Phonon-Induced Superconductivity and the Staggered Magnetic Field on a Square Lattice

We have considered phonon-induced superconductivity on a square lattice. The antiferromagnetic correlations that are present in high-temperature superconductors (HTSC) have been simulated by the staggered magnetic field. The Eliashberg equations have been generalized to account for the momentum dependent order parameter, and the superconducting transition temperature Tc has been evaluated within the strong-coupling theory. The two-dimensional band structure has explicitly been taken into account. It occurs that the results obtained for Tc when considering d-wave symmetry of the superconducting state much better reflect the experimentally observed behavior than those derived for s-wave symmetry. The isotope shift exponent α has also been evaluated. One can observe that the introduction of the staggered magnetic field leads to the decrease of this quantity. Therefore, the presence of the staggered magnetic field may contribute to experimentally observed values of α smaller than the BCS value of 1/2