Analysis of characteristic temperatures in high-Tcsystems

Using a self-consistent diagrammatic theory of the one-band Hubbard model, we find that three characteristic temperatures $T^{*},$ $T_c^{*},$ and $T_c$ may characterize the behavior of high-$T_c$ superconductors. The temperature $T^{*}$ defines the onset of a pseudogap in the density of states and of anomalous normal-state behavior. At $T_c^{*}$ local mean-field-like Cooper-pair formation begins with $T_c^{*}<T^{*}.$ Due to phase fluctuations of the order parameter, global spin-fluctuation-induced $d_{x^2-y^2}$-wave superconductivity occurs only at $T_c$ below $T_c^{*}.$ The suppression of $T_c^{*}\to T_c$ is strong for underdoped systems yielding an optimal doping where $T_c$ is largest. The doping dependence of the penetration depth and the influence of Cooper pairing and antiferromagnetic short-range correlations on photoemission experiments are discussed.