The single and coupled BHZ quantum dots with spin–orbit interaction

Abstract 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 ± π ∕ 4 due to the competition between RSOI and DSOI. The single BHZ QDs 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.