  The quantum spin Hall effect has been predicted theoretically and observed
experimentally in InAs/GaSb quantum wells as a result of inverted band
structures, for which electron bands in InAs layers are below heavy hole bands
in GaSb layers in energy. The hybridization between electron bands and heavy
hole bands leads to a hybridization gap away from k=0. A recent puzzling
observation in experiments is that when the system is tuned to more inverted
regime by a gate voltage (a larger inverted gap at k=0), the hybridization gap
decreases. Motivated by this experiment, we explore the dependence of
hybridization gap as a function of external electric fields based on the
eight-band Kane model. We identify two regimes when varying electric fields:
(1) both inverted and hybridization gaps increase and (2) inverted gap
increases while hybridization gap decreases. Based on the effective model, we
find that light-hole bands in GaSb layers play an important role in determining
hybridization gap. In addition, a large external electric field can induce a
strong Rashba splitting and also influence hybridization gap.
