拓扑绝缘体中两带模型的规范理论

A GAUGE THEORY IN TWO-BAND MODEL OF TOPOLOGICAL INSULATOR

基于量子霍尔效应发展而来的拓扑绝缘体是凝聚态物理重要的科学前沿之一。通常可用第一陈数(Chern number)这一拓扑不变量来描述时间反演对称性破缺的拓扑绝缘体。传统上表征拓扑绝缘体的拓扑场论是一种有效场论,其中的基本场由"统计规范势"来充当,给出的是系统的大范围拓扑性质。本文当中我们对两带模型(two-band model)引入一种新的拓扑规范理论,它以群空间的哈密顿矢量和布洛赫波函数为基本场,可诱导出单极(monopole)与半子(meron)拓扑缺陷。

Topological insulators, as the generalization of quantum Hall effect, are one of the most important scientific frontiers in condensed matter physics. Usually, the first Chern number as a topological invariant is employed to characterize the topological insulators with broken time-reversal symmetry. The traditional topological field theory to treat topological insulators is an effective field theory that describes the global topological properties, in which the role of the basic field is played by the so-called statistical gauge potential. In this paper, we propose a new topological gauge theory for the two-band model, which takes the Hamiltonian vector in the group space and Bloch wave functions as the basic fields. This new theory is able to give rise to the topological defects of monopoles and merons.