Self-Spin-Controlled Rotation of Spatial States of a Dirac Electron in a Cylindrical Potential via Spin-Orbit Interaction

TL;DR

This paper demonstrates that a Dirac electron's spatial state can be self-controlled to rotate via spin-orbit interaction in a cylindrical potential, with effects observable even at non-relativistic speeds.

Contribution

It provides a detailed analysis linking Dirac equation solutions to spin-orbit effects, clarifying the physical origin of spin-controlled spatial state rotation in electrons.

Findings

Spin and orbital angular momenta interact, affecting phase velocity.

Spin-orbit splitting causes spatial state rotation.

Effects are present at non-relativistic velocities.

Abstract

Solution of the Dirac equation predicts that when an electron with non-zero orbital angular momentum propagates in a cylindrically symmetric potential, its spin and orbital degrees of freedom interact, causing the electron's phase velocity to depend on whether its spin and orbital angular momenta vectors are oriented parallel or anti-parallel with respect to each other. This spin-orbit splitting of the electronic dispersion curves can result in a rotation of the electron's spatial state in a manner controlled by the electron's own spin z-component value. These effects persist at non-relativistic velocities. To clarify the physical origin of this effect, we compare solutions of the Dirac equation to perturbative predictions of the Schrodinger-Pauli equation with a spin-orbit term, using the standard Foldy-Wouthuysen Hamiltonian. This clearly shows that the origin of the effect is the familiar relativistic spin-orbit interaction.