Cooper Pairing Near the Boundary in the -U Hubbard Model

The Cooper pairing near the boundary of a superconductor is analyzed by using the linear-response theory The system is described by the square lattice (t, -U) Hubbard model occupying half space. At half filling, the pairing also corresponds to the antiferromagnetic ordering in the repulsive Hubbard model. The numerical result clearly shows that, at weak to intermediate coupling (U/t ≤ l), the boundary exerts strong influence on the order parameter; the weaker the coupling, the deeper the order parameter is suppressed near the boundary. The present scheme is valid in the whole temperature regime of Cooper pairing.