Two-dimensional Dirac particles in a P\"oschl-Teller waveguide
Abstract
We obtain exact solutions to the two-dimensional (2D) Dirac equation for the one-dimensional P\"oschl-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.
Keywords
Cite
@article{arxiv.1709.07147,
title = {Two-dimensional Dirac particles in a P\"oschl-Teller waveguide},
author = {R. R. Hartmann and M. E. Portnoi},
journal= {arXiv preprint arXiv:1709.07147},
year = {2017}
}
Comments
13 pages, 5 figures