Spin-dependent tunneling rates for electrostatically defined GaAs quantum dots

The tunneling rates for spin-up and -down electrons are investigated for a GaAs quantum dot in an in-plane magnetic field by using a real-time single-electron counting scheme with a nearby charge detector. An extremely small spin-polarized current on the order of attoamperes is analyzed with the spin and energy dependences of the tunneling rates. Fully spin-polarized current is obtained when only a spin-up Zeeman sublevel is located in the transport window. When both Zeeman sublevels are allowed to contribute to the transport, we find that the tunneling rate for spin-up electrons is considerably higher than that for spin-down electrons. This partially spin-polarized current can be explained by the exchange-enhanced spin splitting in low-density regions near the tunneling barriers.

Figure 1

(a) Scanning electron micrograph of a device consisting of a quantum dot (QD) and a quantum point contact (QPC) charge detector. The QPC current $I_{\mathrm{PC}}$ is measured at the bias voltage $V_{\mathrm{PC}}$ = 0.6 mV. Schematic energy diagrams for (b) the spin filtering condition and (c) the nonfiltering condition. (d) Charge stability diagram obtained by charge detection. Finite QD bias $V_{\mathrm{QD}}$ = 1.0 mV was applied to open the transport regions, which are located between the double lines in the dashed circles. (e) $I_{\mathrm{PC}}$ traces as a function of $\Delta V_{\mathrm{C}}$ for sweeping $V_{\mathrm{C}}=\Delta V_{\mathrm{C}}-$ 1.12 V around the transport region between the $N=0$ and $N=1$ Coulomb blockade regions. $V_{\mathrm{L}}=\Delta V_{\mathrm{LR}}-682$ mV and $V_{\mathrm{R}}=\Delta V_{\mathrm{LR}}-605$ mV were simultaneously changed with the parameter $\Delta V_{\mathrm{LR}}$, while $V_{\mathrm{QD}}$ = 0.5 mV and $B=$ 5 T were fixed. Each trace is offset horizontally to align the step structures and vertically for clarity.

Figure 2

(a) Transport spectroscopy obtained by charge detection, measured at $V_{\mathrm{L}}=-675$ mV and $V_{\mathrm{R}}=-593$ mV. The inset illustrates spin-filtering (SF) and nonfiltering (NF) regions. (b) Magnetic field dependence of the Zeeman splitting.

Figure 3

(a) Typical histogram of the dwell time in the empty state $T_{\mathrm{E}}$ for $N=[0,1]$. The inset represents typical switching events in $I_{\mathrm{PC}}$. Gate voltage dependence of (b) the transport rate ${\Gamma }_{\mathrm{cur}}$, (c) incoming rate, and (d) outgoing rate. Data were taken at $B=8$ T, $V_{\mathrm{QD}}=0.8$ mV, $V_{\mathrm{L}}=-646$ mV, $V_{\mathrm{C}}=\Delta V_{\mathrm{C}}-1.219$ V, and $V_{\mathrm{R}}=-581$ mV. The insets of (b) show the energy diagrams for the SF and NF regions. (e) Detailed measurement of ${\Gamma }_{\mathrm{i}}$ around the onset, which is fitted with the Fermi distribution function (solid line). Data were taken at $B=$ 8 T, $V_{\mathrm{QD}}=1.0$ mV, $V_{\mathrm{L}}=-675$ mV, $V_{\mathrm{C}}=\Delta V_{\mathrm{C}}-1.15$ V, and $V_{\mathrm{R}}=-593$ mV.

Figure 4

(b) Gate voltage dependence of ${\Gamma }_{\mathrm{i},\uparrow }$ and ${\Gamma }_{\mathrm{i},\downarrow }$ and (a) their ratio $\chi$. Data were taken at $B=8$ T, $V_{\mathrm{QD}}=\pm 0.5$ mV, $V_{\mathrm{L}}=\Delta V_{\mathrm{LR}}-657$ mV, $V_{\mathrm{C}}=-1.185$ V, and $V_{\mathrm{R}}=-\Delta V_{\mathrm{LR}}-590$ mV. (c) Magnetic field dependence of $\chi \equiv {\Gamma }_{\mathrm{i},\downarrow }/{\Gamma }_{\mathrm{i},\uparrow }$. (d) and (e) Schematic energy diagram for spin-up (red lines) and spin-down (blue) electrons around a quantum dot in (e). Local density of states in the lead is shown in (d).