Stability Diagram of a Few-Electron Triple Dot

Individual and coupled quantum dots containing one or two electrons have been realized and are regarded as components for future quantum information circuits. In this Letter we map out experimentally the stability diagram of the few-electron triple dot system, the electron configuration map as a function of the external tuning parameters, and reveal experimentally for the first time the existence of quadruple points, a signature of the three dots being in resonance. In the vicinity of these quadruple points we observe a duplication of charge transfer transitions related to charge and spin reconfigurations triggered by changes in the total electron occupation number. The experimental results are largely reproduced by equivalent circuit analysis and Hubbard models. Our results are relevant for future quantum mechanical engineering applications within both quantum information and quantum cellular automata architectures.

Figure 1

Stability diagram of the triatom. Three different sets of parallel lines correspond to the addition spectrum of dot: $A$ (red), $B$ (blue), and $C$ (green). Dashed ovals correspond to three different triple points, where chemical potentials of two dots and the leads coincide. Inset: Scanning electron micrograph of a device, schematically indicating the position of the three dots.

Figure 2

Evolution in the (0, 0, 0) to (1, 1, 1) region as two triple points are gradually merged. Dashed lines have been drawn over interdot charge transfer lines for clarity. (a) Triple points where dots $A$ and $B$ are in resonance (light blue circle) and dots $B$ and C are in resonance (pink circle). (b) The two triple points are closer together and a new structure starts to appear on the right side of the $C=1$ line, (c) The two triple points coincide, creating a quadruple point where the three dots are in resonance. We observe the appearance of a new line on the right side of the $C=1$ line. (d) The triple points move apart again, the original charge transfer line has disappeared. (e) The sequence of events starts to repeat itself around the $C=2$ line.

Figure 3

Theoretical models for the triple dot. (a) Schematics of the circuit model. (b) Theoretical stability diagram using the equivalent circuit model. (c) Hubbard model stability diagram.

Figure 4

Schematic evolution of the triatom configuration in the vicinity of two different quadruple points as gate $5B$ is made less negative. (a) Starting with one electron in $A$ (1, 0, 0), the electron is transferred to $B$ (0, 1, 0), the addition of an extra electron to $C$ triggers an electronic rearrangement in the other dots and the first electron is transferred from $B$ to $A$ (1, 0, 1), finally the electron is retransferred from $A$ to $B$ (0, 1, 1). (b) Starting with one electron in $A$ and 1 electron in $B$ (1, 1, 0), the electron from $A$ is transferred to $B$ (0, 2, 0), the addition of an extra electron in $C$ creates again a charge rearrangement (1, 1, 1), but this time involving a spin rearrangement at low magnetic fields. Finally an electron is transferred from $A$ to $B$ again (0, 2, 1).