中文摘要：

一般认为，量子自旋霍尔效应只有受到时间反演对称性的保护才是稳定的。但是，因为在实际材料中破坏时间反演对称性的微扰往往无法避免，这种受时间反演对称性保护的量子自旋霍尔效应在真实环境中并不稳定。本综述将介绍近期在寻找无需时间反演对称性保护的量子自旋霍尔效应方向上的系列研究进展。我们将证明量子自旋霍尔体系的非平庸拓扑性质在时间反演对称性被破坏后仍然可以完好存在，并通过一个规范讨论，将边缘态一般性质和体能带的非平庸拓扑性质联系起来。进一步，将探讨通过人工消除边缘态时间反演对称性而实现稳定的量子自旋霍尔效应的方案。此外，我们还将介绍白旋陈数理论，白旋陈数是在没有时间反演对称性存在时，表征量子自旋霍尔体系所处不同拓扑相的有效工具。

英文摘要：

In this review, we introduce a series of recent developments in the search of the quan- tum spin Hall effect in the absence of time-reversal symmetry. We first show that the nontrivial topological properties of the quantum spin Hall system remain to be intact when the time-reversal symmetry is broken weakly. Then by a Laughlin-like gauge argument, the connection between the general properties of the edge states and the bulk band topology is established. Furthermore, the possibility to realize robust quantum spin Hall effect by artificial removal of the time-reversal symmetry of the edge states is explored. We will also introduce the spin Chern number theory, as a powerful tool to characterize topological phases without the TR symmetry.