We investigate theoretically electronic structures of the Bernevig–Hughes–Zhang (BHZ) quantum dots (QDs) with both Rashba spin–orbit interaction (RSOI) and Dresselhaus spin–orbit interaction (DSOI) in the topological insulator regime. For a single QD, the ground state’s electron distribution shows a crescent shape along with specific crystallographic directions $\pm \pi ∕4$ due to the competition between RSOI and DSOI. The single BHZ QD can be tuned to coupled QDs with increasing the gate voltage, and the competition between SOIs and double parabolic confinement potential could rotate the electron distribution of the ground state. Furthermore, we find that the BHZ QDs with SOIs produce similar electronic density distribution to the non-topological quantum ring with SOIs. The BHZ QDs with SOIs could be utilized to explore the evolutionary properties of the BHZ model and may implement some topological electronics applications.

我们在拓扑绝缘体体系中研究具有Rashba自旋-轨道相互作用（RSOI）和Dresselhaus自旋-轨道相互作用（DSOI）的Bernevig-Hughes-Zhang（BHZ）量子点（QDs）的理论电子结构。对于单个量子点，基态的电子分布显示新月形以及特定的晶体学方向$\pm \pi ∕4$由于RSOI和DSOI之间的竞争。随着栅极电压的增加，单个BHZ QD可以调谐到耦合的QD，SOI和双抛物线约束电位之间的竞争会旋转基态的电子分布。此外，我们发现具有SOI的BHZ量子点产生的电子密度分布与具有SOI的非拓扑量子环相似。具有SOI的BHZ QD可用于探索BHZ模型的演化特性，并可实现某些拓扑电子应用。