Roton Instabilities and Wigner Crystallization of Rotating Dipolar Fermions in the Fractional Quantum Hall Regime

We point out the possibility of occurring instabilities in Laughlin liquids of rotating dipolar fermions with zero thickness. Previously such a system was predicted to be the Laughlin liquid for filling factors being greater and equal to 1/7. However, from intra-Landau-level excitations of the liquid in the single-mode approximation, the roton minima become negative and Laughlin liquids are unstable for filling factors being less and equal to 1/7. We then conclude that there are correlated Wigner crystals for filling factors being less and equal to 1/7.