Superconducting Properties from First Principles Calculations: An Ab-Initio Study of the properties of Superconductors under Perturbations

Abstract

Superconductors are commonly used in many magnet systems available to day. One of the most popular is Nb3Sn, due to its high upper critical field and uncomplicated structure. It is however, not particularly well under stood at the microscopic scale with respect to grain boundaries and strain. Grain boundaries appear when forming the material and are used as an effective way to increase the upper critical field by increasing the normal state resistivity, but there is a trade-off, as the critical current density drops as the material becomes more disordered. In addition, when the material is strained by magnetic fields, the superconducting properties will vary. Much experimental work has been performed to study these experimental effects, but a first-principles study gives a unique insight into the intrinsic properties of the material itself. This thesis gives a record of investigations into the strain and grain boundary dependence of Nb3Sn as well as determining whether we can use density functional theory to determine superconducting properties from first principles. This work includes an efficient implementation of a method to calculate the electron-phonon coupling matrix elements from first principles via density functional perturbation theory. This method is tested on some simple metallic elements and shown to provide coupling strengths close in agreement to experimental work.