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.

Anisotropy of electron and holegtensors of quantum dots: An intuitive picture based on spin-correlated orbital currents

“…We note that this relation can be derived using the Zeeman interaction and time-reversal symmetry; the factor 2 arises from Kramer's degeneracy. It has been shown [20] that μ z spin is nearly always equal to μ B . In Fig.…”

“…This dependence is therefore related to the size dependence of the integrated current [20]. For the small heights considered here, the integrated current gets smaller with decreasing height: the valence-band contributions to the electron ground state are quenched through their dependence on the confinement energy.…”

“…It vanishes at the edge and center, and it peaks about midway between. This resembles a current loop, and this intuitive physical picture is capable of explaining the size and composition dependence of the spin-correlated orbital moment in various systems [20]. Although the shape of the nanostructure has been predicted to be influential on the electron g tensor [12,13], an intuitive picture of this relation is still lacking.…”

Strain-inducedg-factor tuning in single InGaAs/GaAs quantum dots

“…The g tensor depends on the exact electronic structure of the QD and therefore also has a strong dependency on the size and shape of quantum dots [6][7][8]. This implies that the g tensor in a QD can be manipulated in situ by changing its electronic structure, for instance by means of an externally applied electrical or elastic stress field.…”

Hole spins in an InAs/GaAs quantum dot molecule subject to lateral electric fields

“…Previous work on InAs QDMs has shown that the Zeeman splitting between spin projections can be a function of applied vertical electric field due to the changing spatial distribution of electron or hole wavefunctions. 13,15,[39][40][41][42] In our case, the changing Zeeman splitting originates, at least in part, from the changing spatial extent of the hole wavefunctions induced by the applied lateral electric field. This dependence of the hole wavefunction distribution on lateral field is displayed in Figure 2c.…”