Andreas Theiler: Magnetic impurities in conventional superconductors: Effects of superconducting order parameter suppression on Yu–Shiba–Rusinov and Majorana bound states

Abstract

Although impurities in condensed matter systems are commonly regarded as disruptive to ideal bulk behaviour, they can also create local environments where the interplay between a defect and its host material can reveal rich and exotic quantum phenomena. Magnetic impurities in conventional superconductors generate Yu–Shiba–Rusinov (YSR) in-gap bound states, which illustrate both aspects. They suppress the local superconducting order parameter through pair breaking while enabling rich quantum effects, including a quantum phase transition. Additionally, they have attracted interest as building blocks for creating topological superconducting platforms capable of hosting Majorana bound states.

This thesis investigates the changes in the local superconducting order parameter caused by magnetic impurities and the impact of these changes on the phenomena associated with the YSR states. For a single magnetic impurity, the YSR states induce a quantum phase transition when the exchange coupling is varied, accompanied by a discontinuous change in the local superconducting order parameter. Modelling this change through a self-consistent treatment of the order parameter leads to significant modifications of the YSR spectrum in the form of a finite energy gap at the quantum phase transition, as well as changes in ground-state properties at low temperatures. In contrast, observables such as the Josephson current through a YSR state remain largely insensitive to the detailed order parameter profile. Extending the analysis to a topological system containing a chain of magnetic impurities, the suppressed order parameter enhances hybridisation between Majorana bound states and YSR in-gap states, leading to larger Majorana bound state energy oscillations. Furthermore, because a self-consistent treatment of the superconducting order parameter is computationally intensive, these results help clarify when such a treatment is essential and when a constant order parameter approximation provides an adequate description.