Spin transport in a Rashba-coupled two-dimensional quantum ring: An analytical model

We study controlled spin transport through a two-dimensional (2D) spin-orbit coupled quantum ring of finite width. Complete analytical expressions for the energy spectrum and wave function of a 2D ring are obtained in the presence of both an external magnetic field and Rashba spin-orbit interaction. These results have been used to investigate the magnetoconductance of the ring in which an interface electric field leads to the Rashba mechanism. Nonperiodicity of the ground-state angular momentum transition with respect to the external magnetic field is observed for a 2D ring which is in contrast to the perfectly periodic transition spectrum of the one-dimensional (1D) ring. Our analytical model has successfully reproduced the salient features of the magnetoconductance of the ring. In 1D as well as 2D ring geometries, the probability amplitude for the transfer of electron spin, polarized in the direction of an external magnetic field, is found to be maximum irrespective of the polarization of the incoming spin. Since the spin polarization of the transmitted electron changes continuously with Rashba coupling, this system can act as a tunable spin switch electrically controlled by gate voltage.

Figure 1

Schematic illustration of the two-dimensional ring symmetrically coupled to two contact leads A and B.

Figure 2

Energy levels of the 2D ${\mathrm{In}}_{0.1}{\mathrm{Ga}}_{0.9}\mathrm{As}\text{/}\mathrm{GaAs}$ closed ring system for the lowest two radial modes corresponding to $n=0$ (green), 1 (red), and $\left|l\right|\le 4$.

Figure 3

Energy spectrum of the two-dimensional (left panel) and one-dimensional (right panel) ${\mathrm{In}}_{0.1}{\mathrm{Ga}}_{0.9}\mathrm{As}\text{/}\mathrm{GaAs}$ quantum rings for the three different values of Rashba SOI. All the external parameters of both rings are same, and the Zeeman interaction is neglected $(g=0)$. Spin-up and spin-down energy levels are shown by red (thick) and green (thin) colored graphs, respectively.

Figure 4

Energy spectra of (a) a 2D quantum ring and (b) a 1D quantum ring in the presence of Zeeman interaction $(g=-2.15)$ and Rashba SO coupling $\alpha =1\mathrm{meV}\mathrm{nm}$. All other parameters are the same as in Fig. 3. Spin-up and spin-down energy levels are shown by red (thick) and green (thin) colored graphs respectively.

Figure 5

Few lowest-energy levels of clockwise as well as counterclockwise moving electrons in the 2D quantum ring as a function of Rashba SOI for the external magnetic-field $B=10\mathrm{mT}$. Solid curves show the spin-up electrons, whereas spin-down electrons have been shown by dashed curves.

Figure 6

The conductance components $G^{\uparrow \uparrow }$(red), $G^{\uparrow \downarrow }$(green), $G^{\downarrow \uparrow }$(light blue), and $G^{\downarrow \downarrow }$(dark blue) of the 2D ring (left panel) and 1D ring (right panel) for two different values of Rashba coupling $\alpha =0.5$ and $3.0\mathrm{meV}\mathrm{nm}$. Fermi energy is kept fixed at 0.25 meV.

Figure 7

The spin-polarized conductance of the 2D ring (left panel) and the 1D ring (right panel) as a function of RSOI. No external magnetic field is applied here, and Fermi energy is kept fixed at 0.25 meV.