Towards a Dephasing Diode: Asymmetric and Geometric Dephasing

We study the effect of a noisy environment on spin and charge transport in ballistic quantum wires with spin-orbit coupling (Rashba coupling). We find that the wire then acts as a dephasing diode, inducing very different dephasing of the spins of right and left movers. We also show how Berry phase (geometric phase) in a curved wire can induce such asymmetric dephasing, in addition to purely geometric dephasing. We propose ways to measure these effects through spin detectors, spin-echo techniques, and Aharanov-Bohm interferometry.

Figure 1

The geometries we consider, with applied field, $B$ and Rashba field, $B_R$. In (c), the BP changes sign for wires reflected in the $x$-axis ($\Theta \to -\Theta$). In (d), the source injects a superposition of $\uparrow$ and $\downarrow$ eigenmodes, and the spin flip takes $\uparrow \leftrightarrow \downarrow$. In (e), spin-polarized electrons are injected at $\mathcal{L}$. Some are detected at $\mathcal{R}$, but most escape into $D_{1,2}$.

Figure 2

(a) A sketch of the dispersion curve for $\widehat{\mathcal{H}}$ in Eq. (1); dashed parabolas have $B_x=B_z=0$ [21]. (b) The effective field felt by spin states at $E_F$ (for $B_x=B_y=0$). Since $p_{\uparrow }^{\mathcal{R}}>p_{\downarrow }^{\mathcal{R}}$, the two states have nonorthogonal spins (their overall orthogonality is due to $p_{\uparrow }^{\mathcal{R}}\ne p_{\downarrow }^{\mathcal{R}}$).