The nanometer-scale gap inhomogeneity revealed by recent scanning tunnel microscope images of ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{CaCu}}_2{\mathrm{O}}_{8+x}$ (BSCCO) surface suggests that the “gap coherence length” is of that order. Thus a robust pairing gap can develop despite the poorly screened Coulomb interaction. This can be taken as an evidence that the pairing in high-$T_c$ materials hardly affects the charge correlation and hence occurs primarily among the spin degrees of freedom. We provide theoretical support for this point of view.

• Received 12 June 2001

DOI:https://doi.org/10.1103/PhysRevB.65.054501