Spin-polarized current generation from quantum dots without magnetic fields

An unpolarized charge current passing through a chaotic quantum dot with spin-orbit coupling can produce a spin-polarized exit current without magnetic fields or ferromagnets. We use random matrix theory to estimate the typical spin polarization as a function of the number of channels in each lead in the limit of large spin-orbit coupling. We find rms spin polarizations up to 45% with one input channel and two output channels. Finite temperature and dephasing both suppress the effect, and we include dephasing effects using a variation of the third lead model. If there is only one channel in the output lead, no spin polarization can be produced, but we show that dephasing lifts this restriction.

Figure 1

(Color online) A special model quantum dot with $N=1$ channels in the left lead and $M=2$ channels in the right lead. A skew scatterer sends all $\widehat{z}$ spins to the top channel and all $-\widehat{z}$ spins to the bottom channel. The shaded area in the bottom channel has Rashba spin-orbit coupling of precisely the strength to rotate a down spin at the Fermi energy to an up spin, thus producing a perfectly spin-polarized exit current from any input current, while respecting time-reversal symmetry.

Figure 2

(Color online) Generic device with one input channel. Unpolarized current, consisting of equal parts spin-up and spin-down components, is incident on a chaotic quantum dot from a single channel on the left. The irregularly shaped region in the middle is a quantum dot in the strong spin-orbit regime. The spin-up incident current has a probability to exit into each of the three channels of the right lead with a different spin direction in each channel, indicated by the direction of the dark arrows. Similarly for the spin-down incident current, indicated by the light arrows. The exit channels are shown spatially separated, for convenience. There is also a probability to scatter back into the left lead (not shown). The total spin current in the exit lead is given by summing the probabilities and directions of the six spin polarizations shown, which is the meaning of Eq. (4) and is indicated by the arrow on the right.

Figure 3

(Color online) Numerical (symbols) and analytical (lines) results for normalized mean conductance $⟨g⟩$, rms spin conductance $g^s$, and rms spin polarization $p$ of current exiting a chaotic quantum dot with $N$ $\left(M\right)$ channels in the entrance (exit) lead. An average over $60000$ $S$ matrices from the CSE was performed for each data point. The lines are from Eqs. (19, 20, 21).

Figure 4

(Color online) Model with spin-conserving dephasing lead. Numerical (symbols) and analytical (lines) results for normalized mean conductance $⟨g⟩$, rms spin conductance $g^s$, and rms spin polarization $p$ of current exiting a chaotic quantum dot with $N=1$ channel in the entrance lead. $M$ and $N_{\varphi }$ are the numbers of channels in the exit and dephasing leads, respectively. An average over $60000$ $S$ matrices from the CSE was performed for each data point. The lines are from Eqs. (28, 29).