Intrinsic Metastabilities in the Charge Configuration of a Double Quantum Dot

We report a thermally activated metastability in a GaAs double quantum dot exhibiting real-time charge switching in diamond shaped regions of the charge stability diagram. Accidental charge traps and sensor backaction are excluded as the origin of the switching. We present an extension of the canonical double dot theory based on an intrinsic, thermal electron exchange process through the reservoirs, giving excellent agreement with the experiment. The electron spin is randomized by the exchange process, thus facilitating fast, gate-controlled spin initialization. At the same time, this process sets an intrinsic upper limit to the spin relaxation time.

Figure 1

(a) Scanning electron micrograph of a nominally identical device, with contacts (yellow) and gates (white boxes). Gates $p1$–$p3$, wl, wr, and $n$ are used to form the DD in the center while $L1$–$L3$ control the left and $R1$–$R3$ the right sensor dot. (b) Numerical derivative $\mathrm{\Delta }g$ with respect to $p3$ of the left sensor conductance. (c) Larger CSD with gate configuration as in Fig. 2. Circles indicate vertices where the metastability was observed.

Figure 2

Sensor $\mathrm{\Delta }g$ (a) and standard deviation of $g$ (b) from 20 ms measurement windows with reduced tunnel rates compared to Fig. 1. Dashed lines indicate the borders of the metastable diamond while solid lines show the reservoir transitions, obtained from (a). The white and yellow dots show gate voltage configurations used in Figs. 3 and 4.

Figure 3

(a),(b) Switching rates on a log color scale. (c) Switching frequency $f$ on a linear color scale. (d) Probability $P_R$ of finding an electron in the right dot. (e) Real-time trace and (f) ${\mathrm{\Gamma }}_R(T)$ with exponential fit (red) to the high-$T$ data, both taken at the center of the diamond [white dot in Fig. 2]. Data recorded at $30\mu \mathrm{V}$ sensor bias voltage.

Figure 4

(a) Illustration of the model: (I) slow, thermally activated tunneling into the reservoir, followed by (II) tunneling into the metastable (1, 0) state. (b) Both ${\mu }_1(1,0)$ and ${\mu }_2(0,1)$ but not ${\mu }_{1,2}(1,1)$ are below the reservoir Fermi energy within the shaded diamond of metastability. (c) Real-time sensor data for reduced reservoir coupling at 200 mK in the center of the diamond [white dot, Fig. 2]. Switching via the intermediate states (0, 0) and (1, 1) is seen. (d) Four state Markov chain of the model. (e) Histogram of data from (c) as a function of the sensor signal, normalized to the (0, 1) and (1, 0) positions. (f) For comparison, at the (0, 0) triple point [yellow dot, Fig. 2], the (1, 1) state is not seen.

Figure 5

Modeled quantities analogous to Figs. 3 ($T_e=60\mathrm{mK}$, ${\mathrm{\Gamma }}_{1,2}=20\mathrm{kHz}$), agreeing well with experiments. ${\mathrm{\Gamma }}_{L,R}$ are shown with the color scale saturated at the lowest rates seen.