Correlation Effects in Topological Insulators

支配单个电子和原子行为的定律是简单、优雅和少数的。但是，我们如何解释我们观察到的物质所呈现的无穷多种形式呢？凝聚态物理学试图解释这些观察结果，并发现物质的新状态。物质的不同状态可以被认为是一组电子或原子可以组织成的不同模式，就像一组舞者可以表演不同的舞蹈一样。这个领域的一个引人入胜的问题是，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（TIs），一种新的物质量子态，引发了凝聚态物理学的真正爆发。顾名思义，它在拓扑结构上与传统绝缘体不同。拓扑学是研究几何形状整体特性的数学，它指出，如果两个几何形状不能平滑地相互变形，那么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描述。描述传统绝缘体的抽象几何形状不能平滑地变形成描述TI的形状，就像橡皮筋不能在不先切割的情况下变成Möbius条一样。这种数学上的区别体现在ti的物理性质上。它就像普通的电绝缘体，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，它确实在其表面导电，而且几乎没有损耗。如果这种惊人的物理特性可以在微处理器中加以利用，它可以使设计更小、更高效的移动计算设备成为可能。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得多。**最初几年的TI理论研究，包括我自己的工作，都集中在忽略电子间静电斥力的TI理想化模型上。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，现在正将该领域指向一个新的方向。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，甚至增强ti的应用潜力。通过将我们的研究重点放在TI内部电子彼此强烈相互作用的大部分未开发的制度上，我们将有助于我们对物质量子态的基本理解，并希望进一步将其用于现实世界的应用。我们对量子材料领域关键问题的研究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发现基金将支持培训8名人员——本科生、研究生和博士后——在现代凝聚态理论贸易工具方面具有高水平的专业知识。这包括各种先进的分析和数字技能，广泛适用于学术界内外，并将促进加拿大知识型经济的发展。

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.