Figure 1

(a) Schematic of the carbon nanotube double quantum dot device. (b) Energy level diagram of the double quantum dot in the spin blockade regime. (c),(d) Charge stability diagrams for $V_{\mathrm{sd}}=-1\mathrm{mV}$ and $V_{\mathrm{sd}}=+1\mathrm{mV}$ measured at temperature $T\sim 60\mathrm{mK}$. The circles indicate the regions of spin blockade. Insets: Detailed measurements of the bias triangles at the $(0,1)$ to $(1,2)$ charge transition measured at $\pm 2\mathrm{mV}$ bias. Note the difference in the current scales.Reuse & Permissions

Figure 2

(a) Bias triangles at the $(0,1)$ to $(1,2)$ charge transition for $V_{\mathrm{sd}}=-1\mathrm{mV}$ and $B=0\mathrm{T}$ for five different barrier gate voltages. (b) Normalized current as a function of the detuning and magnetic field for $V_{\mathrm{bar}}=0$, 10, and 15 mV. The detuning axes follow the dashed white lines in (a) for the three respective barrier gate voltages. In the leftmost panel, two sets of curves of high current are visible. In the middle panel, an additional set of curves appears close to zero magnetic field. The rightmost panel shows a series of additional faintly visible current peaks as illustrated by the line trace and the inset, which shows part of the measurement ($|B|\le 0.37\mathrm{T}$) with enhanced contrast. The evolution with the detuning and magnetic field of the features closely follows that predicted by the model (dashed curves) as described in the main text. The free fitting parameters are the interdot tunnel coupling and the strength of the Heisenberg interaction between the double dot and a spin-$1/2$ impurity.Reuse & Permissions

Figure 3

(a) Energy of the relevant two-electron states of a double quantum dot as a function of the detuning. The black line represents the $(1,1)$ triplet states ($S=1$), while the red and orange curves represent mixtures of a $(0,2)$ singlet state with a $(1,1)$ singlet state ($S=0$). For nonzero magnetic field, the triplet state energies split. (b) Energy of the relevant two-electron states of a double quantum dot including a spin-$1/2$ impurity as a function of detuning. The impurity spin couples via an isotropic Heisenberg interaction with a coupling strength $J_{\mathrm{imp}}$ to one of the dot spins; see the inset. The black line represents a $S=3/2$ quartet. The remaining curves are $S=1/2$ doublets. Spin selection rules allow transitions with $\Delta m_s=\pm 1$: $Q3\leftrightarrow D1$, $Q3\leftrightarrow D3$, $Q4\leftrightarrow D2$, $Q4\leftrightarrow D4$, and $D2\leftrightarrow D3$, while other, forbidden, transitions are $Q4\leftrightarrow D1$ and $Q4\leftrightarrow D3$. (c) Calculated current as a function of the magnetic field and detuning. Left: For no impurity spin ($J_{\mathrm{imp}}=0$) and $t=70\mu \mathrm{eV}$. Middle: For an impurity spin with $J_{\mathrm{imp}}=8\mu \mathrm{eV}$ and $t=87\mu \mathrm{eV}$, no spin-flip tunneling. Right: For impurity spin with $J_{\mathrm{imp}}=6\mu \mathrm{eV}$ and $t=170\mu \mathrm{eV}$, in the presence of spin-flip tunneling with $t_s=7.5\mu \mathrm{eV}$. Note that the origin of the curve $D2\leftrightarrow D3$ in the rightmost plot is the large interdot tunnel coupling and not the spin-orbit interaction.Reuse & Permissions