  We study by a consistent mean-field scheme the role on the single- and
two-particle properties of a local electron-electron repulsion in the Bernevig,
Hughes and Zhang model of a quantum spin Hall insulator. We find that the
interaction fosters the intrusion between the topological and non-topological
insulators of a new insulating and magnetoelectric phase that breaks
spontaneously inversion and time reversal symmetries, but not their product.
The approach to this phase from both topological and non-topological sides is
signalled by the softening of two exciton branches, i.e., whose binding energy
reaches the gap value, that possess, in most cases, finite and opposite Chern
numbers, thus allowing this phase being regarded as a condensate of topological
excitons. We also discuss how those excitons, and especially their surface
counterparts, may influence the physical observables.
