Charge ordering and interlayer phase coherence in quantum Hall superlattices

The possibility of the existence of states with a spontaneous interlayer phase coherence in multilayer electron systems in a high perpendicular magnetic field is investigated. It is shown that phase coherence can be established in such systems only within individual pairs of adjacent layers, while such coherence does not exist between layers of different pairs. The conditions for stability of a state with interlayer phase coherence against transition to a charge-ordered state are determined. It is shown that in a system with $N⩽10$ layers there is stability at any value of the interlayer distance $d.$ For $N>10$ there are two intervals of stability: at sufficiently large and at sufficiently small $d.$ For $N→∞$ the stability interval in the region of small $d$ vanishes.