R. R. Hartmann, M. E. Portnoi
We present exact analytical solutions for the 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.
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http://arxiv.org/abs/1305.4652
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