  We study the energy spectra of bound states in quantum dots (QDs) formed by
an electrostatic potential in two-dimensional topological insulator (TI) and
their transformation with changes in QD depth and radius. It is found that,
unlike a trivial insulator, the energy difference between the levels of the
ground state and first excited state can decrease with decreasing the radius
and increasing the depth of the QD so that these levels intersect under some
critical conditions. The crossing of the levels results in unusual features of
optical properties caused by intracenter electron transitions. In particular,
it leads to significant changes of light absorption due to electron transitions
between such levels and to the transient electroluminescence induced by
electrical tuning of QD and TI parameters. In the case of magnetic TIs, the
polarization direction of the absorbed or emitted circularly polarized light is
changed due to the level crossing.
