Interaction Effects and Topology in Relativistic Quantum Materials

量子力学和爱因斯坦的相对论构成了现代物理学的两大基本支柱。传统的凝聚态物理在很大程度上依赖于其中的第一个，大多数物质的性质本质上都是量子力学的——相对论只起了很小的作用。从2005年开始，凝聚态物理学经历了一场深刻而意想不到的革命，事后看来，这场革命可以被称为“相对论”。最终发现了一种叫做拓扑绝缘体（TI）的新物质。在这些新材料中，量子力学和相对论相结合产生了一个显著的结果：它可以被描述为晶体固体，其体积是绝缘的（不导电），但其表面是金属，因此是良导体。在过去的十年中，人们对拓扑绝缘体进行了广泛的研究，许多固体已经被实验确定为ti。目前正在进行丰富的实验项目，以测试与它们相关的各种理论提出的现象。世界范围内也在努力利用其独特的特性进行实际应用。一个平行研究的相关类别的材料称为拓扑超导体（TSCs）也已开始。到目前为止，我们还没有一个证实的实验实现天然TSC材料，但某些人工工程结构被认为具有TSC的行为。本提案涉及拓扑绝缘体和超导体中新量子现象的理论探索。

Quantum mechanics and Einstein's theory of relativity form two fundamental pillars of modern physics. Traditional condensed matter physics depends heavily on the first one of these most material properties are inherently quantum mechanical -- with relativity playing only a minor role. Beginning in 2005 condensed matter physics underwent a profound and rather unexpected revolution, which in the hindsight could be termed “relativistic”. It culminated in the discovery of a new form of matter called topological insulator (TI). In these novel materials quantum mechanics and relativity combine to produce a remarkable outcome: TIs can be described as crystalline solids whose bulk is insulating (does not conduct electricity) but whose surfaces are metallic and thus good conductors. In the past decade topological insulators have been extensively studied and numerous solids have been experimentally identified as TIs. Rich experimental programs to test for the variety of theoretically proposed phenomena associated with them are now ongoing. Worldwide effort to harness their unique properties for practical applications is also underway. A parallel study of the related class of materials called topological superconductors (TSCs) has also been initiated. Thus far we do not have a confirmed experimental realization of a natural TSC material but certain artificially engineered structures are thought to behave as TSCs. This proposal is concerned with theoretical explorations of novel quantum phenomena in topological insulators and superconductors. The main goal of the proposed research is to develop understanding of the effect of interactions between electrons in these novel states of relativistic quantum matter. The intersection of topology, relativity and interaction physics is a new and largely uncharted frontier of condensed matter research. The band theory of solids that forms the foundation of our understanding of these materials assumes that interactions are weak and can thus be neglected. While this is a valid assumption in many crystalline solids there are also important instances when the assumption fails. Strong interactions then give rise to new states of matter, fundamentally impossible in non-interacting systems. Well known examples of such interaction-enabled phases of matter include Mott insulators, high-temperature cuprate superconductors, certain quantum magnets and the fractional quantum Hall liquids. Historically, discovery of each of these material classes opened up new areas of inquiry, established new paradigms and enabled key advances in devices and technologies. The proposed research will seek to establish new paradigms for interacting topological quantum matter, paradigms that are experimentally testable and likely to inform future technologies.