  The upper critical field Hc2 is a fundamental measure of the pairing
strength, yet there is no agreement on its magnitude and doping dependence in
cuprate superconductors. We have used thermal conductivity as a direct probe of
Hc2 in the cuprates YBa2Cu3Oy and YBa2Cu4O8 to show that there is no vortex
liquid at T = 0, allowing us to use high-field resistivity measurements to map
out the doping dependence of Hc2 across the phase diagram. Hc2(p) exhibits two
peaks, each located at a critical point where the Fermi surface undergoes a
transformation. The condensation energy obtained directly from Hc2, and
previous Hc1 data, undergoes a 20-fold collapse below the higher critical
point. These data provide quantitative information on the impact of competing
phases in suppressing superconductivity in cuprates.
