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

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.