Quasi-exact solution to the Dirac equation for the hyperbolic-secant potential

@article{Hartmann2014QuasiexactST,
  title={Quasi-exact solution to the Dirac equation for the hyperbolic-secant potential},
  author={Richard Rudolph Hartmann and Mikhail E Portnoi},
  journal={Physical Review A},
  year={2014},
  volume={89},
  pages={012101}
}
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… 

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