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

We have studied the momentum dependence of the energy gap of Bi ₂(Sr,R)₂CuO_y 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, Δ_pg, Δ_sc0, and Δsc0eff, 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.