Detection and control of charge states in a quintuple quantum dot.

A semiconductor quintuple quantum dot with two charge sensors and an additional contact to the center dot from an electron reservoir is fabricated to demonstrate the concept of scalable architecture. This design enables formation of the five dots as confirmed by measurements of the charge states of the three nearest dots to the respective charge sensor. The gate performance of the measured stability diagram is well reproduced by a capacitance model. These results provide an important step towards realizing controllable large scale multiple quantum dot systems.

Quantum dots (QDs) are artificial systems in which electrons are confined in all three dimensions and the electronic states are determined by the confining potential and Coulombic interaction1. For multiple QDs the electronic states are furthermore influenced by the tunneling and interaction between dots. QDs can offer intriguing systems for constructing fermion Hubbard models2 and also implementing elements of quantum computing34567. Increasing the number of QDs is a necessary step towards these goals and has been attempted using various kinds of materials such as semiconductor heterostructures, nanowires89 and self-assembled dots101112. Single to quadruple QDs have been fabricated in semiconductor heterostrcuture131415 and applied to quantum bits using the charge or spin degree of freedom16171819202122.

Scale-up of QD systems whose electronic states can be precisely manipulated and detected requires several technical advances. In the conventional device architecture, the electronic states are electrically manipulated by two plunger gates and detected by a single charge sensor232425262728. Double or triple QDs (DQD or TQD) are the typical cases in which the charge states can be manipulated by two plunger gates attached to the two dots and detected by a charge sensor. This technique has been applied to quadruple QDs but not more, probably because the sensor sensitivity decreases with the distance to the target QD and also because more plunger gates must be appropriately adjusted to address the individual QDs. In addition multiple QDs are usually constructed by connecting dots in a row with a tunnel-coupled reservoir at each end. This geometry makes it difficult to load electrons from the reservoirs to the inner dots29. In general a set of two plunger gates, one charge sensor and two reservoirs is appropriate to address a triple QD. Therefore splitting into TQDs may be a straightforward approach to scale up the QD architecture3031.

In this work, we fabricate a semiconductor quintuple quantum dot (5QD) or series coupled five QDs with a concept relevant for further increasing the number of QDs. Our 5QD has a reservoir connected to the leftmost, center and rightmost dots, to facilitate loading of electrons to all dots. In addition, two RF charge sensors are independently and simultaneously operated using a frequency multiplexing technique30 to complementarily and precisely read out the charge states. We modify the charge configuration with gate voltages to demonstrate the utility of this architecture by comparing the measured stability diagrams with capacitance model calculations32.

Results

Device and measurement setup

Figure 1(a) shows a scanning electron micrograph of the device and a schematic of the measurement setup. By applying negative voltages to the gate electrodes, five QDs (QD1 to QD5), and two QD charge sensors (sensors 1 and 2) are formed at the dotted circles, and arrows, respectively. Sensors 1 and 2 can efficiently detect the three leftmost dots (QD1 to QD3), and the three rightmost (QD3 to QD5) dots, respectively. The plunger gate P tunes predominantly the energy level of QD, while the tunnel gate T tunes the tunnel coupling between QD and QD. To induce an additional reservoir coupling at QD3, a gap is made in the horizontal line gate (between CL and CR). Electrons are then loaded from the three reservoirs to all dots. This helps to initialize the charge states of the 5QD.

Figure 1

(a) Scanning electron micrograph of the 5QD device and schematic of the measurement setup. (b) |S21| of the resonance circuit as a function of the carrier microwave frequency. The left (right) dip is caused by the resonator including sensor 1 (sensor 2). The center dip is caused by an unused resonator not connected to the device. The traces show the results with different conductance of the sensors (sensor 1 from 0.88 to 0.19 e2/h and sensor 2 from 0.77 to 0.03 e2/h). (c) ((d)) Changes of the RF signal from sensor1, VRF1, as a function of (c) and from sensor 2, VRF2 as a function of (d).

