Robust path-dependent spin rotation on the nanoscale in a semiconductor quantum well

Abstract

Spintronics, using spin transport physics to manipulate information encoded in spin polarization, requires the ability to scalably manipulate electron spins, which is most easily achieved without magnetic materials or applied magnetic fields. Coherent spin rotation in the spin-orbit fields of a quantum well can yield efficient spin manipulation that depends only on the path traversed by a packet of electronic spin, and not on the speed with which the path is traversed. For a configuration with no applied magnetic field, where an electron spin is driven around three straight legs, with the first and last parallel, and the intermediate leg perpendicular to them and half their length, transport around the path will cause a robust, electrically controllable spin rotation. The angle of the spin rotation depends on the lengths of those legs. However, it is also possible to switch between integer π rotations of the electron spin (about a fixed axis in the plane of the quantum well) in a specific device with a fixed path by adjusting a vertical electric field applied to the quantum well. This spin rotation is described by a generalized Berry's phase and is not a dynamical effect, so it is invariant with respect to the current, source-drain voltage, travel time, and temperature (within a parabolic band approximation). The simplest realization would be a device with a narrow GaAs channel between undoped AlGaAs barriers with spin-selective injection and detection. For a ten nanometer thick GaAs/AlGaAs quantum well the long legs of the device would ideally be on the order of 10-100 nm in length, and transport should be in the drift-diffusion regime. In a spin-orbit field arising from the Rashba effect (due to a vertical electric field applied to the quantum well), or arising from other momentum-dependent spin-orbit fields (due to strain or crystal symmetry), during transport the spin of an electron will precess by an amount exactly proportional to the distance it travels about an axis determined by the travel direction. We can take advantage of this to manipulate the spin by pushing it along a path which can be designed to cause arbitrary rotations about an arbitrary axis not limited to the plane of the quantum well. To generate rotations about an arbitrary axis we must have the electron take a detour between the injection and detection sites. If the electrons are forced to travel along three sides of an appropriately shaped parallelogram the spin rotation will be about any desired out-of-plane axis.