Z_2拓扑不变量与拓扑绝缘体

文章回顾了几种Z2拓扑数的计算方法,并详细介绍了一种用非阿贝尔贝里联络表示绝缘体Z2不变量的计算方法.这种方法可以确定出一般能带绝缘体的拓扑性质,而不需要限定波函数的规范.利用这种新方法,文章作者计算了二维石墨烯(graphene)系统的Z2拓扑数,得到了和以前研究相一致的结论.

Z_2 topological invariant and topological insulators

We briefly review some of the equivalent ways of determining the Z2 invariant in 2D insulators. We introduce a new expression for this invariant in band insulators using non-Abelian Berry's connection. The new expression can be used to determine the topological nature of a general band insulator in a way that does not require any gauge fixing. By this means, we have recalculated the Z2 topological index for 2D graphene systems, and have obtained results consistent with previous studies.