Density Waves and Supersolidity in Rapidly Rotating Atomic Fermi Gases

We study theoretically the low-temperature phases of a two-component atomic Fermi gas with attractive $s$-wave interactions under conditions of rapid rotation. We find that, in the extreme quantum limit, when all particles occupy the lowest Landau level, the normal state is unstable to the formation of charge density wave (CDW) order. At lower rotation rates, when many Landau levels are occupied, we show that the low-temperature phases can be supersolids, involving both CDW and superconducting order.