New superconducting states in the Hubbard model

By acting on the excited states at half-filling in the positive-$U$ Hubbard model with the $\eta$-pairing operators, we found some new superconducting states in the Hubbard model away from half-filling. Such eigenstates are different from the zero-pair and one-pair states introduced by Yang. It is shown that the one-pair states are not the ground-states and possess ODLRO.