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We consider a strongly repulsive fermionic gas in a two-dimensional opticallattice confined by a harmonic trapping potential. To address the stronglyrepulsive regime, we consider the $t-J$ Hamiltonian. The presence of theharmonic trapping potential enables the stabilization of coexisting andcompeting phases. In particular, at low temperatures, this allows therealization of a d-wave superfluid region surrounded by purely (gapless) normaledges. Solving the Bogoliubov-de Gennes equations and comparing with the localdensity approximation, we show that the proximity to the Mott insulator isrevealed by a downturn of the Fermi liquid order parameter at the center of thetrap where the d-wave gap has a maximum. The density profile evolves linearlywith distance.

d-wave Superfluid with Gapless Edges in a Cold Atom Trap