  Mainstream among topological insulators, GaSb/InAs quantum wells present a
broken gap alignment for the energy bands which supports the quantum spin Hall
insulator phase and forms an important building block in the search of exotic
states of matter. Such structures allow the band-gap inversion with electrons
and holes confined in adjacent layers, providing a fertile ground to tune the
corresponding topological properties. Using a full 3D 8-band ${\bf k}\cdot{\bf
p}$ method we investigate the inverted band structure of GaSb/InAs/GaSb and
InAs/GaSb/InAs multilayers and the behavior of the helical edge states, under
the influence of an electric field applied along the growth direction. By
tuning the electric field modulus, we induce the change of the energy levels of
both conduction and valence bands, resulting in a quantum spin Hall insulator
phase where the helical edge states are predominantly confined in the GaSb
layer. In particular, we found that InAs/GaSb/InAs has a large hybridization
gap of about $12\,\textrm{meV}$ and, therefore, are promising to observe
massless Dirac fermions with a large Fermi velocity. Our comprehensive
characterization of GaSb/InAs multilayers creates a basis platform upon which
further optimization of III-V heterostructures can be contrasted.
