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We study the influence of an in-plane magnetic field and Coulomb interactionson the physics of quantum spin Hall insulators, like those in InAs/GaSb andHgTe/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 thestrength of the in-plane magnetic field increases, the density-wave region ofthe phase diagram expands and distinct density-wave states appear. We discusspossible experimental implications of our results.

In-plane magnetic field induced density wave states near quantum spin Hall phase transitions