Tunable band gap inversion in broken gap quantum wells

In a GaSb/InAs quantum well (QW), the broken gap alignment of the energy bands enables the inversion of the fundamental gap with electrons and holes confined in different layers. In view of this peculiar feature, broken gap GaSb/InAs QWs provide a wide range of possibilities to tune the gap inversion, forming a playground for the study of the two-dimensional quantum spin Hall insulator phase, which is supported by an inverted bandstructure where the electron-hole hybridization plays a central role. In this work we consider a symmetric GaSb/InAs/GaSb QW and use the eight-band Luttinger-Kohn model to study the evolution of the fundamental gap as a function of the QW width and, in particular, the influence of an external electric field. Without external fields, the system presents an "ordinary" behavior until the critical length of the InAs layer (~10.3 nm), where the conduction and valence states become degenerate leading to the collapse of the fundamental band gap. The application of an external field along the growth direction breaks the spatial inversion symmetry, reopening the gap with an inversion between electron and heavy-hole bands. This inverted electron-hole bandstructure assures the existence of the two-dimensional quantum spin Hall insulator phase in a system in which this property can be externally tuned by an applied electric field.