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Pair formation in the periodic Anderson lattice.

We have investigated the possibility of pair formation in the periodic-Anderson-lattice model with a localized level having on-site Coulomb interaction, embedded in a conduction band with hybridization interaction between the localized electron and the conduction electrons. We have obtained conditions for pair formation involving the positions of the Fermi surface and the localized level. If the conduction band is free-electron-like then these conditions are always violated and pair formation is never possible. If, on the other hand, the conduction band is narrow, or hybridization occurs over a narrow momentum domain, then pairing may occur for certain relative positions of the different energies. Even then, pairing is not possible if the strength of the Coulomb interaction is large. Finite-temperature analysis gives the temperature dependence of the gap parameter and the condensation energy. A non-BCS dependence of the critical temperature on the renormalized Coulomb strength has been obtained. In the presence of a large external magnetic field the reentrant nature of the two phases is seen. Finally, except for an isolated value of the localized level the phase transition has been found to be of the first order.