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第一种最基本的材料性质是量子力学的--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。 这项拟议研究的主要目标是加深对这些新态相对论量子物质中电子之间相互作用的影响的理解。拓扑学、相对论和相互作用物理学的交叉是凝聚态研究的一个新的、在很大程度上未知的前沿。固体能带理论是我们理解这些材料的基础，它假定相互作用很弱，因此可以忽略不计。虽然这在许多晶体固体中是一个有效的假设，但也有一些重要的情况是假设失败了。强烈的相互作用会产生新的物质状态，这在非相互作用的系统中基本上是不可能的。这种相互作用启用的物质相的众所周知的例子包括Mott绝缘体、高温铜酸盐超导体、某些量子磁体和分数量子霍尔液体。从历史上看，这些材料类别中的每一个的发现都开辟了新的研究领域，建立了新的范例，并使设备和技术取得了重大进展。这项拟议的研究将寻求建立拓扑量子物质相互作用的新范式，这些范式可以在实验上进行测试，并可能为未来的技术提供信息。

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.