Electric field tuning of spin splitting in topological insulator quantum dots doped with a single magnetic ion

We investigate theoretically the electron spin states in a disk-shaped topological insulator quantum dot (TIQD) containing a single magnetic Mn²⁺ ion. We demonstrate that the energy spectra and the density distributions of the symmetry-protected edge states in a HgTe TIQD can be modulated effectively by a single magnetic impurity Mn²⁺. Additionally, when an in-plane external electric field is applied., it not only tunes the spin splittings of edge states via the s(p)-d exchange interaction between the electron (hole) and the magnetic Mn²⁺ ion respectively, but also gives rise to the bright-to-dark transitions in the optical transition spectrum. Such spin properties of TIQDs with single Mn²⁺ ion as illustrated in this work could offer a new platform for topological electro-optical devices.