Supersolidity of a dipolar Fermi gas in a cubic optical lattice

Abstract

We study the phase diagram of a dipolar Fermi gas at half-filling in a cubic optical lattice with dipole moments aligned along the $z$ axis. The anisotropic dipole-dipole interaction leads to the competition between ${p}_{z}$-wave superfluid and nematic charge-density-wave (CDW) orders at low temperatures. We find that the superfluid phase survives with weak interactions and the CDW phase dominates with strong interactions. In-between, the supersolid phase appears as a balance between superfluid and CDW orders. The superfluid density is anisotropic in the supersolid and superfluid phases. In the CDW phase, there is a semimetal-to-insulator transition with increase of the interaction strength. Experimental implications are discussed.