  Starting from an array of four-leg Hubbard ladders weakly doped away from
half-filling and weakly coupled by inter-ladder tunneling, we derive an
effective low energy model which contains a partially truncated Fermi surface
and a well defined Cooperon excitation formed by a bound pair of holes. An
attractive interaction in the Cooper channel is generated on the Fermi surface
through virtual scattering into the Cooperon state. Although the model is
derived in the weak coupling limit of a four-leg ladder array, an examination
of exact results on finite clusters for the strong coupling t-J model suggests
the essential features are also present for a strong coupling Hubbard model on
a square lattice near half-filling.
