Disorder and proximity driven phenomena in s-wave superconductors

Abstract

In this thesis, we have investigated two important issues in s-wave superconductors, namely effects of disorder and the proximity to normal metal on the superconducting state. The present thesis employs the framework of dynamical mean field theory (DMFT). We have developed extensions to the well-benchmarked impurity solver - iterated perturbation theory for superconductivity (IPTSC), and have used it within DMFT to study the above mentioned phenomena. The thesis has been divided into three chapters. Chapters two and three deal with effects of disorder on s-wave superconductors and chapter four deals with proximity of s-wave superconductor to normal metal. The three chapters are summarized below. In Chapter 2, the disordered attractive Hubbard model is studied by combining dynamical mean field theory (DMFT), coherent potential approximation (CPA) and iterated perturbation for superconductivity (IPTSC) as an impurity solver. The disorder is modeled by taking random values of site-energies. We find that the superconducting order parameter (Φ) decreases with increasing disorder strength (x) and beyond a critical value of x = xc, it completely vanishes, and system becomes non-superconducting. The spectral gap (Eg) shows non-monotonic behaviour. For weak x, Eg decreases with increasing x, and after a certain value of x, it increases with increasing x. Even after the destruction of superconductivity (Φ = 0), the spectral gap persists, thus the system goes being a superconductor to an insulator with increasing disorder. We have calculated the phase diagram in interaction-disorder plane. It is found that xc initially increases with increasing interaction (U), reaches a maximum and then decreases with increasing U. Thus superconductivity becomes less robust in presence of disorder