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We study interaction effect of quantum spin Hall state in InAs/GaSb quantumwells under an in-plane magnetic field by using the self-consistent mean fieldtheory. We construct a phase diagram as a function of intra-layer andinter-layer interactions, and identify two novel phases, a charge/spin densitywave phase and an exciton condensate phase. The charge/spin density wave phaseis topologically non-trivial with helical edge transport at the boundary, whilethe exciton condensate phase is topologically trivial. The Zeeman effect isstrongly renormalized due to interaction in certain parameter regimes of thesystem, leading to a much smaller g-factor, which may stabilize the helicaledge transport.

Topological Charge/spin density Wave in InAs/GaSb Quantum Wells under an In-plane Magnetic Field