The insulating state of matter: a geometrical theory
The insulating state of matter: a geometrical theory
复制标题
DOI：
10.1140/epjb/e2010-10874-4
复制
发表时间：
2010-12
期刊：
影响因子：
--
通讯作者：
Raffaele Resta
中科院分区：
文献类型：
--
作者：
Raffaele Resta
1964年，科恩发表了里程碑式的论文“绝缘态理论”，根据该理论，绝缘体和金属的基态不同。即使在系统被任何探针激发之前，基态中也存在不同的电子组织，这是区分绝缘体和金属的关键特征。然而，直到 20 世纪 90 年代末，绝缘态理论仍然有些不完整。本次审查涉及最近的事态发展。任何绝缘体的多体地波函数都可以通过几何概念（贝里相、连接、曲率、陈数、量子度量）来表征。其中，尖锐表征物质绝缘态的就是量子度量。该理论涉及几种绝缘体的共同点：带状绝缘体、莫特绝缘体、安德森绝缘体、量子霍尔绝缘体、陈省身绝缘体和拓扑绝缘体。
In 1964 Kohn published the milestone paper “Theory of the insulating state”, according to which insulators and metals differ in theirground state. Even before the system is excited by any probe, a different organization of the electrons is present in the ground state and this is the key feature discriminating between insulators and metals. However, the theory of the insulating state remained somewhat incomplete until the late 1990s; this review addresses the recent developments. The many-body ground wavefunction of any insulator is characterized by means of geometrical concepts (Berry phase, connection, curvature, Chern number, quantum metric). Among them, it is the quantum metric which sharply characterizes the insulating state of matter. The theory deals on a common ground with several kinds of insulators: band insulators, Mott insulators, Anderson insulators, quantum Hall insulators, Chern and topological insulators.