Pairing of Composite-Electrons and Composite-Holes in $\nu_T=1$ Quantum Hall Bilayers

Motivated by recent experimental indications of preformed electron-hole pairs in $\nu_T=1$ quantum Hall bilayers at relatively large separation, we formulate a Chern-Simons (CS) theory of the coupled composite electron liquid (CEL) and composite hole liquid (CHL). We show that the effective action of the CS gauge field fluctuations around the saddle-point leads to stable pairing between CEL and CHL. We find that the CEL-CHL pairing theory leads to a dominant $s$-wave channel in contrast to the dominant $p$-wave channel found in the CEL-CEL pairing theory. Moreover, the CEL-CHL pairing is generally stronger than the CEL-CEL pairing across the whole frequency spectrum. Finally, we discuss possible differences between the two pairing mechanisms that may be probed in experiments.