Singlet-triplet spin blockade and charge sensing in a few-electron double quantum dot

Singlet-triplet spin blockade in a few-electron lateral double quantum dot is investigated using simultaneous transport and charge-sensing measurements. Transport from the (1,1) to the (0,2) electron occupancy states is strongly suppressed relative to the opposite bias [(0,2)–(1,1)]. At large bias, spin blockade ceases as the (0,2) triplet state enters the transport window, giving a direct measure of exchange splitting of the (0,2) state as a function of magnetic field. A simple model for current and steady-state charge distribution in spin-blockade conditions is developed and found to be in excellent agreement with experiment. Three other transitions [(1,1)–(2,0), (1,3)–(2,2), and (1,3)–(0,4)] exhibit spin blockade while other nearby transitions and opposite bias configurations do not, consistent with simple even-odd shell filling.

Figure 1

(a) Electron micrograph of a device identical in design to the one measured. Gates 2–6 and 12 define the double dot, 1 and 7 form QPC charge sensors, 8 separates the left QPC and double dot current paths, and 9–11 are unused. Black spots (●) denote ohmic contacts. The origin of spin blockade, when the left dot has 0-1 electrons and the right dot 1–2 electrons, is illustrated in (b) and (c). Opposite spins represent a singlet, same spins a triplet. The left dot accepts any spin but the right can only form a spin singlet, blocking negative bias current once the wrong spin occupies the left dot. A charge sensor $\left(G_{S2}\right)$ also registers the blockade, as a second electron is sometimes in the right dot at positive bias, but not at negative bias.

Figure 2

(Color online) (a) Magnitude of current $I_D$ as a function of $V_2$ and $V_6$ across the (1,0)–(0,1) transition at $0.5\mathrm{mV}$ bias. Ordered pairs $(m,n)$ denote electrons on the left $\left(m\right)$ and right $\left(n\right)$ dots, with $N$ total electrons present during interdot tunneling. The red (●), orange (▾), and yellow (▴) diagrams illustrate the level alignments bounding a bias triangle. The same configuration at $-0.5\mathrm{mV}$ bias, (c), shows almost perfect symmetry. (b) and (d) show the equivalent data at the (1,1)–(0,2) transition. Current flows freely at positive bias, as depicted in the green diagram (∎). Negative bias current is suppressed by spin blockade (blue diagram, ◆) except on the lower (purple diagram, ★) and upper edges. Insets to (b) and (d) show results of a rate equation model which captures most features of the data (see text).

Figure 3

(Color online) Charge sensor signal $G_{S2}$ measured simultaneously with each panel of Fig. 2. A plane is subtracted from each panel to remove direct gate-QPC coupling. The first electron, (a) and (c), again shows bias symmetry while the second, (b) and (d), is missing features at negative bias. The model used in Fig. 2 also reproduces the charge sensor data, as shown in the insets to (b) and (d), with slight disagreement due to second-order processes (see text).

Figure 4

(Color online) Measurements of the singlet-triplet splitting, ${\Delta }_{\mathit{ST}}$. At $+1\mathrm{mV}$ bias, $I_D$ (a) and $G_{S2}$ (b) as a function of $V_2$ and $V_6$ at the (1,1)–(0,2) transition show features where triplet current is allowed (black diagram, ×) rather than just singlet current (green, ∎). At negative bias, $I_D$ (c) turns on and $G_{S2}$ (d) changes when triplet states break the spin blockade (pink + vs blue ◆). Several ${\Delta }_{\mathit{ST}}$ values are measured from (a) to (d), which we attribute to gate voltage dependence of ${\Delta }_{\mathit{ST}}$. As ${\mathrm{B}}_{\perp }$ increases, (e), ${\Delta }_{\mathit{ST}}$ decreases rapidly. The dependence of ${\Delta }_{\mathit{ST}}$ on ${\mathrm{B}}_{\perp }$ is shown in (f), with the solid and open series both taken at negative bias from different gate voltage configurations.

Figure 5

(Color online) Spin blockade at other charge transitions. (a) $G_{S2}$ over a wide range of $V_2$ and $V_6$, differentiated numerically in $V_6$, maps out the first several charges added to each dot. Bipolar transitions at higher occupation numbers (upper right corner) result from large dot conductance affecting the charge sensor measurement due to the shared drain reservoir. (b) Locations of current suppression due to spin blockade in an even-odd level filling model. $I_D$ vs $V_2$ and $V_6$ at each of these eight transitions for positive (upper half) and negative (lower half) bias are shown in panels (c)–(j). Dashed white outlines are guides to the eye indicating the full bias triangle size. One outline in each panel is drawn by hand, then rotated 180° and overlaid on the opposite bias data to ensure equal size. White arrows indicate the boundaries of observed spin blockade regions.