Quasi-exact solution to the Dirac equation for the hyperbolic-secant potential
Hartmann, Richard R.; Portnoi, M.E.
Date: 2 January 2014
Article
Journal
Physical Review A - Atomic, Molecular, and Optical Physics
Publisher
American Physical Society
Publisher DOI
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 ...
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.
Physics and Astronomy
Faculty of Environment, Science and Economy
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