Spin interference effects in ring conductors subject to Rashba coupling

Quantum interference effects in rings provide suitable means for controlling spin at mesoscopic scales. Here we apply such control mechanisms to coherent spin-dependent transport in one- and two-dimensional rings subject to Rashba spin-orbit coupling. We first study the spin-induced modulation of unpolarized currents as a function of the Rashba coupling strength. The results suggest the possibility of all-electrical spintronic devices. Moreover, we find signatures of Berry phases in the conductance previously unnoticed. Second, we show that the polarization direction of initially polarized, transmitted spins can be tuned via an additional small magnetic control flux. In particular, this enables to precisely reverse the polarization direction at half a flux quantum. We present full numerical calculations for realistic two-dimensional ballistic microstructures and explain our findings in a simple analytical model for one-dimensional rings.

Figure 1

(a) 1D ring of radius $r_0$ subject to Rashba coupling in the presence of an additional, vertical magnetic field $\mathbf{B}$ (flux $\varphi =\pi r_0^{2}B$). Spin carriers traveling around the ring see a momentum $\left(\mathbf{k}\right)$ dependent in-plane Rashba field ${\mathbf{B}}_{\mathrm{R}}$, which is orientationally inhomogeneous. (b) Up and down spin eigenstates do not generally align with the total effective field ${\mathbf{B}}_{\text{eff}}=\mathbf{B}+{\mathbf{B}}_{\mathrm{R}}$.

Figure 2

Conductance-modulation profile of 1D rings [Fig. 1a] as a function of the dimensionless Rashba strength $Q_{\mathrm{R}}$ in the absence of external magnetic field $(\mathbf{B}=0)$. The curves show our result (14) for $G$ (solid line) compared to the originally incomplete $G_{\text{NMT}}$ of Eq. (16) (dashed line).

Figure 3

2D ring of mean radius $r_0$ and width $w$ used for numerical calculations of the conductance. The gray zone corresponds to the region subject to a finite Rashba coupling. This is switched on and off adiabatically within the leads by using a linear function. An additional, vertical magnetic field $\mathbf{B}$ generates a flux $\varphi =\pi r_0^{2}B$.

Figure 4

Numerical calculation of the conductance-modulation profile (solid line) of a single-mode 2D ring (Fig. 3, aspect ratio $w∕r_0\approx 0.3$) as a function of the dimensionless Rashba strength $Q_{\mathrm{R}}$ in the absence of an external magnetic field $(\mathbf{B}=0)$. Dashed line: corresponding 1D result, Eq. (14) (same as the solid line in Fig. 2) including a fitting prefactor at $Q_{\mathrm{R}}=0$ for comparison.

Figure 5

Numerical results for the conductance of spin-up polarized incoming carriers (see Fig. 3) through a single-mode 2D ring (aspect ratio $w∕r_0\approx 0.3$) as a function of a flux $\varphi =\pi r_0^{2}B$ in the presence of Rashba coupling of increasing strength: $Q_{\mathrm{R}}\approx 0.2$ (a), 1.0 (b), and 1.7 (c) (see Fig. 4 for comparison at $\varphi =0$). The overall conductance (solid line) is split into its components $G^{\uparrow \uparrow }$ (dashed) and $G^{\downarrow \uparrow }$ (dotted). Note the continuous change of the spin polarization with $\varphi$ and the spin switching at $\varphi ={\varphi }_0∕2$.