  The band-inverted electron-hole bilayers, such as InAs/GaSb, are an
interesting playground for the interplay of quantum spin Hall effect and
correlation effects because of the small density of electrons and holes and the
relatively small hybridization between the electron and hole bands. It has been
proposed that Coulomb interactions lead to a time-reversal symmetry broken
phase when the electron and hole densities are tuned from the trivial to the
quantum spin Hall insulator regime. We show that the transport properties of
the system in the time-reversal symmetry broken phase are consistent with the
recent experimental observations in InAs/GaSb. Moreover, we carry out a quantum
transport study on a Corbino disc where the bulk and edge contributions to the
conductance can be separated. We show that the edge becomes smoothly conducting
and the bulk is always insulating when one tunes the system from the trivial to
the quantum spin Hall insulator phase, providing unambiguous transport
signatures of the time-reversal symmetry broken phase.
