We study numerically the superconductivity in a system whose normal
state is characterized by the presence of a phenomenological pseudogap,
Eg/t, in the energy spectrum, for
. T*
is called the crossover temperature and it is defined in the high-temperature
superconductors (HTSC) where the static spin susceptibility,
χ(T), is a
maximum. At T*
one also observes the formation of a pseudogap in the density of states around the chemical
potential (Maier et al 2002 Preprint cond-mat/0208419). In order to fix ideas, we have
chosen the pseudogap and the superconducting gap to have the same symmetry. We
have adopted the scenario where the pseudogap and the superconducting gap
are independent of each other (Tallon and Loram 2001 Physica C 349 53), for
which the pseudogap enters in the superconducting phase going down to zero
at zero temperature. We have found that
we require a critical value of the superconducting interaction,
V/t, to produce a finite superconducting critical temperature,
Tc/t, and the superconductor order parameter at
T/t = 0,
Δ0/t. These results have
been obtained for both μ/t = 0
and
. We have obtained a phase diagram, namely,
V/t
versus Eg/t, at half-filling. We have compared our results with the analytical calculations of ţifrea et al (2002 Physica C 371 104), the recent work of ţifrea and Moca (2003 Preprint
cond-mat/0307362 (2004 Europhys. J. B, at press)) and other relevant theoretical results.