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 Bi-2(Sr, R)(2)CuOy by angle-resolved 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), T-onset (onset temperature of fluctuating superconductivity), and T-c (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 T-onset.