Quantum Oscillation in Excitonic Insulating Electron-Hole Bilayer

We study the quantum oscillations of inter-layer capacitance in an excitonic insulating electron-hole double layer with the Hartree Fock mean-field theory. Such oscillations could be simply understood from the physical picture ``exciton formed by electron/hole Landau levels'', where the direct gap between the electron-hole Landau levels will oscillate with exciton chemical potential and the inverse of the magnetic field. We also find that the excitonic order parameters can be destroyed by a strong magnetic field. At this time, the system becomes two independent quantum Hall liquids and the inter-layer capacitance oscillates to zero at zero temperature.