Finding ways to achieve higher values of the transition temperature, Tc, in superconductors remains a great challenge. The superconducting phase is often one of several competing types of electronic order, including antiferromagnetism and charge density waves1, 2, 3, 4, 5. An emerging trend documented in heavy-fermion1 and organic2 conductors is that the maximum Tc 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, 4, 5) that possess two crystallographically inequivalent CuO2 planes in the unit cell. However, whether the competing electronic state can be suppressed to enhance Tc in HTSCs remains an open question. Here we show that pressure-driven phase competition leads to an unusual two-step enhancement of Tc in optimally doped trilayer Bi2Sr2Ca2Cu3O10+δ (Bi2223). We find that Tc first increases with pressure and then decreases after passing through a maximum. Unexpectedly, Tc 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.
Figures at a glance
Figure 1: Magnetic susceptibility measurement set-up. 
a, Schematic of the crystal structure of Bi2Sr2Ca2Cu3O10+δ. b, Schematic of the double-frequency modulation set-up for the diamond anvil cell. The sample, together with ruby, is located inside the hole in a non-magnetic gasket. The coil system includes a signal coil, a compensating coil, a high-frequency excitation coil and a low-frequency modulating coil. c, The sample and ruby in a neon environment in the gasket hole at 36.4 GPa and 80 K. d, A signal coil wound around a diamond anvil and a compensating coil connected in opposition.
Figure 2: Magnetic susceptibility signals of Bi2Sr2Ca2Cu3O10+δ single crystals at various pressures. 
a, Typical amplitude records for a crystal, with an initial size of 80 × 80 × 10 μm3, on warming. To obtain the strong amplitude signal, we kept the sample signal in phase with the background. b, Typical phase records for a crystal, with an initial size of 50 × 70 × 10 μm3, on warming. To obtain the strong phase signal, we kept the sample signal phase at 90° to the background phase during the measurements. The arrows indicate the superconducting transitions.
Figure 3: Pressure dependence of Tc in optimally doped Bi2Sr2Ca2Cu3O10+δ. 
The symbols represent independent runs on the samples cleaved from the same crystal. The triangle represents Tc at ambient pressure, and the two yellow bars are the Tc values derived from Raman measurements at 15.0 and 33.6 GPa. The dashed line indicates the boundary between the two pressure regimes. The insets show the pressure-driven transition of the inner CuO2 plane (IP) from the competing order (CO) to the superconducting state. OP, outer plane. The arrows indicate electron spin; the up and down spins enclosed by ovals indicate condensed Cooper pairs. Error bars, 1 s.d.
Figure 4: Raman spectra of a Bi2Sr2Ca2Cu3O10+δ single crystal at 33.6 GPa. 
a, Representative Raman results in the frequency range of 100–900 cm−1. b, Raman spectra of the B1g mode and the in-phase A1g mode, and the corresponding fitted Fano profiles (red) plus a linear background. The dashed blue lines indicate the positions of the modes. c, Temperature dependences of the fitted frequencies of the B1g and in-phase A1g modes (circles). The solid diamonds are the frequencies corrected for a small change in pressure with temperature. The dashed line indicates Tc. The red lines are guides to the eye.
