Exciton Condensation in Landau Levels of Quantum Spin Hall Insulators

We theoretically study the quantum spin Hall insulator (QSHI) in a perpendicular magnetic field. In the noninteracting case, the QSHI with space inversion and/or uniaxial spin rotation symmetry undergoes a topological transition into a normal insulator phase at a critical magnetic field B_{c}. The exciton condensation in the lowest Landau levels is triggered by Coulomb interactions in the vicinity of B_{c} at low temperature and spontaneously breaks the inversion and the spin rotation symmetries. We propose that the electron spin resonance spectroscopy with the ac magnetic field also aligned in the perpendicular direction can directly probe the exciton condensation order. Our results should apply to QSHIs such as the InAs/GaSb quantum wells and monolayer transition-metal dichalcogenides.