Single- and few-electron states in topological-insulator quantum dots

We theoretically investigate the single- and few-electron states of HgTe topological insulator quantum dots using the configuration interaction method and find distinguishing features for both cases. For a single electron, the kinetic energy of the edge states follows an "edge" quantization rule and is robust against the deformation of the circular quantum dot into various elliptic ones, in contrast to the bulk states of the quantum dot. For two electrons, the ratio between the kinetic energy and the Coulomb energy is insensitive to the dot size when the dot is circular, but can be tuned over a relatively wide range by deforming the circular dot into elliptic ones, in contrast to conventional quantum dots, where the kinetic (Coulomb) energy dominates for small (large) dots. For a few electrons, the electrons first fill the edge states in the bulk band gap, and the addition energy and ground state spin exhibit universal even-odd oscillation due to the shape-independent two-fold degeneracy of the edge states. The size of this edge shell can be controlled by tuning the dot size or the band gap of the HgTe quantum well via lateral or vertical electric gating, respectively.