modes and terahertz transitions for two-dimensional Dirac fermions in a smooth double-well potential
- mKdV equation approach to zero energy states of graphene
- Trapping charge carriers in low-dimensional Dirac materials
- Time Evolution of Electron Waves in Graphene Superlattices
- Eigenvalues of a one-dimensional Dirac operator pencil
- Dirac fermions in armchair graphene nanoribbons trapped by electric quantum dots
- Dirac equation with complex potentials
- Klein Bound States in Single-Layer Graphene
- Physical Properties of Zener Tunnelling Nano-devices in Graphene
- The selection rule of graphene in a composite magnetic field
- Revisiting the Thomas-Fermi Potential for Three-Dimensional Condensed Matter Systems
- Zero energy states of Dirac equation in -dimensional curved spacetime