  We study the competition between unconventional superconducting pairing and
charge density wave (CDW) formation for the two-dimensional Edwards Hamiltonian
at half filling, a very general two-dimensional transport model in which
fermionic charge carriers couple to a correlated background medium. Using the
projective renormalization method we find that a strong renormalization of the
original fermionic band causes a new hole-like Fermi surface to emerge near the
center of the Brillouin zone, before it eventually gives rise to the formation
of a charge density wave. On the new, disconnected parts of the Fermi surface
superconductivity is induced with a sign-changing order parameter. We discuss
these findings in the light of recent experiments on iron-based oxypnictide
superconductors.
