Localization of an Electron Transiting Through a System of N Identical and Periodically Located Two-Dimensional δ-Potentials

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.