Three energy scales characterizing the competing pseudogap state, the incoherent, and the coherent superconducting state in high-Tc cuprates

We have studied the momentum dependence of the energy gap of Bi2(Sr,R)2CuOy by angleresolved photoemission spectroscopy (ARPES), particularly focusing on the difference between R=La and Eu. By comparing the gap function and characteristic temperatures between the two sets of samples, we show that there exist three distinct energy scales, {\Delta}pg, {\Delta}sc0, and {\Delta}eff sc0, which correspond to T* (pseudogap temperature), Tonset (onset temperature of fluctuating superconductivity), and Tc (critical temperature of coherent superconductivity). The results not only support the existence of a pseudogap state below T* that competes with superconductivity but also the duality of competition and superconducting fluctuation at momenta around the antinode below Tonset.