Coexistence of superconductivity and antiferromagnetism in heavy-fermion intermetallides

Using the two-time retarded Green's function, we study the conditions for realizing the phase of the superconductivity and antiferromagnetism coexistence in the framework of the effective Hamiltonian for the periodic Anderson model. Such a phase was experimentally observed in rare-earth intermetallides with heavy fermions under an external pressure. In the chosen model, the Cooper instability is induced in the presence of long-range antiferromagnetic ordering as a result of the combined effect of a superexchange interaction in the subsystem of localized electrons and the hybridization between two groups of electrons. Applying an external pressure induces an increase in the energy of the localized level accompanied by an abrupt destruction of the long-range antiferromagnetic ordering in a certain region of the phase diagram. The superconductivity order parameter has a maximum value at the destruction point. We show that the decrease in the antiferromagnetic-sublattice magnetization with increasing pressure leads to a significant increase in the masses of Fermi quasiparticles, and the sign of the current carriers reverses at the critical point. The obtained results qualitatively agree well with the experimental data for the heavy-fermion intermetallide CeRhIn$_5$.