Superfluidity of indirect excitons vs quantum Hall correlation in double Hall systems: Different types of physical mechanisms of correlation organization in Hall bilayers

Bilayer Hall systems can be divided into two groups-with and without tunneling of carriers across the barrier between layers. We demonstrate that these both classes differ in topology sense which leads to the distinct quantum Hall hierarchy. In the case of forbidden interlayer carrier tunneling we developed the Metropolis Monte Carlo simulation for an energy competition of the reentrant integer quantum Hall state against the superfluid Bose Einstein condensate of indirect excitons in double-layer 2D Hall systems, GaAs/GaAlAs/GaAs and b-graphene/hBN/b-graphene, with complementary layer filling, νbot+νtop=1. The resulted phase diagrams for both systems have been determined in consistence with the experimental data.