Stationary and Transient Leakage Current in the Pauli Spin Blockade

We study the effects of cotunneling and a nonuniform Zeeman splitting on the stationary and transient leakage current through a double quantum dot in the Pauli spin blockade regime. We find that the stationary current due to cotunneling vanishes at low temperature and large applied magnetic field, allowing for the dynamical (rapid) preparation of a pure spin ground state, even at large voltage bias. Additionally, we analyze current that flows between blocking events, characterized, in general, by a fractional effective charge $e^{*}$. This charge can be used as a sensitive probe of spin-relaxation mechanisms and can be used to determine the visibility of Rabi oscillations.

Figure 1

A DQD coupled to leads (a). The charge stability diagram is shown in (b). At low temperature, inelastic cotunneling (c) induces transitions to lower-energy dot levels. Two-electron states at $ϵ=0$ are shown in (d) with allowed $T=0$ cotunneling transitions indicated with straight dashed arrows and curved arrows indicating sequential-tunneling processes.

Figure 2

Leakage current in the PSB regime due to inelastic cotunneling processes. We have taken $ϵ=0$, ${\Gamma }_L={\Gamma }_R=10\mu \mathrm{eV}$, $t=100\mu \mathrm{eV}$, $\Delta =1\mathrm{meV}$, and $g=2.0$. We show the evolution of $I(B)$ as $\delta B$ is varied from 0 mT (dashed line), to 20 mT (dotted line), 200 mT (solid line), and for $W_{T_0\to \sigma }\gg W_{\alpha \to \beta }$, $T=0$ [dash-dotted line, from Eq. (7)]. Evolution of the curve for $\delta B=200\mathrm{mT}$ as temperature is raised is shown in the inset.

Figure 3

Average number $m(T_M)$ of electrons passing through the DQD within measurement time $T_M$. All values are as in Fig. 2 with the addition of $b=1.01\sqrt{2}t$, $T=0$, and ${\Gamma }_R=10{\Gamma }_L=10\mu \mathrm{eV}$. $m(T_M)$ is shown for $\delta B=0\mathrm{mT}$ (solid line), $\delta B=3\mathrm{mT}$ (dash-dotted line), and $\delta B=100\mathrm{mT}$ (dashed line). The predicted saturation points for three of four levels blocking ($m=1/3$), two of four levels blocking ($m=1$), and one of four levels blocking ($m=3$) are shown with dotted lines. The decay cascade (inset) defines the branching ratios $p$ and $q$.