Two-dimensional Dirac particles in a Pöschl-Teller waveguide

Authors

R. R. Hartmann, De La Salle University, Manila
M. E. Portnoi, University of Exeter

College

College of Science

Department/Unit

Physics

Document Type

Article

Source Title

Scientific Reports

Volume

7

Issue

1

Publication Date

12-1-2017

Abstract

© 2017 The Author(s). 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.

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Digitial Object Identifier (DOI)

10.1038/s41598-017-11411-w

Recommended Citation

Hartmann, R. R., & Portnoi, M. E. (2017). Two-dimensional Dirac particles in a Pöschl-Teller waveguide. Scientific Reports, 7 (1) https://doi.org/10.1038/s41598-017-11411-w

Disciplines

Physics

Keywords

Wave guides; Dirac equation

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