Density-wave instability and collective modes in a bilayer of soft-core fermions

We study the dynamics of a bilayer system of fermions with repulsive soft-core Rydberg-dressed interactions

within the mean-field random-phase approximation. We study the symmetric and antisymmetric

collective density modes of the symmetric (equal density) bilayer and find that the dispersion of the

modes signals the emergence of the density wave instability. Depending on the density of fermions in

each layer, interaction strength, and the spacing between two layers, the homogeneous superfluid phase

becomes unstable in either (or both) of these two channels, leading to density and pseudo-spin-density

wave instabilities in the system.