Interplay of interlayer pairing and many-body screening in a bilayer of dipolar fermions

Abstract: In a bilayer system of fermionic dipoles, a full control over the strength of the attractive interactions between two layers leads to the BCS-BEC crossover. Here, using the BCS mean field theory, we study such a crossover in symmetric bilayers of ultracold dipolar fermions with their dipole moments being perpendicular to layers. In particular, we investigate how the pairing between two layers and the many-body screening of interlayer interaction affect each other. We compare results for pairings obtained with three different approximations for the interlayer interactions namely, bare dipole-dipole interaction, the random-phase approximation for screening obtained in the normal phase, and the self-consistent superfluid phase screening within the random-phase approximation. We find that at weak couplings the screening further suppresses the pairing while at strong couplings, the screening would be suppressed due to the pairing gap in the quasi-particle spectrum. Therefore a self-consistent treatment of both screening and pairing on equal footings is necessary for obtaining a correct picture of the phase diagram and order parameter at both small and large layer spacings and densities. We also notice that the highly speculated density-wave instability in bilayers with the parallel polarization of dipoles in two layers is simply an artifact of the incorrect screening scheme.