用Wannier函数刻画拓扑绝缘体和拓扑半金属的普适性
Universal characterizing topological insulator and topological semi-metal with Wannier functions
摘要：
占据带的Wannier函数的非平凡演化是理解拓扑绝缘体的一个很好的起点。通过将WFs的定义从投影位置算符的本征态修改为投影模位置算符的本征态，我们能够将WFs的使用扩展到Weyl金属，其中旧定义中的WFs由于在费米能量处缺乏带隙而失败。这一推广有助于我们在同一个框架下对拓扑绝缘体和拓扑半金属进行普遍的理解。在定义中使用模位置算子的另一个优点是可以容易地获得被占用频带的高维WF。我们展示了他们的应用之一，示意性地解释了为什么绕组数$ν_{3D}=ν_{2D}$的三维拓扑绝缘体的DIII类在物理评论快报。114，016801（2015）。
英文摘要：
The nontrivial evolution of Wannier functions (WF) for the occupied bands is a good starting point to understand topological insulator. By modifying the definition of WFs from the eigenstates of the projected position operator to those of the projected modular position operator, we are able to extend the usage of WFs to Weyl metal where the WFs in the old definition fails because of the lack of band gap at the Fermi energy. This extension helps us to universally understand topological insulator and topological semi-metal in a same framework. Another advantage of using the modular position operators in the definition is that the higher dimensional WFs for the occupied bands can be easily obtained. We show one of their applications by schematically explaining why the winding numbers $ν_{3D}=ν_{2D}$ for the 3D topological insulators of DIII class presented in Phys. Rev. Lett. 114, 016801(2015).
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