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

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.

14 pages, 5 figures, 2 appendices, final version

References in corpus (1)

• Photons in polychromatic rotating modes

Cited by in corpus (4)

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• Position, spin and orbital angular momentum of a relativistic electron
• Scattering of a twisted electron wavepacket by a finite laser pulse
• Charged Dirac fermions with anomalous magnetic moment in the presence of the chiral magnetic effect and of a noncommutative phase space