  We study ultracold fermionic atoms trapped in an optical lattice with
harmonic confinement by combining the real-space dynamical mean-field theory
with a two-site impurity solver. By calculating the local particle density and
the pair potential in the systems with different clusters, we discuss the
stability of a supersolid state, where an s-wave superfluid coexists with a
density-wave state of checkerboard pattern. It is clarified that a confining
potential plays an essential role in stabilizing the supersolid state. The
phase diagrams are obtained for several effective particle densities.
