Abstract
Electron states in graphene with a one-dimensional potential have been studied. An approximate solution has been obtained for a small angle between vectors of the incident electron momentum and potential gradient. Exactly solvable problems with a potential of the smoothened step type U(x) = Utanh(x/a) and a potential with a singularity U(x) = −U/(|x| + d) are considered. The transmission/reflection coefficients and phases for various potential barriers are determined. A quasi-classical solution is obtained.
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Original Russian Text © D.S. Miserev, M.V. Entin, 2012, published in Zhurnal Eksperimental’noi i Teoreticheskoi Fiziki, 2012, Vol. 142, No. 4, pp. 784–796.
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Miserev, D.S., Entin, M.V. Quantum mechanics of graphene with a one-dimensional potential. J. Exp. Theor. Phys. 115, 694–705 (2012). https://doi.org/10.1134/S1063776112090087
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DOI: https://doi.org/10.1134/S1063776112090087