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.