Kinetic energy change with doping upon superfluid condensation in high-temperature superconductors

In conventional BCS superconductors, the electronic kinetic energy increases upon superfluid condensation (the change Delta E-kin is positive). Here we show that in the high critical temperature superconductor Bi2Sr2CaCu2O8+delta, Delta E-kin crosses over from a fully compatible conventional BCS behavior (Delta E-kin>0) to an unconventional behavior (Delta E-kin< 0) as the free carrier density decreases. If a single mechanism is responsible for superconductivity across the whole phase diagram of high critical temperature superconductors, this mechanism should allow for a smooth transition between two such regimes around optimal doping.