Superconductivity in the generalized periodic Anderson model with strong local attraction

We study a generalized periodic Anderson model with on-site hybridization between wide- and narrow-band electrons and strong and local coupling with the lattice deformation. Provided that the interaction with the lattice is strong enough, the narrow-band electrons will be turned into small polarons which interact attractively with each other over short distances, leading to the formation of local pairs of narrow-band electrons. This leads to a pinning of the Fermi level which is due to the fact that narrow-band electrons exist only in pair states. By means of a generalized Schrieffer-Wolff transformation we eliminate hybridization and obtain an effective Hamiltonian which describes a contact interaction between local pairs and wide-band electrons as well as the direct hopping of local pairs and interparticle Coulomb interactions. In such a system the two types of mechanisms which can lead to superconductivity have been studied. The first one is due to direct local pair hopping and involves exclusively the narrow-band subsystem giving rise to a superconductivity analogous to superfluidity in ${}_{}{}^4{}_{}{}^{}\mathrm{He}$. The second one is due to a contact interaction between local pairs and pairs of wide-band electrons. This leads to a superconducting state involving both subsystems where the local pairs of the narrow-band subsystem induce Cooper pairing amongst the electrons of the wide-band subsystem. Consequently, the single-particle spectrum of the wide-band electrons opens up a gap around the position of the narrow band of electrons in pair states.