Direct measurement of the upper critical field in cuprate superconductors

In the quest to increase the critical temperature T_c of cuprate superconductors, it is essential to identify the factors that limit the strength of superconductivity. The upper critical field H_c2 is a fundamental measure of that strength, yet there is no agreement on its magnitude and doping dependence in cuprate superconductors. Here we show that the thermal conductivity can be used to directly detect H_c2 in the cuprates YBa₂Cu₃O_y, YBa₂Cu₄O₈ and Tl₂Ba₂CuO_6+δ, allowing us to map out H_c2 across the doping phase diagram. It exhibits two peaks, each located at a critical point where the Fermi surface of YBa₂Cu₃O_y is known to undergo a transformation. Below the higher critical point, the condensation energy, obtained directly from H_c2, suffers a sudden 20-fold collapse. This reveals that phase competition - associated with Fermi-surface reconstruction and charge-density-wave order - is a key limiting factor in the superconductivity of cuprates.