Finite-momentum condensate of magnetic excitons in a bilayer quantum Hall system

We study the bilayer quantum Hall system at total filling factor νT=1 within a bosonization formalism which allows us to approximately treat the magnetic exciton as a boson. We show that in the region where the distance between the two layers is comparable to the magnetic length, the ground state of the system can be seen as a finite-momentum condensate of magnetic excitons provided that the excitation spectrum is gapped. We analyze the stability of such a phase within the Bogoliubov approximation first assuming that only one momentum Q is macroscopically occupied and later we consider the same situation for two modes ±Q. We find strong evidences that a first-order quantum phase transition at small interlayer separation takes place from a zero-momentum condensate phase, which corresponds to Halperin 111 state, to a finite-momentum condensate of magnetic excitons.