Topological physics beneath magnetic structures and interfaces on superconductors

很长一段时间以来，人们都知道磁性杂质会在超导体中诱导束缚态[1]，但直到最近几年才意识到，排列这些态[2]会导致所得波函数的扭曲，这被称为改变的拓扑指数。这种拓扑状态的研究现已成为一个非常活跃的研究领域。一个强有力的推动者是最近的一个新发现，即任何量子技术都必须依赖于某种形式的拓扑状态。在这个博士项目中，我们将研究拓扑特性如何出现在嵌入超导体的界面或磁性结构上，在大多数方法所考虑的严格的维度解耦是不可能的。这将建立在我们最近的工作[3，4]。一个特别的重点将被赋予由磁散射体和超导体之间的相互作用所产生的状态之间的相互作用，以及特定的不稳定性，可以导致新的量子相位。[1]L. Yu，Acta Phys. Sin. 21，75（1965）; H. Shiba，Prog. Theor. 40，435（1968）; A. I. Rusinov，JETP Lett. 9，85（1969）。[2]F.皮恩特卡湖I. Glazman和F. von Oppen，Phys. Rev. B 88，155420（2013）; S.纳杰佩日岛K. Drozdov，J. Li，H. Chen，S. Jeon，J. Seo，A. H.麦克唐纳，B。A. Bernevig和A. Yazdani，Science 346，6209（2014）. [3]C. J. F.卡罗尔和B。Braunecker，arXiv：1709.06093. [4]C. J. F.卡罗尔和B。Braunecker arXiv：2108.05768

It has been known for a long time that magnetic impurities induce bound states in superconductors [1] but only in recent years it was realised that lining up such states [2] can lead to a twist in the resulting wave function that is known as a changed topological index. The study of such topological states has by now become a highly active field of research. A strong promotor is the rather recent insight that any quantum technology will have to rely on some form of topological states. In this PhD project we will investigate how topological properties appear at interfaces or magnetic structures embedded on superconductors, in a set-up where a strict dimensional decoupling as considered by most approaches is not possible. This will build on our recent work [3,4]. A particular emphasis will be given to interactions between the states generated by the interaction between the magnetic scatterers and the superconductor, and to particular instabilities that can lead to novel quantum phases.[1] L. Yu, Acta Phys. Sin. 21, 75 (1965); H. Shiba, Prog. Theor. Phys. 40, 435 (1968); A. I. Rusinov, JETP Lett. 9, 85 (1969).[2] F. Pientka, L. I. Glazman, and F. von Oppen, Phys. Rev. B 88, 155420 (2013); S. Nadj-Perge, I. K. Drozdov, J. Li, H. Chen, S. Jeon, J. Seo, A. H. MacDonald, B. A. Bernevig, and A. Yazdani, Science 346, 6209 (2014).[3] C. J. F. Carroll and B. Braunecker, arXiv:1709.06093.[4] C. J. F. Carroll and B. Braunecker arXiv:2108.05768