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We present theoretical arguments and experimental support for the idea thathigh-Tc superconductivity can occur with s-wave, d-wave, or mixed-wave pairingin the context of a magnetic mechanism. The size and shape of the gap isdifferent for different materials. The theoretical arguments are based on thet-J model as derived from the Hubbard model so that it necessarily includesthree-site terms. We argue that this should be the basic minimal model forhigh-Tc systems. We analyze this model starting with the dilute limit which canbe solved exactly, passing then to the Cooper problem which is numericallytractable, then ending with a mean field approach. It is found that therelative stability of s-wave and d-wave depends on the size and the shape ofthe Fermi surface. We identify three striking trends. First, materials withlarge next-nearest-neighbor hopping (such as YBa(2)Cu(3)O(7-x)) are nearly pured-wave, whereas nearest-neighbor materials (such as La(2-x)Sr(x)CuO(4)) tend tobe more s-wave-like. Second, low hole doping materials tend to be pure d-wave,but high hole doping leads to s-wave. Finally, the optimum hole doping levelincreases as the next-nearest-neighbor hopping increases. We examine theexperimental evidence and find support for this idea that gap function in thehigh-temperature superconductors is material-specific.

Material-specific gap function in thet-Jmodel of high-temperature superconductors