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个基本支柱。传统的凝聚态物理在很大程度上依赖于其中的第一种--大多数材料的性质天生就是量子力学--相对论只起到很小的作用。从2005年开始，凝聚态物理经历了一场深刻的、相当意想不到的革命，事后看来，这场革命可以被称为“相对论”。它的结果是发现了一种新的物质形式，称为拓扑绝缘体(TI)。在这些新材料中，量子力学和相对论结合在一起产生了一个显着的结果：它可以被描述为晶体固体，其体积是绝缘的(不导电)，但其表面是金属的，因此是良好的导体。在过去的十年里，拓扑绝缘体得到了广泛的研究，许多固体被实验鉴定为TiS。目前正在进行丰富的实验计划，以测试与它们相关的各种理论上提出的现象。世界范围内也在努力利用其独特的特性进行实际应用。此外，还启动了一项关于被称为拓扑超导体(TSCs)的相关材料类别的平行研究。到目前为止，我们还没有得到证实的天然TSC材料的实验实现，但某些人工工程结构被认为具有TSC的行为。这一提议涉及对拓扑绝缘体和超导体中新的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.