The QD charge sensors are connected to RF resonators configured by the inductors L1 = 270 nH and L2 = 470 nH and the stray capacitances Cp1 and Cp2(≈0.4 pF) for the RF reflectometry. Figure 1(b) shows the reflected RF signal |S21| from the resonance circuit measured by the setup of Fig. 1(a). We observe dips caused by the resonance circuits including sensor 1 and sensor 2 at 207 MHz and 240 MHz respectively. We can detect the change of the sensor conductance through the reflected signal: |S21| at f1 changes by 17 dB due to the conductance change of sensor 1 from 0.88 to 0.19 e2/h (the red traces). Similarly the reflected signal at f2 changes by 23 dB depending on the conductance change of sensor 2 from 0.77 to 0.03 e2/h (the blue traces).

To read out the reflected signals at different frequencies, the room temperature part of the measurement circuit is configured by two sets of local oscillators and mixers (Fig. 1(a)). In this room temperature circuit, two RF carriers are combined and the reflected signal of each charge sensor is picked up by the mixer operating at each carrier frequency simultaneously. Note that simultaneous readout may be important for measurement of temporal correlation of charge or spin between different dots3334. The changes of the RF signal from sensor 1 (VRF1) and sensor 2 (VRF2) are shown in Fig. 1(c) and (d) as a function of the sensor gate voltages and respectively. Note that due to a difference in phase, the reflected signals change in opposite directions in Fig. 1(d). In the following measurement, gate voltages and are adjusted to the condition most sensitive to electrostatic changes of the surrounding environment.

Tuning of the 5QD

Gate tuning of the 5QD is simplified by splitting the five QDs into two TQDs and manipulating the charge states on the two different stability diagrams. Figure 2 shows the numerical derivative of the RF reflectometry signal measured by sensor 1, , in the − plane (a) and by sensor 2, , in the − plane (b), respectively. In each diagram, we observe three sets of distinct charge transition lines with three different slopes, which are defined by the capacitive couplings between the dots and the modulating gates. Each set of charging lines (from the more horizontal to the more vertical) is assigned to charging QD1 to QD3 in (a) and QD5 to QD3 in (b). We adjust the voltages on , , and to make all tunnel or electrostatic couplings between adjacent dots roughly the same judging from the size of avoided crossings between two different charge transition lines. Here we confirm that couplings between distant dots are small, because the corresponding charging lines just cross with each other with no anticrossing. Since the two diagrams share a common P3 axis in the same range, we are able to evaluate appropriate voltages of all gates to manipulate the charge state of the 5QD.

Figure 2

Stability diagram measured for QD1 to QD3 in as a function of and (a) and for QD3 to QD5 in as a function of and (b). At the center of each stability diagram all plunger gate voltage conditions are  = −286 mV,  = −1140 mV,  = −1120 mV,  = −1260 mV and  = −298 mV. The 5QD can be tuned by separating it into two TQDs since QD3 is contacted to the lead.

Stability diagram of the 5QD

We use the gate voltage setting derived from Fig. 2 as a guide to establish the stability diagram of the 5QD. Figure 3(a) and (b) show the diagram in the plane of and measured using sensor 1 () and 2 (), respectively. The other gate voltages are fixed at  = −1585 mV,  = −1020 mV, and  = −470 mV. The values of to are the same as used in Fig. 2. In both figures, five sets of charge transition lines with different slopes are distinguished and from the slopes we are able to assign them to charging five different dots: QD1 to QD5 from vertical to horizontal. The difference in the spacing of the charge transition lines of QD1 and QD5 is caused by the difference in the lever arm of the gates or the charging energy. Figure 3(a) and (b) are measured simultaneously using the multiplex technique of RF reflectometry. Note the charge transition lines of QD1 to QD3 are clearly visible whereas those of QD4 and QD5 are less visible in Fig. 3(a). In contrast the charging lines of QD3 to QD5 are more visible in Fig. 3(b). This observation indicates that each sensor is sensitive to charging of at least three nearest QDs and that two sensors can together detect all charge transitions of the 5QD. Note that the dots in Fig. 3(a) and (b) are not in a few electron regime due to limitation of the gate voltage range and contain dozens of electrons judging from the spacing of the charge transition lines14. Also QD3 has the most electrons due to the gate electrode design. We will be able to reduce the number of electrons by reducing the gaps between the gates to form smaller dots.

