Bilayer paired quantum Hall states and Coulomb drag

We consider a number of strongly correlated quantum Hall states that are likely to be realized in bilayer quantum Hall systems at total Landau level filling fraction ${\nu }_T=1.\mathrm{}$ One state, the $(3,3,-1)$ state, can occur as an instability of a compressible state in the large ${d/l}_B$ limit, where d and $l_B$ are the interlayer distance and magnetic length, respectively. This state has a hierarchical descendent that is interlayer coherent. Another interlayer coherent state, which is expected in the small ${d/l}_B$ limit is the well-known Halperin $\mathrm{}(1,1,1)\mathrm{}$ state. Using the concept of composite fermion pairing, we discuss the wave functions that describe these states. We construct a phase diagram using the Chern-Simons Landau-Ginzburg theory and discuss the transitions between the various phases. We propose that the longitudinal and Hall-drag resistivities can be used together with interlayer tunneling to experimentally distinguish these different quantum Hall states. Our work indicates the bilayer ${\nu }_T=1\mathrm{}$ quantum Hall phase diagram to be considerably richer than that assumed so far in the literature.