  In conventional BCS superconductors, the electronic kinetic energy increases
upon superfluid condensation (the change DEkin is positive). Here we show that
in the high critical temperature superconductor Bi-2212, DEkin crosses over
from a fully compatible conventional BCS behavior (DEkin>0) to an
unconventional behavior (DEkin<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 such two regimes around optimal doping.
