  By investigating the bulk superconducting state via dc magnetization
measurements, we have discovered a common resurgence of the superconductive
transition temperatures (Tcs) of the monolayer Bi2Sr2CuO6+{\delta} (Bi2201) and
bilayer Bi2Sr2CaCu2O8+{\delta} (Bi2212) to beyond the maximum Tcs (Tc-maxs)
predicted by the universal relation between Tc and doping (p) or pressure (P)
at higher pressures. The Tc of under-doped Bi2201 initially increases from 9.6
K at ambient to a peak at ~ 23 K at ~ 26 GPa and then drops as expected from
the universal Tc-P relation. However, at pressures above ~ 40 GPa, Tc rises
rapidly without any sign of saturation up to ~ 30 K at ~ 51 GPa. Similarly, the
Tc for the slightly overdoped Bi2212 increases after passing a broad valley
between 20-36 GPa and reaches ~ 90 K without any sign of saturation at ~ 56
GPa. We have therefore attributed this Tc-resurgence to a possible
pressure-induced electronic transition in the cuprate compounds due to a charge
transfer between the Cu 3d_(x^2-y^2 ) and the O 2p bands projected from a
hybrid bonding state, leading to an increase of the density of states at the
Fermi level, in agreement with our density functional theory calculations.
Similar Tc-P behavior has also been reported in the trilayer
Br2Sr2Ca2Cu3O10+{\delta} (Bi2223). These observations suggest that higher Tcs
than those previously reported for the layered cuprate high temperature
superconductors can be achieved by breaking away from the universal Tc-P
relation through the application of higher pressures.
