Spin-polarized electric currents in quantum transport through tubular two-dimensional electron gases

Scattering theory is employed to derive a Landauer-type formula for the spin and the charge currents, through a finite region where spin-orbit interactions are effective. It is shown that the transmission matrix yields the spatial direction and the magnitude of the spin polarization. This formula is used to study the currents through a tubular two-dimensional electron gas. In this cylindrical geometry, which may be realized in experiment, the transverse conduction channels are not mixed (provided that the spin-orbit coupling is uniform). It is then found that for modest boundary scattering, each step in the quantized conductance is split into two, and the new steps have a nonzero spin conductance with the spin polarization perpendicular to the direction of the current.

Figure 1

(Color online) A schematic representation of our model: a hollow cylinder, containing a region, $\left|x\right|\le d$, where a spin-orbit interaction, of strength $\alpha$, is active. The electrons are moving on the surface of the tube ballistically, and thus mode mixing is hindered. Short-range boundary scattering, of strength $\zeta$, separates the spin-orbit coupled region from the free regions. The boundaries in between these regions are marked by thick solid lines.

Figure 2

(Color online) The transmission $\mathcal{T}$ through a stripe with spin-orbit interaction (thick line), the $y$ component of the spin transmission $V_y$ (dotted line), and the staircase structure obtained in the absence of the spin-orbit coupling (thin line) in a perfect system, as a function of the energy. Here, the spin-orbit strength is $\alpha =0.9\pi$.

Figure 3

(Color online) Same as Fig. 2, but in the presence of potential barriers at the boundaries, $\zeta =1.2$. Here, $\alpha =0.9\pi$.

Figure 4

(Color online) Same as Fig. 2, but with stronger boundary scattering, $\zeta =4$, and $\alpha =.9\pi$.