  We investigate the electron states and optical absorption in square- and
hexagonal-shaped two-dimensional (2D) HgTe quantum dots and quantum rings in
the presence of a perpendicular magnetic field. The electronic structure is
modeled by means of the $sp^3d^5s^*$ tight-binding method within the
nearest-neighbor approximation. Both bulklike and edge states appear in the
energy spectrum. The bulklike states in quantum rings exhibit Aharonov-Bohm
oscillations in magnetic field, whereas no such oscillations are found in
quantum dots, which is ascribed to the different topology of the two systems.
When magnetic field varies, all the edge states in square quantum dots appear
as quasibands composed of almost fully flat levels, whereas some edge states in
quantum rings are found to oscillate with magnetic field. However, the edge
states in hexagonal quantum dots are localized like in rings. The absorption
spectra of all the structures consist of numerous absorption lines, which
substantially overlap even for small line broadening. The absorption lines in
the infrared are found to originate from transitions between edge states. It is
shown that the magnetic field can be used to efficiently tune the optical
absorption of HgTe 2D quantum dot and quantum ring systems.

Mesoscale and Nanoscale Physics