Dynamic nuclear polarization with three electrons in a vertical double quantum dot

We report the observation of dynamic nuclear polarization in a vertical double quantum dot, as a result of a hyperfine interaction with three confined electrons. Our data allow us to distinguish three pumping regimes, characterized by different magnitudes and directions of polarization. Corresponding electron-nuclear spin dynamics is understood by considering relevant three-electron states mixed by hyperfine interaction. Also, an extremely long nuclear spin relaxation time is reported.

Figure 1

(a) Schematic view of the GaAs vertical double quantum dot device. (b), (c) $d{I}_{\mathrm{dot}}/d{V}_{\mathrm{SD}}$ vs $V_{\mathrm{SD}}$ and $V_{\mathrm{G}}$. (b) is obtained by sweeping $V_{\mathrm{SD}}$ from $-2$ to 8 mV at different $V_{\mathrm{G}}$, while (c) is obtained by sweeping $V_{\mathrm{SD}}$ from 8 to $-2$ mV. $N$ indicates the number of confined electrons in a particular Coulomb blockade region. (d) Electrochemical potential diagram illustrating the mechanism of Q-SB emergence. (e) $I_{\mathrm{dot}}$ vs $V_{\mathrm{SD}}$, measured by sweeping $V_{\mathrm{SD}}$ up (black trace) and down (gray trace), at $V_{\mathrm{G}}=-0.92$ V [along the arrows marked on (b) and (c)].

Figure 2

(a)–(c) $I_{\mathrm{dot}}$ vs $V_{\mathrm{SD}}$, measured after pumping the nuclei at different values of $V_{\mathrm{pump}}$. (d) $V_{\mathrm{peak}}$ vs $V_{\mathrm{pump}}$: Dark gray symbols correspond to the $I_{\mathrm{dot}}$ maximum at lower $V_{\mathrm{SD}}$, and light gray symbols correspond to the $I_{\mathrm{dot}}$ maximum at higher $V_{\mathrm{SD}}$. $i$, $ii$, and $iii$ indicate $V_{\mathrm{pump}}$ ranges within the Q-SB regime, characterized by different signs of $I_{\mathrm{dot}}$ maxima displacement with respect to position, corresponding to the $V_{\mathrm{pump}}=0$ trace. ${\Delta }_{\mathrm{PP}}$ denotes the gap between current maxima. Dotted lines are guides for the eye.

Figure 3

Energy diagrams of three-electron states involved in the DNP pumping, plotted vs $V_{\mathrm{SD}}$, in (a) the absence and (b) presence of an external magnetic field. $D(1,2)$, $D_{\mathrm{e}}(1,2)$, and $D(0,3)$ denote (1,2)-ground, (1,2)-excited, and (0,3) charge states with $S=1/2$, and $Q(1,2)$ denotes a (1,2) charge state with $S=3/2$. The gray circles in (b) indicate where $Q$ and $D$ states are mixed by the hyperfine interaction and DNP pumping is possible. The dark gray and light gray circles correspond to the direction of the emerging nuclear field $B_N$ with and against the external field, respectively. (c) ${\Delta }_{\mathrm{PP}}$ vs $V_{\mathrm{pump}}$. The dashed-dotted lines are guides for the eye.

Figure 4

DNP relaxation data, plotted as ${\Delta }_{\mathrm{PP}}/{\Delta }_{\mathrm{PP}}^{\mathrm{MAX}}$ vs $\tau$, under different relaxation conditions: $V_{\mathrm{wait}}=0$ at 0.2 K (black triangles); $V_{\mathrm{wait}}=0$ at 0.9 K (gray triangles); $V_{\mathrm{wait}}=-5$ mV at 0.2 K (white triangles). The indicated value ${\Delta }_{\mathrm{PP}}^0/{\Delta }_{\mathrm{PP}}^{\mathrm{MAX}}$ corresponds to zero DNP. Solid lines fit experimental data with biexponential decay. The decay rates (in min) are $53\pm 15$ and $3348\pm 818$, $68\pm 5$ and $2688\pm 570$, and $0.4\pm 0.03$ and $5.5\pm 0.8$, correspondingly. The inset shows the same data plotted on a different time scale.