Topological Phases in Correlated Materials

从微处理器到硬盘驱动器，现代电子和计算技术的进步依赖于凝聚态物理研究和新材料发现的过去进展。显然，下一代器件的开发需要我们继续探索新材料并寻求此类系统的设计原理。材料中弱相互作用电子理论在提供具有简单和可控性质的半导体设计原理方面已经相当成功。另一方面，具有共存的电和磁特性的复杂多功能材料目前需求量很大;通过施加电流或反之亦然来控制磁特性的能力是多功能设备中的关键要素。挑战是要找到对杂质足够稳定并且即使在室温下也能发挥作用的材料。为了实现这些目标，目前的研究计划旨在提供理解，设计和控制具有强电子相互作用的复杂材料的理论。特别是，PI计划研究物质的所谓拓扑相;具有体能隙和导电表面/边缘状态的新型电子相。这与最近发展的所谓拓扑绝缘体密切相关;这些绝缘体具有非平凡的表面状态，可用于坚固的磁电器件。PI的目的是超越目前的研究计划，利用电子相互作用，并提出全新的拓扑相类。这是一个非常具有挑战性的理论问题，一直处于当前对固体量子力学性质的理解的前沿。该计划需要开发创新的理论工具来计算拓扑相的物理性质。拟议的研究活动的结果将大大推进对具有强相互作用的复杂材料的理解，并提供控制相互作用的拓扑相的手段，这些相将具有增强的和更强大的多功能特性。

The advancement of modern electronics and computing technologies, from microprocessors to hard drives, rests on the past progress in condensed matter physics research and the discovery of new materials. Clearly, the development of next generation devices requires that we continue to explore new materials and seek for design principles of such systems. Theory of weakly interacting electrons in materials has been quite successful in providing design principles of semiconductors with simple and controllable properties. On the other hand, complex multi-functional materials with coexisting electric and magnetic properties are currently in great demand; the ability to control magnetic properties by applying an electric current or vice versa is a key element in multi-functional devices. The challenge is to come up with the materials that are sufficiently stable against impurities and can perform even at room temperature. Towards these goals, the current research proposal aims to provide theories of the understanding, design, and control of complex materials with strong electron interaction. In particular, the PI plans to investigate the so-called topological phases of matter; novel electronic phases with a bulk energy gap and conducting surface/edge states. This is intimately related to the recent development of the so-called topological insulators; these are insulators with nontrivial surface states that can be useful for robust magneto-electric devices. The PI aims to go beyond the current research scheme by taking the advantage of the electron interaction and suggesting entirely new classes of topological phases. This is a very challenging theoretical problem that has been at the frontier of the current understanding of quantum mechanical properties of solids. The proposed program requires development of innovative theoretical tools to compute physical properties of topological phases. The outcome of the proposed research activities will significantly advance the understanding of complex materials with strong interaction and also provide means to control interacting topological phases that would possess enhanced and much more robust multi-functional properties.