Topological Phases in Correlated Materials

现代电子和计算技术的进步，从微处理器到硬盘驱动器，依赖于过去凝聚态物理研究的进展和新材料的发现。显然，下一代设备的发展需要我们继续探索新材料，并寻求这种系统的设计原则。材料中电子弱相互作用理论已经非常成功地提供了具有简单和可控特性的半导体的设计原理。另一方面，具有电、磁共存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施加电流来控制磁性的能力是多功能设备的关键要素。我们面临的挑战是找到一种对杂质足够稳定，甚至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具有强电子相互作用的复杂材料的理解，设计和控制的理论。特别是，PI计划研究所谓的物质的拓扑相；具有块能隙和导电表面/边缘态的新型电子相。这与最近所谓的拓扑绝缘体的发展密切相关；这些绝缘体具有重要的表面状态，可用于坚固的磁电设备。PI的目标是超越目前的研究方案，利用电子相互作用的优势，提出全新的拓扑相类别。这是一个非常具有挑战性的理论问题，它一直处于当前对固体量子力学性质理解的前沿。提出的方案需要开发创新的理论工具来计算拓扑相的物理性质。所提出的研究活动的结果将大大促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拓扑相的方法，这些拓扑相将具有增强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.