Heavy fermion superconductivity: X-boson treatment

We use the X-boson method to study the heavy fermion superconductivity employing an extension of the periodic Anderson model in the $U = \infty$ limit with a nearest neighbor attractive interaction between the localized $f$-electrons and we show that higher values of the hybridization parameter implies in lower values associated to the maximum of the superconducting critical temperature $T_{c}$, indicating that the real charge transfer between bands tends to destabilizes the Cooper pairing. Moreover, we show that superconductivity are constrained to the vicinity of a range of occupations where the $f$-band density of states at the Fermi level $\rho_{f} (\mu)$ have sufficiently high values, though superconductivity was found both for configurations where the system present intermediate valence and heavy fermion behavior, as experimentally observed. Finally, as the total occupation is raised and for increased hybridization parameter $V$ there is a transition insulator-superconductor, which is related to the existence of a hybridization gap that cannot be obtained by the slave-boson method.