A novel approach in Eliashberg theory of superconductivity with ab-initio static and dynamic Coulomb interaction applicable for real materials

In standard Eliashberg methods the Coulomb interaction is usually restricted to the use of a single phenomenological parameter μ^* adjusted to give the right superconducting critical temperature (T_c). In this work we present a parameter-free Eliashberg approach, in which we treat the screened Coulomb interaction within the random phase approximation (RPA) in its static and full dynamic limit. The full energy range of the Coulomb interaction is taken into account, which becomes computationally affordable with the introduction of a suitable isotropic approximation. We have tested the method on a set of conventional superconductors. We will discuss the reliability of the predicted T_c both by using a static and a dynamic Coulomb interaction.