Abstract
The scattering of a quantum particle (an electron) on a chain of N non-overlapping identical and periodically located 5-shaped two-dimensional scattering centers is considered. When taking into account the transverse dimensions of the chain, this scattering is a multi-channel. The asymptotic value of an impedance of the chain is estimated when N tends to infinity. It is shown that the results a two dimensionality of motion of particle at a one-channel scattering coincide with the results of one-dimensional theory of scattering. Only the shift of the boundaries of the energy gap occurs. The picture is radically changing in the case of multichannel scattering: the impedance of the chain tends to infinity when N→ ∞. This means that in the 2D periodic conduction system with the nanometer widths the localization of the single-particle quantum states of an electron is possible. This result does not depend on the energy of the incident particle.
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Russian Text © The Author(s), 2019, published in Izvestiya Natsional'noi Akademii Nauk Armenii, Fizika, 2019, Vol. 54, No. 3, pp. 327–340.
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Sedrakian, D.M., Badalyan, D.H. Localization of an Electron Transiting Through a System of N Identical and Periodically Located Two-Dimensional δ-Potentials. J. Contemp. Phys. 54, 242–252 (2019). https://doi.org/10.3103/S1068337219030034
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DOI: https://doi.org/10.3103/S1068337219030034