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A recently developed projector-based renormalization approach is used to study the two dimensional extended periodic Anderson model. In the extended model an additional local Coulomb repulsion $U_$ between the $f$ and conduction electrons is considered. First, for a one-dimensional lattice it is shown that $U_$ enhances the valence transition for the $f$ electron when the local $f$ energy is shifted through the Fermi level. Also, it is shown that singlet pairing superconducting correlations are dominant as compared to spin and charge correlations even for small values of $U_$. To evaluate the superconducting order parameters for two dimensions we start from an Hamiltonian which includes small gauge symmetry breaking fields. Self-consistent equations for determining the superconducting gaps are derived and numerical results show that, close to a sharp valent transition regime, the $d$-wave superconducting gaps are dominant which once more affirm the valent fluctuation mechanism mediate superconducting state in heavy-fermion system under high pressure. |
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