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

References in corpus (7)

• Chiral tunneling and the Klein paradox in graphene
• Dirac materials
• Gate-controlled Guiding of Electrons in Graphene
• Semiclassical theory of potential scattering for massless Dirac fermions
• Scattering and Bound State Solutions of Asymmetric Hulthén Potential
• Chiral interface states in graphene $p$-$n$ junctions
• Pair states in one-dimensional Dirac systems

Cited by in corpus (4)

• Super-Klein tunneling of Dirac fermions through electrostatic gratings in graphene
• 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
• Trapping charge carriers in low-dimensional Dirac materials