Two-dimensional Dirac particles in a Pöschl-Teller waveguide

Abstract

We obtain exact solutions to the two-dimensional (2D) Dirac equation for the one-dimensional Pöschl-Teller potential which contains an asymmetry term. The eigenfunctions are expressed in terms of Heun confluent functions, while the eigenvalues are determined via the solutions of a simple transcendental equation. For the symmetric case, the eigenfunctions of the supercritical states are expressed as spheroidal wave functions, and approximate analytical expressions are obtained for the corresponding eigenvalues. A universal condition for any square integrable symmetric potential is obtained for the minimum strength of the potential required to hold a bound state of zero energy. Applications for smooth electron waveguides in 2D Dirac-Weyl systems are discussed.

13 pages, 5 figures

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• Scattering of Klein-Gordon particles in the background of mixed scalar-vector generalized symmetric Woods-Saxon potential
• Bound states of the two-dimensional Dirac equation for an energy-dependent hyperbolic Scarf potential
• Bipolar electron waveguides in graphene
• Generalized confluent hypergeometric solutions of the Heun confluent equation
• Dirac-Weyl equation on a hyperbolic graphene surface under perpendicular magnetic fields
• Guided modes and terahertz transitions for two-dimensional Dirac fermions in a smooth double-well potential
• Mapping borophene onto graphene: Quasi-exact solutions for guiding potentials in tilted Dirac cones
• Trapping charge carriers in low-dimensional Dirac materials
• The asymmetric quantum Rabi model and generalised Pöschl-Teller potentials
• Dirac fermions in armchair graphene nanoribbons trapped by electric quantum dots
• Graphene Dirac fermions in symmetric electric and magnetic fields: the case of an electric square well
• Massive and massless two-dimensional Dirac particles in electric quantum dots
• Experimental Observation of Bound States of 2D Dirac Electrons at Surface Steps of the Topological Insulator Bi${}_2$Se${}_3$
• Qualitative analysis of magnetic waveguides for two-dimensional Dirac fermions
• Lorentzian quantum wells in graphene: the role of shape invariance in zero-energy states trapping
• Designer gapped and tilted Dirac cones in lateral graphene superlattices
• Quantum field theory at finite temperature for 3D periodic backgrounds
• Confinement in bilayer graphene via intra- and inter-layer interactions