Charge stability diagram of serial triple quantum dots

Serial triple quantum dot (STQD) systems have received extensive attention in the past decade, not only because quantum dot scaling up is an indispensable ingredient for integrations, but also because specific charge states of STQD can be employed to achieve fast full-electrical manipulation of spin qubits. For the latter, a comprehensive understanding of the relationship between neighboring charge occupancy states of STQD is essential for three-electron exchange-only spin qubit-based quantum computations. Charge stability diagram is usually employed to map out the charge occupation states about the plunger gate voltages of STQDs and to study the degeneracy among charge occupation states. Experimentally, two- rather than three-dimensional charge stability diagram was obtained in a lot of early studies by keeping one of plunger gates unchanged to reduce complexity. The obtained two-dimensional diagram could only provide limited information and was subject to blurred boundary of charge occupation states due to the low tunneling current and the energy level broading effects. It was, therefore, challenging to search for the working points where quantum manipulation can be performed promptly and accurately.In principle, three-dimensional charge occupation stability diagram can be efficiently constructed by numerical simulations based on Constant Interaction (CI) model. In this study, we calculated the electrochemical potential of STQD about three plunger gate voltages by using the CI model-based capacitance network to reproduce any desired two-dimensional charge stability diagrams. The simulated diagram not only well agreed with the diagrams obtained from the early experimental data of STQD, but also provided high clarity of the charge state boundaries with tunable parameters. The systematical study of two-dimensional charge stability diagram reviewed the energy degeneracy triple and quadruple points of STQD charge occupation states and concluded the energy degeneracy points in three types to compare with experimental data. For each of the energy degeneracy point, we discussed both the electron and hole transport by using the electrochemical potential alignment schematics. We revealed common and unique triple points of STQD in contrast to those of double quantum dot. The quadruple points of STQD were also addressed in manipulation of quantum cellular automata and quantum logical gate. The comprehensive understanding on these energy degeneracy points can efficiently guide experiments to build an optimal working point of the STQD system for quantum computations and simulations.