Correlated Quantum Systems: Topological Phases, Non-Fermi-liquids and Entanglement

我的研究项目的目的是了解电子在固体中自我组织的不同方式。令人惊讶的是，量子力学的基本定律，加上控制电子运动的简单静电相互作用，产生了大量不同相的物质，如金属、绝缘体、超导体和磁体。在过去的十年里，发现了一类全新的物质相：拓扑绝缘体。这些材料中的大部分都不导电，但表面却导电。人们可能会认为这是一场意外，可以割断导电表面层，但实际上，块状材料的任何裂解都会暴露出一个新的导电表面。 我的研究计划的一个主要目标是对所有这种块状拓扑绝缘体和相关的物质相进行分类，并了解它们的表面行为。这一研究方向解决了固体物理学前沿的基本问题，提供了与现代数学中活跃领域的联系，如拓扑学和范畴理论，并进一步为物质拓扑相在量子计算中的技术应用铺平了道路。 除了研究奇异的绝缘体，我还在研究不寻常的导体(金属)。简单金属，如铜，被朗道费米-液体理论描述得非常成功，然而，有一些材料，统称为“奇怪的金属”，其行为强烈偏离费米-液体理论。这些材料包括铜酸盐、铁砷和某些重费米子材料家族。像简单金属一样，当温度降到临界温度T_c以下时，奇怪的金属通常会变成超导；然而，T_c的大小往往比简单金属高得多。我的研究计划的一个目标是发展一种关于奇怪金属及其超导不稳定性的理论--这是系统地设计用于应用目的的高超导T_c新材料的长期努力的必要的第一步。

The aim of my research program is to understand the different ways that electrons can organize themselves in solids. Amazingly, the basic laws of quantum mechanics, together with simple electrostatic interactions governing electron motion, give rise to a great array of different phases of matter, such as metals, insulators, superconductors, and magnets. In the last ten years, an entirely new class of phases of matter was discovered: topological insulators. The bulk of these materials does not conduct electricity, however the surface does. One may think that this is an accident and that one can cut the conducting surface layer away, but in fact, any cleave of the bulk material always exposes a new conducting surface. A primary goal of my research program is to classify all such bulk topological insulators and related phases of matter and to understand their surface behaviour. This direction of research addresses fundamental questions at the forefront of solid state physics, provides a link to active areas in modern mathematics, such as topology and category theory, and furthermore, paves the way for technological applications of topological phases of matter in quantum computing. Aside from studying exotic insulators, I am also pursuing unusual conductors (metals). Simple metals, like copper, are very successfully described by Landau Fermi-liquid theory, however, there are a number of materials, collectively referred to as “strange metals,” whose behaviour strongly deviates from Fermi-liquid theory. These include cuprate, iron-arsenic and certain heavy-fermion material families. Like simple metals, strange metals often turn superconducting when the temperature is lowered below a critical temperature Tc; however, the magnitude of Tc is often much higher than in simple metals. A goal of my research program is to develop a theory of strange metals and their superconducting instabilities - a necessary first step in the long-term effort to systematically design new materials with high superconducting Tc for application purposes.