Topological physics beneath magnetic structures and interfaces on superconductors

很长一段时间以来，人们就知道磁性杂质在超导体中诱导束缚态[1]，但直到最近几年人们才意识到，排列这样的态[2]会导致由此产生的波函数的扭曲，这种扭曲被称为改变的拓扑指数。这种拓扑态的研究目前已经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种见解，即任何量子技术都必须依赖于某种形式的拓扑态。在这个PHD项目中，我们将研究拓扑性质如何出现在嵌入在超导体上的界面或磁性结构中，在这种设置中，大多数方法认为严格的维度解耦是不可能的。这将建立在我们最近工作的基础上[3，4]。将特别强调由磁散射体和超导体之间的相互作用产生的状态之间的相互作用，以及可能导致新的量子相的特殊不稳定性。罪孽。21，75(1965)；H.Shiba，Prog.西奥。太棒了。40,435(1968)；A.I.Rusinov，JETP Lett。9，85(1969).[2]F.Pientka，L.I.Glazman和F.von Oppen，Phys.155420(2013年)；S.Nadj-Perge，I.K.Drozdov，J.Li，H.Chen，S.Jeon，J.Seo，A.H.MacDonald，B.A.Bernevig和A.Yazdani，Science 346,6209(2014年)。[3]C.J.F.Carroll和B.Braunecker，arxiv：1709.06093.[4]C.J.F.Carroll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