Generalized cuprate gap symmetry and higher d -wave harmonics: Effects of correlation length, doping, temperature, and impurity scattering

Although d x2 - y2 gap symmetry is well established for the hole-doped cuprates, and for at least a portion of the electron-doped cuprates, the possibility of higher-harmonic gap functions remains. Here we analyze the higher-harmonic problem within a spin-fluctuation-mediated pairing framework by solving the BCS gap equation on a quasicylindrical Fermi surface, explicitly considering deviations from a cylindrical Fermi surface, with specified band structure. We find a number of interesting effects: the shape of the gap function is virtually insensitive to the value of the correlation length assumed; the gap near the node gets steeper with underdoping, implying a flatter density of states; the higher-harmonic components show a complex doping dependence; and the shape of the gap function is insensitive to impurity scattering in the unitary and Born limits.