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The onset temperature of superconducting fluctuation Tonset of Bi2Sr2-xRxCuOy (R=La and Eu) was studied by measuring the Nernst effect. We found that Tonset has a x and R dependence that is quite different from both the pseudogap temperature T* and the critical temperature Tc. Our results support the picture that the incoherent superconductivity, which has been observed below Tonset, is qualitatively different from the pseudogap phenomenon that is characterized by T*. The experimentally obtained phase diagram indicates that the pseudogap state suppresses Tc and enhances superconducting fluctuation while having only small influence on Tonset.

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