Josephson tunnelling into a thin film spin-triplet superconductor

人们普遍认为，超导体Sr2RuO4几乎是独一无二的，因为它可能是库珀对形成自旋S=1的三重态，使其成为自旋三重态超流体He-3的固态类似物[1]。在可能的S=1配对态中有几种可能性，其中LZ=+/-1手征态通常是最有可能的[1，2]，尽管最近也提出了其他的可能性[3]。到目前为止，对这种材料的实验几乎完全集中在大块晶体上。然而，最近几个月，世界各地的三个小组终于成功地生长出了超导薄膜[4，5，6]。这种薄膜提供了一种操纵T_c的新方法，事实上，如果薄膜生长在将a-b晶格常数扩大几个百分点的衬底上，那么T_c将显著增加，从而有效地在两个方向上起到负的单轴应变的作用。操纵薄膜几何结构的可能性也为通过约瑟夫森隧道直接探测库珀对状态的实验提供了广泛的新机会。特别是，以前还没有一个系统可以直接使用约瑟夫森效应来探测库珀对的自旋态。在高度简化的模型[7]中，已经在这个方向上做了一些初步的理论工作，但现在需要通过更现实的计算来完善这一点，这些计算具有真实的能带结构和配对态。在2018年安尼特教授访问位于斯图加特的MPI固态研究中心期间，在安尼特教授和D·曼斯克博士[7]和他的博士后团队、MPI的学生以及他们在东京的实验伙伴[4]之间的讨论之后，这种计算的必要性变得明显起来。在布里斯托尔，我们有一个很好的块体材料模型，它包括一个真实的能带结构和一个多带S=1对状态，考虑和不考虑自旋-轨道耦合的影响。这个模型已经被证明能够对整体的热力学和输运性质以及内在的光学和磁效应产生准确的物理预测，例如与配对态的手征性质相关的克尔效应和轨道矩[8]。然而，这个模型还没有被应用到隧穿到薄膜样品的理论中，这种类型的样品现在正在进行实验。PHD项目的目标将是更新扩展晶格薄膜中存在的新的能带结构的理论模型，然后考虑各种情况下的隧道效应，例如在Sr2RuO4到Sr2RuO4的结中，或者与其他材料的结中，如立方的SrRuO3或Mott绝缘Ca2RuO4或其他与感兴趣的薄膜晶格兼容的材料，因此是未来实验的候选材料。这项工作将使用一系列的理论工具，包括从头算能带结构计算，能隙的自洽计算，然后是描述隧道电流的Bogoliubov de Gennes方程的紧束缚解。隧道电流计算的新特点将是发现它是否由电荷和自旋超流分量组成，从而可能提供一种新的直接测量库珀对自旋的方法。该项目也与EPSRC正在进行的一个由EPSRC资助的项目有关，但与之分开，该项目最近已延长至2020年夏天。

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.