Interaction Effects and Topology in Relativistic Quantum Materials

相对论量子材料中的相互作用效应和拓扑

• 批准号: RGPIN-2016-03810
• 负责人: Franz, Marcel
• 金额: $ 3.64万
• 依托单位: University of British Columbia
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2018
• 资助国家: 加拿大
• 起止时间: 2018-01-01 至 2019-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=651083
• 关键词: Interaction; Effects; Topology; Relativistic; Quantum

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.**

量子力学和爱因斯坦的相对论构成了现代物理学的两大支柱。传统的凝聚态物理学在很大程度上依赖于其中的第一个-大多数材料性质本质上是量子力学的-相对论只起次要作用。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，事后可以称之为“相对论”。它最终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，量子力学和相对论联合收割机产生了一个显著的结果：TI可以被描述为晶体固体，其主体是绝缘的（不导电），但其表面是金属的，因此是良好的导体。在过去的十年中，拓扑绝缘体得到了广泛的研究，许多固体已被实验确定为TI。丰富的实验计划，以测试各种理论上提出的现象与他们有关，现在正在进行中。世界范围内也在努力利用其独特的性能进行实际应用。一个平行的研究相关类别的材料称为拓扑超导体（TSC）也已启动。 到目前为止，我们还没有天然TSC材料的确认实验实现，但某些人工工程结构被认为表现为TSC。 这个提议是关于拓扑绝缘体和超导体中新量子现象的理论探索。拟议研究的主要目标是发展对这些相对论量子物质新状态中电子之间相互作用的理解。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、基本上未知的前沿。固体的能带理论是我们理解这些材料的基础，它假设相互作用很弱，因此可以忽略不计。虽然这是一个有效的假设，在许多结晶固体也有重要的情况下，假设失败。强相互作用会产生新的物质状态，这在非相互作用系统中根本不可能。这种相互作用使物质相的众所周知的例子包括莫特绝缘体，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，这些材料类别的发现开辟了新的研究领域，建立了新的范式，并使设备和技术取得了关键进展。拟议的研究将寻求建立相互作用的拓扑量子物质的新范式，这些范式是实验可测试的，并可能为未来的技术提供信息。