  The electronic structure of InAs/AlSb/GaSb quantum wells embedded in AlSb
barriers and in the presence of a perpendicular magnetic field is studied
theoretically within the $14$-band ${\bf k}\cdot{\bf p}$ approach without
making the axial approximation. At zero magnetic field, for a quantum well with
a wide InAs layer and a wide GaSb layer, the energy of an electron-like subband
can be lower than the energy of hole-like subbands. As the strength of the
magnetic field increases, the Landau levels of this electron-like subband grow
in energy and intersect the Landau levels of the hole-like subbands. The
electron-hole hybridization leads to a series of anti-crossing splittings of
the Landau levels. The energies of some Landau level transitions and their
corresponding transition strengthes are calculated. The magnetic field
dependence of some dominant transitions is shown with their corresponding
initial-states and final-states indicated. This information should be useful in
analyzing an experimentally measured magneto-optical spectrum. At high magnetic
fields, multiple transitions due to the initial-state splitting can be
observed. The dominant transitions at high fields can be roughly viewed as two
spin-split Landau level transitions with many electron-hole hybridization
induced splittings. The energy separations between the dominant transitions may
decrease or increase versus the magnetic field locally, or may be almost field
independent. The separations can be tuned by changing the width of InAs layer
or the width of middle AlSb layer. When the magnetic field is tilted, the
electron-like Landau level transitions show additional anti-crossing splittings
due to the subband-Landau level coupling.
