Quantum rings as electron spin beam splitters

Quantum interference and spin-orbit interaction in a one-dimensional mesoscopic semiconductor ring with one input and two output leads can act as a spin beam splitter. Different polarization can be achieved in the two output channels from an originally totally unpolarized incoming spin state, very much like in a Stern-Gerlach apparatus. We determine the relevant parameters such that the device has unit efficiency.

Figure 1

The geometry of the device and the relevant wave functions in the different domains.

Figure 2

Determination of the parameter values corresponding to perfect polarization: Equations (13a, 13b) with the plus (minus) sign are satisfied along the gray and the thin (thick) black lines, respectively. At each intersection of a black and a gray line the ring acts as a perfect polarizing device. This figure corresponds to a geometry given by ${\gamma }_1=\pi ∕2$, ${\gamma }_2=3\pi ∕2$.

Figure 3

The transmission probability of a perfectly polarizing ring as a function of ${\gamma }_2=2\pi -{\gamma }_1$. The parameter $ka$ changes in the range of [19.0, 21.0], while $0<\omega ∕\Omega <5$, and the plot corresponds to the condition $h_1+h_2=0$.