The Klein paradox in a magnetic field: effects of electron spin

TL;DR

This paper investigates how an external magnetic field influences the Klein paradox, revealing spin-reversal phenomena and proposing potential applications as an electron spin filter.

Contribution

It extends the understanding of the Klein paradox by incorporating magnetic fields and spin effects, highlighting spin-flip processes and their implications.

Findings

Magnetic field induces spin-reversed electron components.

Spin-flip scattering is caused by spin-orbit interaction.

Potential step scattering can act as an electron spin filter.

Abstract

Reflection and transmission of electrons scattered by a rectangular potential step in the presence of an external magnetic field parallel to the electron beam is described with the use of the Dirac equation. It is shown that in addition to the known effects present in the so called Klein paradox, the presence of magnetic field gives rise to electron components with reversed spin in the reflected and transmitted beams. The spin-flip scattering processes are caused by the spin-orbit interaction activated by electric field of the potential step and transverse momentum components of electron motion induced by the magnetic field. The contemporary understanding of the Klein paradox, consisting in the finite transmission even when the potential height tends to infinity, is generalized to the presence of magnetic field and spin-reversed electron beams. The spin-reversed beams are shown to occur also for electrons moving above the step. It is proposed that, accounting for the anomalous value of the electron spin $g$-factor related to radiation corrections, the reflection and transmission scattering from the potential step can be used as an electron spin filter.