Quasi-exact solution to the Dirac equation for the hyperbolic secant potential
Mesoscale and Nanoscale Physics
2014-01-06 v2 Quantum Physics
Abstract
We analyze bound modes of two-dimensional massless Dirac fermions confined within a hyperbolic secant potential, which provides a good fit for potential profiles of existing top-gated graphene structures. We show that bound states of both positive and negative energies exist in the energy spectrum and that there is a threshold value of the characteristic potential strength for which the first mode appears. Analytical solutions are presented in several limited cases and supercriticality is discussed.
Cite
@article{arxiv.1305.4652,
title = {Quasi-exact solution to the Dirac equation for the hyperbolic secant potential},
author = {R. R. Hartmann and M. E. Portnoi},
journal= {arXiv preprint arXiv:1305.4652},
year = {2014}
}
Comments
8 pages, 4 figures. Figure 2 removed, 2 additional figures and references added