Josephson tunnelling into a thin film spin-triplet superconductor

The superconductor Sr2RuO4 is widely believed to be almost unique in that it may be one where the Cooper pairs form into a spin S=1 triplet state, making it a solid-state analogue of the spin-triplet superfluid He-3[1]. Among possible S=1 pairing states there are several possibilities, of which the Lz=+/-1 chiral states are generally the most likely [1,2], although others have also been proposed recently [3]. Until now experiments on this material have almost exclusively concentrated on bulk crystals. However, in recent months three groups around the world have finally succeeded in growing thin films which become superconducting [4,5,6]. The thin films provide a new way to manipulate Tc, and indeed Tc has been shown to increase significantly if the films are grown on substrates which expand the a-b lattice constants by a few percent, effectively acting like a negative uniaxial strain in both directions.

The possibilities of manipulating thin film geometry also provides a wide range of new opportunities for experiments which directly probe the Cooper pair state via Josephson tunnelling. In particular, there has been no previous system in which the Josephson effect could be directly used to probe the spin state of a Cooper pair. Some preliminary theoretical work has been done in this direction in highly simplified models [7], but this now needs to be refined by more realistic calculations with realistic band structures and pairing states. During the visit in 2018 of Prof Annett to the MPI for Solid State Research in Stuttgart the need of such calculations became clear following discussions between Prof Annett and Dr D Manske [7] and his group of postdocs and students at the MPI as well as their experimental partners in Tokyo [4]. In Bristol we have a well developed model of the bulk material, which includes a realistic band structure and a multi-band S=1 pairing state, with and without the effects of spin-orbit coupling. This model has already been shown to produce accurate physical predictions for bulk thermodynamic and transport properties as well as intrinsic optical and magnetic effects such as the Kerr effect and orbital moment associated with the chiral nature of the pairing state [8]. However this model has not yet been applied to the theory of tunnelling into thin film samples of the type now open to experiments. The goal of the PhD project will be to update the theoretical model for the new band structure present in expanded lattice thin films, and then to consider tunnelling in various scenarios, eg in junctions of Sr2RuO4 to Sr2RuO4, or junctions with other materials, such as the cubic SrRuO3 or Mott insulating Ca2RuO4 or other materials which are lattice compatible with the thin films of interest and therefore candidates for future experiments. A range of theoretical tools will be used for this work, including ab initio band structure calculation, self-consistent calculations of the gap, and then tight binding solutions of the Bogoliubov de Gennes equations to describe the tunnelling current. The novel feature of the tunnelling current calculations will be to discover whether it consists of both a charge and spin supercurrent components, hence possibly providing a new and direct way of measuring the Cooper pair spin. The project is also related to, but separate from, an ongoing EPSRC funded project, which has recently been extended until summer 2020.