Geometric and compositional influences on spin-orbit induced circulating currents in nanostructures

Abstract

Circulating orbital currents, originating from the spin-orbit interaction, are calculated for semiconductor nanostructures in the shape of spheres, disks, spherical shells, and rings for the electron ground state with spin oriented along a symmetry axis. The currents and resulting orbital and spin magnetic moments, which combine to yield the effective electron $g$ factor, are calculated using a recently introduced formalism that allows the relative contributions of different regions of the nanostructure to be identified at zero magnetic field. For all these spherically or cylindrically symmetric hollow or solid nanostructures, independent of material composition and whether the boundary conditions are hard or soft, the dominant orbital current originates from intermixing of valence-band states in the electron ground state, circulates within the nanostructure, and peaks approximately halfway between the center and edge of the nanostructure in the plane perpendicular to the spin orientation. For a specific material composition and confinement character, the confinement energy and orbital moment are determined by a single size-dependent parameter for spherically symmetrical nanostructures, whereas they can be independently tuned for cylindrically symmetric nanostructures.