Density wave instability in a 2D dipolar Fermi gas

We consider a uniform dipolar Fermi gas in two-dimensions (2D) where the dipole moments of fermions are aligned by an orientable external field. We obtain the ground state of the gas in Hartree-Fock approximation and investigate RPA stability against density fluctuations of finite momentum. It is shown that the density wave instability takes place in a broad region where the system is stable against collapse. We also find that the critical temperature can be a significant fraction of Fermi temperature for a realistic system of polar molecules.