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arXiv · 1305.4652

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

R. R. Hartmann·M. E. Portnoi
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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.

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R. R. Hartmann, M. E. Portnoi. 2013-11-07. Quasi-exact solution to the Dirac equation for the hyperbolic secant potential. https://doi.org/10.1103/physreva.89.012101

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