Interlayer phase coherence and superfluidity of electron-hole pairs in multilayer quantum Hall systems

The states with spontaneous interlayer phase coherence in multilayer quantum Hall systems are studied. It is shown that in systems with the average filling factor per layer equal to one half the phase coherence establishes only in bilayer complexes of adjacent layers, and there is no coherence between layers belonging to different complexes. Conditions of stability for such a state against transitions to the uniform charge-ordered state and the charge density wave state are analyzed. It is shown that in systems with finite number of layers N the state with interlayer phase coherence may exist at interlayer distances d