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 nonzero orbital angular momentum (OAM) 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 angular momentum (SAM) and OAM 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 Schrödinger–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.