Skew scattering due to intrinsic spin-orbit coupling in a two-dimensional electron gas

We present the generalization of the two-dimensional quantum scattering formalism to systems with Rashba spin-orbit coupling. Using symmetry considerations, we show that the differential scattering cross section depends on the spin state of the incident electron, and skew scattering may arise even for central spin-independent scattering potentials. The skew scattering effect is demonstrated by exact results of a simple hard wall impurity model. The magnitude of the effect for short-range impurities is estimated using the first Born approximation. The exact formalism we present can serve as a foundation for further theoretical investigations.

Figure 1

(Color online) Demonstration of the spin dynamics of plane waves (a) with and (b) without definite helicity [Eq. (10)]: (a) $\gamma =(1,0)$ and (b) $\gamma =(1,i)∕\sqrt{2}$. In both figures, the black arrow denotes the direction of propagation $({\phi }_i=0)$, the red arrows denote the local polarization vector, and the circle denotes the origin. ${\mathbf{\pi }}_0$ is the polarization vector in the origin.

Figure 2

(Color online) The quantities $c$, $v_1$, $v_2$, and $v_3$ (in units of $R$) determining the differential scattering cross section [see Eq. (16)] as functions of the scattering angle $\theta =\phi -{\phi }_i$ for a central hard wall potential. $kR=0.04$.

Figure 3

(Color online) Differential scattering cross sections exactly calculated in the hard wall impurity model, corresponding to the incoming plane waves of Fig. 1: (a) $\gamma =(1,0)$ and (b) $\gamma =(1,i)∕\sqrt{2}$. Here, $kR=0.04$ and $k_{\mathrm{so}}∕k=0.1$.