  In this work, a two-dimensional one-band Hubbard model is investigated within
a two-pole approximation. The model presents a non-local attractive potential
$U (U<0)$ that allows the study of d-wave superconductivity and also includes
hopping up to second-nearest-neighbors. The two-pole scheme has been proposed
to improve the Hubbard-I approximation. The analytical results show a more
complex form for the gap $\Delta(T)$, when compared to the one obtained in the
latter approximation. Indeed, new anomalous correlation functions associated
with the superconductivity are involved in the calculation of $\Delta(T)$.
Numerical results in a range of temperatures are presented. Moreover, the
structure of the quasiparticle bands and the topology of the Fermi surface are
studied in detail in the normal state. Connections with some experimental
results are also included.
