Accumulation of opposite spins on the transverse edges of a two-dimensional electron gas in a longitudinal electric field

We show that the spin-orbit interaction induced by the boundary-confining potential causes opposite spin accumulations on the transverse edges in a zonal two-dimensional electron gas in the presence of an external longitudinal electric field. While the bias is reversed, the spin-polarized direction is also reversed. The intensity of the spin accumulation is proportional to the bias voltage. In contrast to the bulk extrinsic and intrinsic spin-Hall effects, the spin accumulation by the confining potential is almost unaffected by impurity and survives even in strong disorder. The result provides a different mechanism to explain the recent experimental data.

Figure 1

Schematic diagram for the transverse-effective potential $V_{\mathit{eff}}\left(y\right)$ in the zonal 2DEG for the positive $+p_x$. The inset is a schematic diagram for the infinite zonal 2DEG device.

Figure 2

(Color online) The transverse distribution of the spin and charge density, $P_s\left(y\right)$ and $P_e\left(y\right)$, vs $y$ for the square confining potential. Left panel: $L=29.3\mathrm{nm}$, right panel: $L=58.6\mathrm{nm}$. Notice that the two curves in the right panel almost overlap together so that they almost cannot be distinguished.

Figure 3

(Color online) The transverse distribution of the spin and charge density, $P_s\left(y\right)$ and $P_e\left(y\right)$, vs $y$ for the parabolic confining potential. Left panel: $L=150a$, right panel: $L=300a$. Notice that the blue dashed curves in the below panel almost overlap perfectly with the black solid curves so that they almost cannot be seen.

Figure 4

The spin polarization $P_s∕P_e$ vs the transverse site $y$ for the square confining potential. Panels (a),(b),(c),(d) correspond to $L=14.6\mathrm{nm}$, $L=29.3\mathrm{nm}$, $L=58.6\mathrm{nm}$, and $L=117.3\mathrm{nm}$, respectively. The insets show the detailed distribution near the edge of $y=0$ in the central panel.

Figure 5

The spin polarization $P_s∕P_e$ vs the transverse site $y$ for the parabolic confining potential. Panels (a),(b),(c),(d) correspond to $L=75a$, $150a$, $300a$, and $600a$, respectively. The insets show the detailed distribution near the edge of $y=0$ in the central panel.

Figure 6

(Color online) The charge-density distribution $P_e$ (a), the spin-density distribution $P_s$ (b), and the spin polarization $P_s∕P_e$ (c) vs the transverse site $y$ for the different disorder $W$, respectively. The other parameters are $E_f=0.1\mathrm{eV}$, $L=150a$, and $V=8\mathrm{eV}$. Notice that the black solid curves and the blue dashed curves in the left panel almost overlap each other, and the three curves in the right panel also overlap perfectly, so that they almost cannot be distinguished.