Asymptotics of electron flow spin-polarization in quantum waveguides of variable cross-section in presence of magnetic field

Lev Baskin, Pekka Neittaanmäki, Oleg Sarafanov

Research outputpeer-review

1 Citation (Scopus)

Abstract

We consider electron motion in quantum waveguides with variable cross-sections. The narrows of the waveguide play the role of effective potential barriers for the longitudinal motion of electrons. Two narrows form a quantum resonator where a resonant tunneling can occur. It means that electrons with energy in a small range pass through the resonator with probability near to 1. In presence of magnetic field, the aforementioned range splits into two intervals. Electrons with spin +1/2 can pass through the resonator only if their energies are in one of these intervals and electrons with spin -1/2 can pass only having energies in the second one. Hence, all electrons in the outgoing flow have similarly oriented spins, i. e. The electron flow becomes polarized. The intervals are rapidly decreasing as the diameter of narrows tends to 0, which presents difficulties for numerical simulation of the phenomenon. The full qualitative description of the phenomenon can be given only by asymptotic analysis. We consider an infinite waveguide with two cylindrical ends and two narrows of small diameter. Part of the resonator is placed into magnetic field. We give an asymptotic description of the electron wave propagation in such a waveguide as diameters of the narrows tend to zero.

Original languageEnglish
Title of host publicationECCOMAS 2012 - European Congress on Computational Methods in Applied Sciences and Engineering, e-Book Full Papers
Pages253-262
Number of pages10
Publication statusPublished - 1 Dec 2012
Event6th European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS 2012 - Vienna
Duration: 10 Sep 201214 Sep 2012

Publication series

NameECCOMAS 2012 - European Congress on Computational Methods in Applied Sciences and Engineering, e-Book Full Papers

Conference

Conference6th European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS 2012
CountryAustria
CityVienna
Period10/09/1214/09/12

Scopus subject areas

  • Computational Theory and Mathematics
  • Applied Mathematics

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