Na(x)CoO(2)center dot yH(2)O must be hydrated to superconduct(1), and its triangular CoO2 layers provide an intriguing contrast with the square CuO2 layers of the high-temperature superconductors. Its superconductivity is often assumed to be unconventional in that the Cooper pairs are not in a spin singlet state with s-wave symmetry, as with conventional superconductors. According to the Pauli exclusion principle, pairs with a singlet (triplet) spin part have a corresponding even (odd) spatial part, designated as s-, p, d- or f-wave pairing in accordance with the pair angular momentum. However, in Na(x)CoO(2)center dot yH(2)O, experimental reports are often contradictory(2-6) and solid evidence for any particular pairing state remains lacking. This has led to an unprecedented number of proposals(2,3,5,7-13) for the pairing symmetry (perhaps the greatest number ever for a single compound), each in agreement with some subset of the available data. Here we test each of the 25 symmetry-allowed pairing states(14) against firmly established properties of the compound. Surprisingly, this eliminates most possible pairings. The two remaining states both have f -wave symmetry, suggesting that Na(x)CoO(2)center dot yH(2)O may be the most exotic superconductor discovered so far. We discuss expected features of these states and suggest experiments to distinguish between them.
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