Crossover temperatures in the normal-state phase diagram of high-Tc superconductors

The widespread reference to phase diagrams for the high-T-c superconductors that involve two crossover temperatures T-L and T-U extending across the underdoped normal-stare region is critically examined in the light of NMR and heat capacity data. We conclude that, in both the q=(0,0) and q=(pi,pi) response, there is only one crossover temperature, best described as the pseudogap energy scale rather than a well-defined onset temperature. This has a strong, linearly decreasing dependence on hole concentration. The lower crossover temperature, T-L, commonly determined from (T1T)-T-63, is shown to be an artefact of convoluting the pseudogap energy scale with an intrinsic linear T dependence arising, in the nearly antiferromagnetic Fermi-liquid model, from the characteristic spin-fluctuation frequency, omega(sf). We conclude that models constructed on the two-crossover temperatures scenario need to be reexamined. [S0163-1829(98)00338-5].