Pauli spin blockade in carbon nanotube double quantum dots

We report Pauli spin blockade in a carbon nanotube double quantum dot defined by tunnel barriers at the contacts and a structural defect in the nanotube. We observe a pronounced current suppression for negative source-drain bias voltages, which is investigated for both symmetric and asymmetric coupling of the quantum dots to the leads. The measured differential conductance agrees well with a theoretical model of a double quantum dot system in the spin-blockade regime, which allows us to estimate the occupation probabilities of the relevant singlet and triplet states. This work shows that effective spin-to-charge conversion in nanotube quantum dots is feasible and opens the possibility of single-spin readout in a material that is not limited by hyperfine interaction with nuclear spins.

Figure 1

(Color online) (a) Schematics of the electrochemical potentials of the relevant one- and two-electron states of a double quantum dot in the absence of a tunnel coupling between them. The level offset between the single-particle states on both dots is given by $\delta ϵ$. The on-site charging energy and electrostatic coupling energy are shown as $U$ and $U^{\prime }$, respectively. (b) When the tunnel coupling $t$ between the quantum dots is significant, the $S\left(1,1\right)$ and $S\left(0,2\right)$ singlet states hybridize to form molecular bonding $\left(S_1\right)$ and antibonding $\left(S_2\right)$ singlet states, which separate from the $T\left(1,1\right)$ triplet states. (c) When a negative bias voltage is applied and one of the $T\left(1,1\right)$ triplet states becomes occupied, the $\left(1,1\right)\to \left(0,2\right)$ transition is not allowed because, by virtue of the Pauli principle, the (0,2) state has to be a spin singlet, and any further current flow is blocked. (d) For opposite bias conditions the $\left(0,2\right)\to \left(1,1\right)$ transition through the singlet states is allowed. Note that for finite detuning, the $S_1$ and $S_2$ singlet states (as well as the triplet states) are still extended molecular states but are dominated by the (0,2) and (1,1) charge states in the way indicated by the schematics.

Figure 2

(Color online) (a) Schematic level diagrams for different transport regimes corresponding to the measurements of panel (c), see symbols. (b) Linear-response conductance of the device measured at $T=1.4\text{K}$. (c) Color-scale plot of the differential conductance $\left(dI/dV\right)$ as a function of source-drain bias voltage $\left(V_{sd}\right)$ and gate voltage $\left(V_g\right)$ for the gate region indicated by the arrows in panel (b). Dark blue corresponds to negative $dI/dV$. The ordered pairs $\left(n,m\right)$ indicate the effective electron occupancy in each quantum dot. (d) Differential conductance for a different region of $V_g$, showing a pronounced asymmetry in both bias and gate voltage.

Figure 3

(Color online) (a) Color-scale plot of the calculated differential conductance as a function of source-drain bias voltage and gate voltage. The model parameters used are $\delta ϵ=5\text{meV}$, $U^{\prime }=12\text{meV}$, $U=17\text{meV}$, (both quantum dots) and $t=0.7\text{meV}$. The relative voltage drop over the tunnel barrier between the two quantum dots is $\Delta V_{\text{QD}}/V_{sd}\sim 0.15$. The temperature is set to $T=4\text{K}$. The symbols correspond to the schematics in Fig. 2. (b) Same as panel (a) for asymmetric coupling of the double quantum dot to the leads as described in the main text.

Figure 4

(Color online) (a) The current and $dI/dV$ can be understood from the evolution of the two singlet states [$S_1$ (red) and $S_2$ (magenta)] and the triplet states (green) as a function of $V_{sd}$. The model parameters used here correspond to the situation of Fig. 3a. The diagonal lines indicate the opening of the bias window as $V_{sd}$ is increased. The electrochemical potential $\mu =6.1\text{meV}$ corresponds to the dotted vertical line in Fig. 3a. (b) Calculated occupation probabilities for the various one- and two-electron states as a function of $V_{sd}$. (c) Peaks in the current and $dI/dV$ are observed when transitions between the one-electron and two-electron states are energetically accessible.

Figure 5

(Color online) (a) Measured current as a function of $V_{sd}$ at gate voltage $V_g=-2.02\text{V}$, corresponding to the dotted vertical line in Fig. 2c. The red oval indicates the regime of Pauli spin blockade with measured leakage current of $\sim 100\text{pA}$. (b) Calculated current traces as a function of electrochemical potential at $V_{sd}=-5.4\text{mV}$ for the model parameters of Fig. 3a. The tunnel couplings are $t=0.7\text{meV}$ (black) and $t=0.3\text{meV}$ (red). Inset: maximum occupation probability of the triplet states.