  We study the influence of an in-plane magnetic field and Coulomb interactions
on the physics of quantum spin Hall insulators, like those in InAs/GaSb and
HgTe/CdTe quantum wells. Using a Hartree-Fock mean-field theory approximation,
we calculate phase diagrams as functions of the band gap, band hybridization,
and magnetic field strength. We show that when the band hybridization is weak,
the system is unstable against the formation of density wave states. As the
strength of the in-plane magnetic field increases, the density-wave region of
the phase diagram expands and distinct density-wave states appear. We discuss
possible experimental implications of our results.

Mesoscale and Nanoscale Physics;Strongly Correlated Electrons