Spin-to-Charge Conversion of Mesoscopic Spin Currents

Recent theoretical investigations have shown that spin currents can be generated by passing electric currents through spin-orbit coupled mesoscopic systems. Measuring these spin currents has, however, not been achieved to date. We show how mesoscopic spin currents in lateral heterostructures can be measured with a single-channel voltage probe. In the presence of a spin current, the charge current $I_{\mathrm{qpc}}$ through the quantum point contact connecting the probe is odd in an externally applied Zeeman field $B$, while it is even in the absence of spin current. Furthermore, the zero-field derivative ${\partial }_B{I}_{\mathrm{qpc}}$ is proportional to the magnitude of the spin current, with a proportionality coefficient that can be determined in an independent measurement. We confirm these findings numerically.

Figure 1

(a) QPC transconductance $dG/d{V}_g$ at a large magnetic field $B\gtrsim 5\mathrm{T}$ showing how the ratio of the $g$ factor and the QPC energy resolution $\hslash \omega$ in Eq. (1) can be determined. (b) Proposed setup for measuring mesoscopic spin currents. A voltage probe is connected to a two-terminal lateral quantum dot via a gate-defined (with gate potential $V_g$) single-channel QPC. The spin current through the QPC is converted into an electric signal by applying a sub-Tesla in-plane magnetic field.

Figure 2

Comparison of the spin current $I_3^{(\alpha )}(B=0)$ (red or gray line; right $y$ axis) and the zero-field derivative ${\partial }_B{I}_3^{(0)}{|}_{B=0}$ of the charge current (black line; left $y$ axis) measured at terminal 3, as a function of the Fermi energy $E_F$. The tags $a\mathrm{\text{−}}c$ refer to panels in Fig. 3.

Figure 3

Spin (red or gray lines) and charge (black lines) currents in terminal 3 as a function of the in-plane magnetic field $B$. (a)–(c) Spin-orbit coupled dots corresponding to the labeled data points in Fig. 2. Dotted lines show the slope of the charge current at $B=0$. (d) Dot without spin-orbit interaction (solid lines) and dot with voltages $V_1=V_2=V/2=-V_3$ (dashed lines).