Disentangling the effects of spin-orbit and hyperfine interactions on spin blockade

We have achieved the few-electron regime in InAs nanowire double quantum dots. Spin blockade is observed for the first two half-filled orbitals, where the transport cycle is interrupted by forbidden transitions between triplet and singlet states. Partial lifting of spin blockade is explained by spin-orbit and hyperfine mechanisms that enable triplet to singlet transitions. The measurements over a wide range of interdot coupling and tunneling rates to the leads are well reproduced by a simple transport model. This allows us to separate and quantify the contributions of the spin-orbit and hyperfine interactions.

Figure 1

(Color online) Few-electron double dot charge stability diagram for $V_{SD}=4\text{mV}$ and $B=0$. The numbers in brackets correspond to the charges on the left and the right dots. Dashed lines separate the charge states. The energy required to add an extra electron is proportional to the spacing between the lines: $\Delta E_L=0.14e\Delta V_2$ and $\Delta E_R=0.12e\Delta V_3$. The encircled regions are investigated in Fig. 2. Upper inset: scanning electron micrograph of a nanowire device. Ti/Au gates with a pitch of 60 nm are labeled 1–5. The black stripe is a layer of ${\text{Si}}_3{\text{N}}_4$. Lower inset: arrows pointing up/down correspond to the transitions at which spin blockade is observed for positive/negative bias.

Figure 2

(Color online) (a) Transport diagram through a spin-blocked charge cycle at small detuning, with the relevant transition rates. [(b) and (c)]: $\left(1,1\right)\to \left(0,2\right)$ tuned to weak interdot coupling for $B=0$ and $B=10\text{mT}$, $V_{SD}=5\text{mV}$. [(d) and (e)]: $\left(3,1\right)\to \left(2,2\right)$ tuned to strong interdot coupling for $B=0$ and $B=150\text{mT}$, $V_{SD}=1.3\text{mV}$. Energy levels of (1,1) and (0,2) states are calculated for the regimes in (b)–(e). The dashed line in (b) indicates a cut along the detuning axis, $\epsilon$.

Figure 3

(Color online) (Left) Measured double dot current as a function of detuning and magnetic field. (Right) Simulations of current for different values of $t_{SO}^2/{\Gamma }_{out}$ averaged over $N_f=1000$ random nuclear configurations. (a) and (b) data from $\left(1,1\right)\to \left(0,2\right)$ transition, and (c) data from $\left(1,3\right)\to \left(2,2\right)$ to illustrate large ${\Gamma }_{rel}$ and ${\Gamma }_{inel}$ (see Fig. 4). Simulation parameters: (a) ${\Gamma }_{out}=100\mu \text{eV}$, $t=6.6\mu \text{eV}$, $t_{SO}=0.7\mu \text{eV}$, ${\Gamma }_{rel}=0$; (b) ${\Gamma }_{out}=70\mu \text{eV}$, $t=32\mu \text{eV}$, $t_{SO}=1.8\mu \text{eV}$, ${\Gamma }_{rel}=0.2\text{MHz}$; and (c) ${\Gamma }_{out}=20\mu \text{eV}$, $t=45\mu \text{eV}$, $t_{SO}=8.2\mu \text{eV}$, ${\Gamma }_{rel}=5.4\text{MHz}$.

Figure 4

(Color online) [(a) and (b)] Line cuts from Fig. 3a. The traces at $\epsilon =1.5\text{meV}$ and $B=0\text{mT}$ are scaled by factors of 5 and 0.15, respectively. Dashed area in (b) is shown in the inset. [(c) and (d)] Line cuts from Fig. 3c and fits to the model for various ${\Gamma }_{rel}$ and ${\Gamma }_{inel}$. In the entire figure solid lines are simulations using parameters from Fig. 3 averaged over (a) $N_f=30000$ and [(b)–(d)] $N_f=5000$ random nuclear configurations.