Condensation energy, optical conductivity and Raman scattering in novel superconductors

After I present an overview of the field of superconductivity in the First Chapter of my thesis, I introduce the theoretical framework of my dissertation studies in Chapter Two, where I discuss the imaginary-axis Eliashberg formalism, a successful theoretical method used to describe the properties of novel superconductors, as well as the approximations made in my analyses.;In Chapter Three, I present a detailed study of the condensation energy in superconductors described by the Eliashberg theory for various forms of the pairing interaction, associated either with phonon or electronic pairing mechanisms that give rise to superconductivity. I derive a leading correction to the Bardeen-Cooper-Schrieffer formula for the condensation energy to first order in the coupling lambda. I compute the pairing gap Delta(o) numerically for weak, intermediate and strong coupling lambda for the various pairing interaction scenarios represented by the parameter gamma. I show that at a given lambda, the value of the condensation energy strongly depends on the functional form of the effective pairing interaction Gamma(o). I demonstrate this by means of deriving the functional dependence of the pairing gap Delta on the effective parameter gamma and show that the strong variation in the dependence of the condensation energy on coupling strength with the type of pairing interaction is due to the strong dependence of Delta on gamma.;In the last Chapter of my thesis, I have argued that the data on optical conductivity and Raman scattering in electron-doped cuprates below Tc support the idea that the d-wave gap in these materials is non-monotonically dependent on the phase angle along the Fermi surface. I have computed the conductivity and Raman intensity for elastic scattering in the Born (weak scattering) and unitary limits (diverging scattering length), and found that a non-monotonic gap gives rise to several specific features in optical and Raman response functions. All these features are present in the experimental data on Nd2-xCe xCuO4 and Pr2-xCe xCuO4 compounds.