Topological order in quantum materials

凝聚态物理的目标是发现和描述宏观物质的新状态。物质相的传统分类很大程度上是基于对称性破缺的概念：例如固体中原子的结晶顺序打破了真空的平移对称性，铁磁体中的宏观磁化破坏了空间的旋转对称性。近年来出现了一种新的相分类范式，它强调材料电子结构的拓扑（即对材料参数的光滑变化不敏感）性质，而不是破缺对称性。在本提案中，我将概述一个研究计划，旨在发展对具有电子结构的非平凡拓扑特性的量子材料物理学的完整理论理解。该提案的重点将放在材料上，这些材料不是绝缘体，但具有拓扑上非平凡的电子结构。

The goal of condensed matter physics is to discover and describe new states of macroscopic matter. The traditional classification of phases of matter is largely based on the idea of broken symmetry: for example crystalline order of atoms in solids breaks translational symmetry of empty space and macroscopic magnetization in ferromagnets breaks rotational symmetry of space. In recent years a new paradigm for classification of phases has been emerging, which emphasizes topological (meaning insensitive to smooth changes in material parameters) properties of the electronic structure of materials, rather than broken symmetries. In this proposal I will outline a research program, aimed towards developing a complete theoretical understanding of the physics of quantum materials with nontrivial topological properties of the electronic structure. The focus of the proposal will be on materials, which are not insulators, and yet possess topologically-nontrivial electronic structure.