Figure 3

Stability diagram in the plane of and for the 5QD measured simultaneously using the multiplex technique: (a) and (b) with  = −1585 mV,  = −1020 mV, and  = −470 mV. (c) Data points extracted from the charge transition lines in (a) and (b): Red, or blue points from (a), or (b), respectively. The grey region shows the area where the sensor sensitivity is too low to apparently distinguish the transition lines. (d) Calculated stability diagram using the capacitive QD model. The capacitance values are estimated from the experiments.

In Fig. 3(c) we show the charging lines for the 5QD by plotting the data points of the dark and white lines in Fig. 3(a) and (b): red and blue points from (a) and (b) and green points from both. Avoided crossings of charging lines of neighboring QDs indicate finite capacitive coupling among all five QDs as is the case in Fig. 2. Also, none of the charge transition lines are fragmented, suggesting that tunneling rates are kept sufficiently high for all QDs. Note that charge sensors are tuned to be most sensitive at the center of stability diagrams and become insensitive in the upper right region (grey region of Fig. 3(c)).

In large systems of multiple QDs, the charge states become complicated and difficult to discriminate. Therefore numerical calculations of stability diagrams are helpful in the process of adjusting gate voltages to search for desirable charge states. We find that the charge stability diagram obtained here is well reproduced in a qualitative manner using a capacitive QD model1535. Figure 3(d) is the calculated stability diagram to reproduce the experiment of Fig. 3(c). The ratios of the capacitance used in the calculation are all taken from the experiment. This simple model shows good agreement with the experiment in which the dots contain many electrons and when we focus on a limited range of the charge stability diagram. We see that the main features in Fig. 3(c) are well reproduced by the calculation (Fig. 3(d)).

Tunability of the 5QD device

Finally we demonstrate the tunability of this device. Figure 4(a) and (c) are the − stability diagrams measured for two different values of −1000 mV, and −1040 mV, respectively but keeping other gate voltage values the same as in Fig. 3(c). The charge transition line of QD3 highlighted in red shifts more than the other charge transition lines. This shift is well reproduced by the calculation of Fig. 4(b) and (d). In the same way, Fig. 4(e) and (g) are the diagrams measured for two different values of of −450 mV and −490 mV, respectively. The charging line of QD4 highlighted in red shifts more than the others as expected from the calculation of Fig. 4(f) and (h).

Figure 4

Comparison between the measured ((a), (c), (e) and (g)) and calculated ((b), (d), (f) and (h)) stability diagrams in the plane of and with and as parameters:  = −1000 mV and  = −470 mV in (a) and (b);  = −1040 mV and  = −470 mV in (c) and (d);  = −1020 mV and  = −450 mV in (e) and (f);  = −1020 mV and  = −490 mV in (g) and (h). The grey region shows the area where some charging lines are not distinguished due to the low sensor sensitivity.

Conclusion

In conclusion, we have fabricated a 5QD device with an additional contact to the center dot from a reservoir and two RF charge sensors, whose design suits further increasing of the number of QDs. We have characterized the gate performance on the charge state stability diagram and well distinguished the charge transition lines corresponding to all five dots thanks to the use of the two charge sensors. We have demonstrated that the gate performance on the stability diagram is well reproduced by the capacitance model. These results are important steps for further scale up of QD system.

Methods

Device structure and measurement

The device was fabricated from a GaAs/AlGaAs heterostructure wafer with an electron sheet carrier density of 5.6 × 1015 m−2 and a mobility of 17 m2/Vs. The two-dimensional electron gas is formed 60 nm under the wafer surface. We patterned a mesa by wet-etching and formed Ti/Au Schottky surface gates by metal deposition, which appear white in Fig. 1(a). All measurements were conducted in a dilution fridge cryostat at a temperature of 27 mK.

Additional Information

How to cite this article: Ito, T. et al. Detection and control of charge states in a quintuple quantum dot. Sci. Rep. 6, 39113; doi: 10.1038/srep39113 (2016).

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