Anomalous Phenomena in Chiral Superconductors

Abstract

The unconventional class of superconductivity comprises a broad range of materials with vast potential for applications in solid state devices. Unconventional superconducting states are capable of supporting a range of exotic properties, such as intrinsic magnetism, anomalous transport and non-trivial topology, making them ideal candidate materials for many fields, particularly those of spintronics and quantum computation. Harnessing these properties remains challenging as such materials are not yet fully understood, and thus the potential of this class remains largely untapped. The work presented here is focussed on chiral superconductors, a type of unconventional superconducting material in which the Cooper pairs form with an intrinsic magnetic moment. Interplay between the magnetisation associated with a chiral order parameter and the transport properties of superconductivity provides a rich platform for the emergence of unique and anomalous phenomena. The intent of this investigation is to derive a broad set of tools with which to study such phenomena in a general superconductor. Key among the results is the derivation of a modern theory to calculate the total orbital magnetic moment generated by the formation of a superconducting state with a chiral order parameter. Also presented are studies of the anomalous Hall and Kerr effects, which are phenomena deeply linked to the orbital moment. A comprehensive understanding of the shared origin of orbital magnetism and anomalous transport is developed through an analysis of the relation of these properties to the Berry curvature of the intrinsic bandstructure. As a physical platform on which to test and analyse these general theories, two distinct tight-binding models of the proposed p-wave superconductor Sr2RuO4 are presented and utilised for model calculations. The exact form of the order parameter in this material remains a source of fierce debate, and the comparison of the two models provides a method with which to study the origins of the key properties of the state from the structure of the gap. It is demonstrated that multi-band effects are essential in the description of the intrinsic phenomena in Sr2RuO4, and that the spin-orbit interaction plays a vital role in generating these properties. An outstanding issue in the identification of the order parameter in Sr2RuO4 is that p-wave symmetry is expected to induce large edge currents, which have not been observed experimentally. The results obtained here provide possible explanations for this perceived contradiction. Also shown are a range of factors which suppress the magnetisation associated with itinerant currents, such as the presence of superconducting gaps on multiple bands with inter-orbital pairing, the influence of the spin-orbit interaction and the addition of longer range pairing terms in the gap structure. Work remains to be done to irrefutably resolve these issues, but an essential foundation is established through the theoretical work presented here. Finally, the groundwork for a number of avenues for further study is laid, including the fine-tuning of the extended pairing model of Sr2RuO4, the study of anomalous phenomena in other chiral superconductors and the generalisation of the finite-temperature contributions to the orbital moment in a superconductor.

Date of Award	1 Oct 2019
Original language	English
Awarding Institution	University of Bristol
Supervisor	James F Annett (Supervisor) & Martin Gradhand (Supervisor)