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Superfluid phases of ultracold Fermi gases on a checkerboard superlattice

We analyze the ground-state phase diagram of two-component Fermi gases loaded into a two-dimensional checkerboard superlattice, i.e. a double-well optical lattice, potential within the BCS mean-field theory. We show that, by coupling the two s-wave sublattice superfluid order parameters, a checkerboard potential gives rise to a Hamiltonian that has the form of a two-band superfluidity with three (two intraband and an interband) nonlocal order parameters. We study the evolution of these order parameters as a function of particle filling, interaction strength and checkerboard potential, and find that the system always prefers the 0-phase solutions, i.e. the phase difference between sublattice order parameters is 0, but never the $π$-phase one. In addition, we find that the ground-state of the system undergo a superfluid-normal quantum phase transition at half fillings beyond a critical checkerboard potential $C$, the threshold of which is precisely determined by the magnitude of the order parameter at $C = 0$, and that the normal state rapidly turns into a checkerboard insulator as $C$ increases.