Topological field theory of time-reversal invariant insulators
Topological field theory of time-reversal invariant insulators
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DOI：
10.1103/physrevb.78.195424
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发表时间：
2008-11-01
影响因子：
3.7
通讯作者：
Zhang, Shou-Cheng
中科院分区：
文献类型：
--
作者：
Qi, Xiao-Liang;Hughes, Taylor L.;Zhang, Shou-Cheng
我们证明了基本的时间反转不变绝缘体存在于4+1维中，其中有效场理论由（4+1）维Chern-Simons理论描述，电子结构的拓扑性质由第二Chern数分类.这些拓扑性质是2+1维时间反转破缺量子霍尔绝缘体的自然推广。2+1维的TRI量子自旋霍尔绝缘体和3+1维的拓扑绝缘体可以通过降维过程从4+1维的基本TRI绝缘体得到后代。由此自然地得到了2+1和3+1维TRI绝缘体的有效拓扑场论和Z（2）拓扑分类。有效拓扑场论完全描述了TRI绝缘子的所有物理可测拓扑响应函数。我们的有效拓扑场理论预言了许多可测量的现象，其中最引人注目的是拓扑磁电效应，其中电场在同一方向上对磁化产生拓扑贡献，具有以精细结构常数α =e（2）/hc的奇数倍量化的普适比例常数。最后，我们提出了一个一般的分类所有拓扑绝缘体在不同的维度和描述他们在一个统一的拓扑陈-西蒙斯场理论相空间。
We show that the fundamental time-reversal invariant (TRI) insulator exists in 4+1 dimensions, where the effective-field theory is described by the (4+1)-dimensional Chern-Simons theory and the topological properties of the electronic structure are classified by the second Chern number. These topological properties are the natural generalizations of the time reversal-breaking quantum Hall insulator in 2+1 dimensions. The TRI quantum spin Hall insulator in 2+1 dimensions and the topological insulator in 3+1 dimensions can be obtained as descendants from the fundamental TRI insulator in 4+1 dimensions through a dimensional reduction procedure. The effective topological field theory and the Z(2) topological classification for the TRI insulators in 2+1 and 3+1 dimensions are naturally obtained from this procedure. All physically measurable topological response functions of the TRI insulators are completely described by the effective topological field theory. Our effective topological field theory predicts a number of measurable phenomena, the most striking of which is the topological magnetoelectric effect, where an electric field generates a topological contribution to the magnetization in the same direction, with a universal constant of proportionality quantized in odd multiples of the fine-structure constant alpha=e(2)/hc. Finally, we present a general classification of all topological insulators in various dimensions and describe them in terms of a unified topological Chern-Simons field theory in phase space.