Correlation Effects in Topological Insulators

拓扑绝缘体中的相关效应

• 批准号: RGPIN-2014-04608
• 负责人: Maciejko, Joseph
• 金额: $ 2.62万
• 依托单位: University of Alberta
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2019
• 资助国家: 加拿大
• 起止时间: 2019-01-01 至 2020-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=686564
• 关键词: Correlation; Effects; Topological; Insulators

The laws governing the behavior of individual electrons and atoms are simple, elegant, and few. But then how can we account for the endless variety of forms which we observe matter to assume? Condensed matter physics seeks to explain these observations and to discover new states of matter. Distinct states of matter can be thought of as distinct patterns into which a group of electrons or atoms can organize themselves, just as a group of dancers can perform different choreographies. A fascinating question in this field is how many such patterns are consistent with the laws of quantum mechanics, and lead to quantum states of matter.**The recent discovery of topological insulators (TIs), a new quantum state of matter, triggered a veritable explosion in condensed matter physics. As their name suggests, TIs are topologically distinct from conventional insulators. Topology, the mathematics of the global properties of geometrical shapes, states that two geometrical shapes are topologically distinct if they cannot be smoothly deformed into one another. All insulators can be described mathematically by abstract geometrical shapes. The abstract geometrical shape describing a conventional insulator cannot be smoothly deformed into one describing a TI, in the same way that a rubber band cannot be transformed into a Möbius strip without first cutting it. This mathematical distinction reveals itself in the physical properties of TIs. TIs, like ordinary electrical insulators such as diamond or silicon, do not allow electrical currents to flow in their interior. Unlike ordinary electrical insulators, TIs do conduct electricity on their surface, and do so almost without dissipation. If this striking physical property can be harnessed in microprocessors, TIs could enable the design of smaller and more efficient mobile computing devices. The surfaces of TIs might also provide the essential ingredient for a quantum computer, a computational device based on the laws of quantum mechanics that is poised to operate exponentially faster than a conventional computer.**The first few years of theoretical TI research, including my own work, focused on idealized models of TIs that ignored the electrostatic repulsive force between electrons. Recent experimental and theoretical developments, as well as the goal of designing viable microelectronics applications, are now pointing the field in a new direction. There are indications that interactions between electrons may lead to novel and unexpected phenomena and even enhance the potential of TIs for applications. By focusing our research on largely unexplored regimes where electrons inside a TI interact strongly with one another, we will contribute to our basic understanding of quantum states of matter and hope to further their use in real-world applications. Our investigations into key issues in the field of TIs will help maintain Canada's leadership in quantum materials research.**Combined with other sources of funding, this NSERC Discovery Grant would support the training of eight personnel - undergraduate and graduate students, and postdoctoral fellows - to high levels of expertise in the tools of the trade of modern condensed matter theory. This includes a variety of advanced analytical and numerical skills that are broadly applicable inside and outside of academia, and will contribute to growing Canada's knowledge-based economy.

支配单个电子和原子行为的定律简单、优美，而且很少。但是，我们如何解释我们观察到的物质所呈现的无穷无尽的各种形式呢？凝聚态物理学试图解释这些观测结果，并发现新的物质状态。不同的物质状态可以被认为是一组电子或原子可以组织自己的不同模式，就像一群舞者可以表演不同的舞蹈一样。这个领域中一个有趣的问题是，有多少这样的模式符合量子力学定律，并导致物质的量子态。最近发现的拓扑绝缘体（TI），一个新的量子态的物质，引发了一个名副其实的爆炸在凝聚态物理。正如其名称所示，TI在拓扑上不同于传统的绝缘体。拓扑学是研究几何形状的全局性质的数学，它指出，如果两个几何形状不能平滑地变形为另一个，则它们在拓扑上是不同的。所有的绝缘体都可以用抽象的几何形状来数学地描述。描述传统绝缘体的抽象几何形状不能平滑地变形为描述TI的几何形状，就像橡皮筋不经切割就不能变形为莫比乌斯带一样，这种数学上的区别体现在TI的物理性质中。TI，像普通的电绝缘体，如金刚石或硅，不允许电流在其内部流动。与普通的电绝缘体不同，TI在其表面上确实导电，并且几乎没有耗散。如果这种惊人的物理特性可以在微处理器中得到利用，TI就可以设计出更小、更高效的移动的计算设备。TI的表面也可能为量子计算机提供必要的成分，量子计算机是一种基于量子力学定律的计算设备，其运行速度比传统计算机快。前几年的理论TI研究，包括我自己的工作，集中在理想化的TI模型，忽略了电子之间的静电排斥力。最近的实验和理论发展，以及设计可行的微电子应用的目标，现在指向一个新的方向领域。有迹象表明，电子之间的相互作用可能会导致新的和意想不到的现象，甚至提高了TI的应用潜力。通过将我们的研究集中在TI内部电子相互作用强烈的基本未探索的制度上，我们将有助于我们对物质量子态的基本理解，并希望进一步在现实世界中应用它们。我们对TI领域关键问题的调查将有助于保持加拿大在量子材料研究方面的领导地位。与其他资金来源相结合，NSERC发现补助金将支持8名人员-本科生和研究生以及博士后研究员-在现代凝聚态理论贸易工具方面的高水平专业知识的培训。这包括广泛适用于学术界内外的各种先进的分析和数字技能，并将有助于加拿大知识经济的发展。