Enhancement of superconductivity by pressure-driven competition in electronic order

Finding ways to achieve higher values of the transition temperature, T-c, in superconductors remains a great challenge. The superconducting phase is often one of several competing types of electronic order, including antiferromagnetism and charge density waves(1-5). An emerging trend documented in heavy-fermion(1) and organic(2) conductors is that the maximum T-c for superconductivity occurs under external conditions that cause the critical temperature for a competing order to go to zero. Recently, such competition has been found in multilayer copper oxide high-temperature superconductors (HTSCs3-5) that possess two crystallographically inequivalent CuO2 planes in the unit cell. However, whether the competing electronic state can be suppressed to enhance T-c in HTSCs remains an open question. Here we show that pressure-driven phase competition leads to an unusual two-step enhancement of T-c in optimally doped trilayer Bi2Sr2Ca2Cu3O10+delta (Bi2223). We find that T-c first increases with pressure and then decreases after passing through a maximum. Unexpectedly, T-c increases again when the pressure is further raised above a critical value of around 24 GPa, surpassing the first maximum. The presence of this critical pressure is a manifestation of the crossover from the competing order to superconductivity in the inner of the three CuO2 planes. We suggest that the increase at higher pressures occurs as a result of competition between pairing and phase ordering in different CuO2 planes.