Topological charge-density and spin-density waves in InAs/GaSb quantum wells under an in-plane magnetic field

We study interaction effect of quantum spin Hall state in InAs/GaSb quantum wells under an in-plane magnetic field by using the self-consistent mean field theory. We construct a phase diagram as a function of intralayer and interlayer interactions, and identify two novel phases, a charge-/spin-density wave phase and an exciton condensate phase. The charge-/spin-density wave phase is topologically nontrivial with helical edge transport at the boundary, while the exciton condensate phase is topologically trivial. The Zeeman effect is strongly renormalized due to interaction in certain parameter regimes of the system, leading to a much smaller $g$ factor, which may stabilize the helical edge transport.