Figure 1

Junction between a HgTe/CdTe QW (light gray) and a metal (dark gray). Due to the applied voltage $V$, electrons are injected from a contact with an angle of incidence $\theta$ with respect to the interface. At the interface they are either reflected or transmitted.Reuse & Permissions

Figure 2

Angle dependence of the transmission probability (left panel) and the amplitude squared of the evanescent mode on the metal side (right panel) for the spin-$\uparrow$ block for a junction between a low-$n$-doped HgTe/CdTe QW and an $n^{\prime }$-doped metal at the Fermi level ($E=0$) as functions of the mass parameter $M$, where $-C_L=1\mathrm{meV}$ and $-C_R=500\mathrm{meV}$. The other parameters are those found in typical HgTe QW experiments, i.e., $A=4$ $\mathrm{eV}\mathring{\mathrm{A}}$, $B=-70$ $\mathrm{eV}{\mathring{\mathrm{A}}}^2$, and $D=-50$ $\mathrm{eV}{\mathring{\mathrm{A}}}^2$. A clear asymmetry is present for negative values of $M$.Reuse & Permissions

Figure 3

Angle dependence of the transmission probability (left panel) and the amplitude squared of the evanescent mode on the metal side (right panel) for the spin-$\uparrow$ block for a junction between a low-$n$-doped HgTe/CdTe QW and a $p$-doped metal at the Fermi level ($E=0$) as a function of the mass parameter $M$, where $-C_L=1\mathrm{meV}$ and $C_R=500\mathrm{meV}$. The values of the parameters $A$, $B$, and $D$ are the same as in Fig. 2. Now, a clear asymmetry is present for values of $M$ close to the critical point.Reuse & Permissions

Figure 4

Angle dependence of the AR probability (left panel) and the amplitude squared of the evanescent (holelike) mode on the HgTe/CdTe QW side (right panel) for an incident spin-$\uparrow$ electron at a junction between a low-$n$-doped HgTe/CdTe QW and a SC at the Fermi level ($\epsilon =0$) as a function of the mass parameter $M$, where $-C_L=5\mathrm{meV}$, $-C_R=1\mathrm{eV}$ and ${\Delta }_0=1\mathrm{meV}$. The values of the parameters $A$, $B$, and $D$ are the same as in Fig. 2. Similarly to Fig. 2, a clear asymmetry is present for negative values of $M$.Reuse & Permissions

Figure 5

Schematic of the AR spin splitter: Electrons are injected from an unpolarized normal metal (pointlike) reservoir R1 (and similarly for R2) due to a bias voltage $V$. As discussed before, we can adjust parameters such that electrons with spin $\downarrow$ (blue full line) arrive at the junction with an angle of incidence favorable for AR. Hence, they are transmitted as Cooper pairs into the SC. This process produces reflected holes with spin $\downarrow$ collected into the first reservoir R1 (blue dashed line). At the same time, this angle of incidence is less favorable for particle-hole conversion of electrons with spin $\uparrow$ (red full line). Thus, these electrons are mostly reflected at the interface to a second reservoir (R2), resulting in a spin imbalance between R1 and R2. Hence, there will be a finite charge current $j_{\rho }$ from the reservoirs R1 and R2 to the SC and there will be a finite spin current $j_{\sigma }$ from R1 to R2. This spin current yields a spin accumulation in the two reservoirs in the direction of the bold arrows.Reuse & Permissions

Figure 6

Bias dependence of the differential spin conductance for a QW/SC contact with $-C_L=50$ $\mathrm{meV}$ and $-C_R=1$ $\mathrm{eV}$. $G_S$ is plotted for different values of the injection energy: $eV=0$ (black dots); $0.3$${\Delta }_0$ (red crosses); $0.6$${\Delta }_0$ (blue circles), and $0.9$${\Delta }_0$ (green triangles). The other parameters are ${\Delta }_0=1$ $\mathrm{meV}$, $A=4$ $\mathrm{eV}\mathring{\mathrm{A}}$, $B=-70$ $\mathrm{eV}{\mathring{\mathrm{A}}}^2$, and $D=-50$ $\mathrm{eV}{\mathring{\mathrm{A}}}^2$. The size of the system is taken as $W=500$ $\mathrm{nm}$ and $L=500$ $\mathrm{nm}$. It is clearly visible that the spin splitter works best at a small bias voltage.Reuse & Permissions