Topological quantum phase transitions in high-temperature superconductors

凝聚态物理学最基本的方面之一是对物质的不同相进行分类。朗道的相变理论给出了一种系统的方法，根据该理论，不同的相具有不同的对称性。这使得可以描述许多热相变(如液-固相变)以及量子相变，即零温相变。除了表现出不同的对称性，相还可以通过它们的拓扑结构来区分，即全局性质，如基态的简并性，这对于量子霍尔效应是重要的。许多实验观察表明，拓扑量子相变也是铜基高温超导体相图的中心。这些材料引起了人们的极大兴趣，不仅是因为定义的高温转变温度和相关的技术潜力，还因为复杂的相图，在许多方面，仍然缺乏理论上的理解。在这个项目中，我们将利用最新的进展，发展现实的理论模型，展示与铜基高温超导体相关的拓扑相，以提高我们对这些材料的微观理解。特别是，对于正常态输运性质、不同相对无序的敏感性、不同的超导不稳定性以及中子散射和拉曼响应中的共振模式的不同模型的预测，将用受控的理论方法进行分析，并与实验观测进行详细的比较。长期目标是建立一个最小和现实的低能量模型，与大量不同的实验相一致。对于其他类别的高温超导体和具有类似唯象性质的进一步强关联材料，预计会有重要的结果。

One of the most fundamental aspects of condensed matter physics is the classification of different phases of matter. A systematic approach is given by Landau's theory of phase transitions according to which different phases are characterized by distinct symmetry properties. This allows describing many thermal transitions (such as the liquid-solid transition) as well as quantum phase transitions, i.e., phase transitions at zero temperature. Instead of exhibiting different symmetries, phases can also be distinguished by their topology, i.e., global properties such as the degeneracy of the ground state, which is, e.g., important for the quantum Hall effects.Many experimental observations indicate that topological quantum phase transitions are also central to the phase diagram of the copper-based high-temperature superconductors. These materials are of high interest, not only because of the defining high transition temperature and the associated technological potential but also due to the complex phase diagram that, in many regards, still lacks theoretical understanding.In this project, we will use the recent progress in developing realistic theoretical models which exhibit the topological phases that are relevant for the copper-based high-temperature superconductors in order to improve our microscopic understanding of these materials. In particular, the predictions of different models for transport properties in the normal state, the sensitivity of the different phases to disorder, the different superconducting instabilities as well as for resonance modes in neutron scattering and Raman response will be analyzed with controlled theoretical approaches and compared in detail with experimental observations. The long-term objective is to establish a minimal and realistic low-energy model that agrees with a large number of different experiments. Important consequences for other classes of high-temperature superconductors and further strongly correlated materials with similar phenomenological properties are expected.