  It is shown that local temporal correlations in addition to non-local spatial
correlations are important to understand the size and the doping dependence of
the d-wave superconducting order parameter of high-temperature superconductors.
To this end, the hole- and electron-doped two-dimensional Hubbard model at zero
temperature is considered and treated by an extension of the variational
cluster approximation. Within this approach, the effects of temporal
correlations can be studied systematically and in a thermodynamically
consistent way by comparing results obtained from different reference clusters.
Contact can be made with previous cellular (plaquette) dynamical mean-field
calculations. This shows that temporal correlations considerably decrease the
order parameter and provide a substantial gain of binding energy. Besides, a
few methodical insights regarding real-space quantum-cluster approaches are
obtained in addition.
