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We study the in-plane and out-of-plane density ordering instabilities ofquasi-two-dimensional fermionic polar molecules in single-layer and multi-layerconfigurations. We locate the soft modes by evaluating linear responsefunctions within the conserving time-dependent Hartree-Fock (TDHF). Theshort-range exchange effects are taken into account by solving theBethe-Salpeter integral equation numerically. An instability phase diagram iscalculated for both single-layer and multi-layer systems and the unstablewave-vector is indicated. In all cases, the in-plane density wave instabilityis found to precede the out-of-plane instability. The unstable wave-vector isfound to be approximately twice the Fermi wave-vector of one of the subbands ata time and can change discontinuously as a function of density and dipolarinteraction strength. In multi-layer configurations, we find a largeenhancement of density wave instability driven by dilute quasiparticles in thefirst excited subband. Finally, we provide a simple qualitative description ofthe phase diagrams using a RPA-like approach. Compared to previous works donewithin the RPA approximation, we find that inclusion of exchange interactionsstabilize the normal liquid phase further and increase the critical dipolarinteraction strength corresponding to the onset of density-wave instability byover a factor of two.

physical review. b, condensed matter and materials physics

Density ordering instabilities of quasi-two-dimensional fermionic polar  molecules in single-layer and multi-layer configurations: exact treatment of  exchange interactions