Noncollinear Andreev reflections in semiconductor nanowires

We show that noncollinear Andreev reflections can be induced at interfaces of semiconductor nanowires with spin-orbit coupling, Zeeman splitting, and proximity-induced superconductivity. In a noncollinear local Andreev reflection, the spin polarizations of the injected and the retro-reflected carriers are typically at an angle that is tunable via system parameters. While in a nonlocal transport, this noncollinearity enables us to identify and block, at different voltage configurations, the noncollinear cross Andreev reflection and the direct charge transfer processes. We demonstrate that the intriguing noncollinearity originates from the spin-dependent coupling between carriers in the lead and the lowest discrete states in the wire, which, for a topological superconducting nanowire, are related to the overlap-induced hybridization of Majorana edge states in a finite system. These interesting phenomena can be observed in semiconductor nanowires of experimentally relevant lengths, and are potentially useful for spintronics.

Figure 1

(a) A semiconductor nanowire with proximity-induced superconductivity is coupled to two leads. Under different voltage configurations, either a resonant CAR (b) or a direct charge transfer (c) can occur. In either case, two different microscopic transport channels, marked by blue-solid and red-dashed lines respectively, exist, which are characterized by the electrons (filled circle) and holes (empty circle)in the leads with noncollinear spin polarizations (black arrows). The nonlocal transport processes can thus be blocked by adjusting the polarizations of the HM leads, such that transport in both microscopic channels become impossible.

Figure 2

The lowest discrete state energy $E_1$ of the wire as a function of the effective Zeeman field $V_z$ for wire length $L=1.2$ (solid line), $1.5$ (dashed line), $2.1$ (dash dot dot line), and $4.5\mu \mathrm{m}$ (dash dot line). The inset: differential conductance $dI/dV$ at various $V_z$. Parameters for the inset: $L=1.2\mu \mathrm{m}$, ${\Gamma }_L^{\pm }=0.2t_0$.

Figure 3

Contour plots of the differential conductance $dI/dV$ (a) and noise Fano factor (b) due to the resonant LAR as functions of azimuthal angles $\theta$ and $\phi$ of the HM magnetic moment. Parameters: $V_z=1.2\Delta$, ${\Gamma }_L^{+}=0.4t_0$, and $L=1.2\mu \mathrm{m}$.

Figure 4

(a) The spatial dependence of $\Delta \theta$, the angle for the local spin orientations of the lowest discrete state in resonance, for varius $V_z$, ${\alpha }_R$ and $L$. (b) Contour plot of the differential conductance $dI/dV$ as a function of $V_z$ and the azimuth angle $\theta$ of the magnetic moment in the HM lead. The dashed lines in (b) indicate the directions opposing the local spin orientations of the lowest discrete state on the edge. Other parameters: ${\Gamma }_L^{+}=0.4t_0$, $V_z=1.2\Delta$, $L=1.2\mu \mathrm{m}$, and ${\alpha }_R=0.25\mathrm{eV}·\AA$.

Figure 5

The contour plots of the noise Fano factor $F$ as functions of ${\theta }_L$ and ${\theta }_R$ for different bias configurations for the resonant CAR: (a) $e{V}_1=e{V}_2=E_1$ and (b) $e{V}_1=-e{V}_2=E_1$. Parameters: $V_z=0.8\Delta$, ${\Gamma }_{\alpha }^{+}=0.4t_0$, and $L=1.2\mu \mathrm{m}$.