Density wave instabilities of tilted fermionic dipoles in a multilayer geometry

We consider the density wave instability of fermionic dipoles aligned by an external field, and moving in equidistant layers at zero temperature. Using a conserving Hartree-Fock approximation, we show that correlations between dipoles in different layers significantly decrease the critical coupling strength for the formation of density waves when the distance between the layers is comparable to the inter-particle distance within each layer. This effect, which is strongest when the dipoles are oriented perpendicular to the planes, causes the density waves in neighboring layers to be in-phase for all orientations of the dipoles. We furthermore demonstrate that the effects of the interlayer interaction can be understood from a classical model. Finally, we show that the interlayer correlations are important for experimentally relevant dipolar molecules, including the chemically stable $^{23}$Na$^{40}$K and $^{40}$K$^{133}$Cs, where the density wave regime is within experimental reach.