Anisotropic Pauli spin blockade in hole quantum dots

We present measurements on gate-defined double quantum dots in Ge-Si core-shell nanowires, which we tune to a regime with visible shell filling in both dots. We observe a Pauli spin blockade and can assign the measured leakage current at low magnetic fields to spin-flip cotunneling, for which we measure a strong anisotropy related to an anisotropic $g$ factor. At higher magnetic fields we see signatures for leakage current caused by spin-orbit coupling between (1,1) singlet and (2,0) triplet states. Taking into account these anisotropic spin-flip mechanisms, we can choose the magnetic field direction with the longest spin lifetime for improved spin-orbit qubits.

Figure 1

(a) False-color atomic-force microscopy image of the device (left) and schematic depiction of the gate configuration (right). (b) Current $I$ vs $V_{\text{g3}}$ and $V_{\text{g5}}$ with $V_{\text{g2}}=2585$ mV, $V_{\text{g4}}=2210$ mV, $V_{\text{g6}}=3195$ mV, and $V_{\text{SD}}=2$ mV. White dashed lines are guides to the eyes for the honeycomb edges. Blue arrows represent $E_{\text{C}}$, and the gaps between adjacent arrows indicate an additional $E_{\text{orb}}$. Circles mark triangle pairs exhibiting PSB. $(m,n)$ denotes the effective hole occupation $m$ and $n$ on the left and right dot, respectively.

Figure 2

Zoom of the bias triangle pairs exhibiting PSB: (a) and (b) with the same barrier gate voltages as in Fig. 1, and (c) at $V_{\text{g2}}=2570\mathrm{mV},V_{\text{g4}}=2210$ mV, and $V_{\text{g6}}=3160$ mV. Line cuts (lowest panels) taken along the dotted lines for the $V_{\text{SD}}$ direction with (blue) and without PSB (green).

Figure 3

(a) Magnetospectroscopy measurements for different magnetic field directions. $V_{\text{g}3}$ is swept from 486.0 to 489.0 mV while keeping $V_{\text{g}5}=360.0$ mV fixed and sweeping $B$ from 1 to $-1$ T. (b) and (c) Line cuts from (a) at fixed $\epsilon$ (open circles) alongside fitted curves (solid lines). The inset shows a high-resolution scan of the central $I\left(B_x\right)$-peak, the $B_x$-axis is here plotted in mT. (d) Schematic depiction of the magnetospectroscopy directions.