Investigating the effect of impurities on the superconducting state

Our understanding of the superconducting state in real materials is still very limited. Not only are the driving mechanisms for many unconventional superconductors poorly understood but also the coupling to magnetic layers or the effect of impurities represent major conceptual challenges. Furthermore, the effects of interfaces, impurities and spin orbit coupling on spin dependent transport, properties well established in the normal state, attract more and more interest. Here we present the implementation of the Bogoliuobov-de Gennes (BdG) equation into a Green${}^{\prime }$s function (KKR) first principles method. Due to it being a Green${}^{\prime }$s function method, it is possible to model bulk materials including impurities and interfaces without the need of artificial supercells. We parameterise the pairing potential but solve the BdG equation self-consistently incorporating the microscopic properties of real materials. Here we are going to present calculations for various test cases of simple superconductors and will investigate the influence of impurities on the superconducting state with a particular future interest in the influence of magnetic impurities.