Topological Superconducting Ring

Abstract

This thesis covers the theoretical analysis of the behaviour of an ion chain on a superconducting ring through which a magnetic flux passes. After the introductory first chapter, in the second chapter we shall cover the behaviour of a non-superconducting ring and show that for a finite ring a persistent current flows. Here we use a tight-binding model and the technique of second quantization to create a suitable model. Following this, in chapter three we describe the behaviour of the superconducting ring using BCS Theory. Here we will see where the topological aspect comes into play in the form of topological regimes. In this chapter we will only be accounting for the movement of the electrons and not the Cooper pairs. This gives incorrect but still interesting results for the energy and current. In the fourth chapter, we include the movement of the Cooper pairs into the analysis and derive a correct equation for the flux generated current. We discuss some of the strange characteristics of the current around the transition points of topological regimes. Finally, we show that in the thermodynamic limit, when you send a flux through a superconducting ring a persistent current will still flow.