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Electron scattering by a crystal layer

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Abstract

We consider the one-particle discrete Schrödinger operator H with a periodic potential perturbed by a function ɛW that is periodic in two variables and exponentially decreasing in the third variable. Here, ɛ is a small parameter. We study the scattering problem for H near the point of extremum with respect to the third quasimomentum coordinate for a certain eigenvalue of the Schrödinger operator with a periodic potential in the cell, in other words, for the small perpendicular component of the angle of particle incidence on the potential barrier ɛW. We obtain simple formulas for the transmission and reflection probabilities.

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Authors and Affiliations

  1. Udmurt State University, Izhevsk, Russia

    T. S. Tinyukova

  2. Physical-Technical Institute, Ural Branch, RAS, Izhevsk, Russia

    Yu. P. Chuburin

Authors
  1. T. S. Tinyukova
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  2. Yu. P. Chuburin
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Correspondence to T. S. Tinyukova.

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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 176, No. 3, pp. 444–457, September 2013.

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Tinyukova, T.S., Chuburin, Y.P. Electron scattering by a crystal layer. Theor Math Phys 176, 1207–1219 (2013). https://doi.org/10.1007/s11232-013-0101-6

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  • DOI: https://doi.org/10.1007/s11232-013-0101-6

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