Relationship between the Fermi surface and the symmetry of the gap function in unconventional superconductors

The relationship between the Fermi surface (FS) and the symmetry of the gap function in unconventional superconductors is argued. It is found that the shapes of the FS are indeed related to the symmetry of the superconducting gap function, and is also influenced by the next nearest-neighbor overlapp ing. The application of the arguments to cuprate superconductors is briefly discussed. There is observed an interesting property that Luttinger's theo rem perfectly holds for various pure gap symmetries in the weak-coupling li mit while it is violated for d(x2-y2)- and d(x2-y2) + id(xy)-wave symmetrie s in a few cases.